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ATS

Bases: FluxDevice

ATS Device.

Source code in jaxquantum/devices/superconducting/ats.py 
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@struct.dataclass
class ATS(FluxDevice):
    """
    ATS Device.
    """

    def common_ops(self):
        """Written in the linear basis."""
        ops = {}

        N = self.N_pre_diag
        ops["id"] = identity(N)
        ops["a"] = destroy(N)
        ops["a_dag"] = create(N)
        ops["phi"] = self.phi_zpf() * (ops["a"] + ops["a_dag"])
        ops["n"] = 1j * self.n_zpf() * (ops["a_dag"] - ops["a"])
        return ops

    def phi_zpf(self):
        """Return Phase ZPF."""
        return (2 * self.params["Ec"] / self.params["El"]) ** (0.25)

    def n_zpf(self):
        """Return Charge ZPF."""
        return (self.params["El"] / (32 * self.params["Ec"])) ** (0.25)

    def get_linear_frequency(self):
        """Get frequency of linear terms."""
        return jnp.sqrt(8 * self.params["El"] * self.params["Ec"])

    def get_H_linear(self):
        """Return linear terms in H."""
        w = self.get_linear_frequency()
        return w * (
            self.linear_ops["a_dag"] @ self.linear_ops["a"]
            + 0.5 * self.linear_ops["id"]
        )

    @staticmethod
    def get_H_nonlinear_static(phi_op, Ej, dEj, Ej2, phi_sum, phi_delta):
        cos_phi_op = cosm(phi_op)
        sin_phi_op = sinm(phi_op)

        cos_2phi_op = cos_phi_op @ cos_phi_op - sin_phi_op @ sin_phi_op
        sin_2phi_op = 2 * cos_phi_op @ sin_phi_op

        H_nl_Ej = (
            -2
            * Ej
            * (
                cos_phi_op * jnp.cos(2 * jnp.pi * phi_delta)
                - sin_phi_op * jnp.sin(2 * jnp.pi * phi_delta)
            )
            * jnp.cos(2 * jnp.pi * phi_sum)
        )
        H_nl_dEj = (
            2
            * dEj
            * (
                sin_phi_op * jnp.cos(2 * jnp.pi * phi_delta)
                + cos_phi_op * jnp.sin(2 * jnp.pi * phi_delta)
            )
            * jnp.sin(2 * jnp.pi * phi_sum)
        )
        H_nl_Ej2 = (
            2
            * Ej2
            * (
                cos_2phi_op * jnp.cos(2 * 2 * jnp.pi * phi_delta)
                - sin_2phi_op * jnp.sin(2 * 2 * jnp.pi * phi_delta)
            )
            * jnp.cos(2 * 2 * jnp.pi * phi_sum)
        )

        H_nl = H_nl_Ej + H_nl_dEj + H_nl_Ej2

        # id_op = jqt.identity_like(phi_op)
        # phi_delta_ext_op = self.params["phi_delta_ext"] * id_op
        # H_nl_old = - 2 * Ej * jqt.cosm(phi_op + 2 * jnp.pi * phi_delta_ext_op) * jnp.cos(2 * jnp.pi * self.params["phi_sum_ext"])
        # H_nl_old += 2 * dEj * jqt.sinm(phi_op + 2 * jnp.pi * phi_delta_ext_op) * jnp.sin(2 * jnp.pi * self.params["phi_sum_ext"])
        # H_nl_old += 2 * Ej2 * jqt.cosm(2*phi_op + 2 * 2 * jnp.pi * phi_delta_ext_op) * jnp.cos(2 * 2 * jnp.pi * self.params["phi_sum_ext"])

        return H_nl

    def get_H_nonlinear(self, phi_op):
        """Return nonlinear terms in H."""

        Ej = self.params["Ej"]
        dEj = self.params["dEj"]
        Ej2 = self.params["Ej2"]

        phi_sum = self.params["phi_sum_ext"]
        phi_delta = self.params["phi_delta_ext"]

        return ATS.get_H_nonlinear_static(phi_op, Ej, dEj, Ej2, phi_sum, phi_delta)

    def get_H_full(self):
        """Return full H in linear basis."""
        phi_b = self.linear_ops["phi"]
        H_nl = self.get_H_nonlinear(phi_b)
        H = self.get_H_linear() + H_nl
        return H

    def potential(self, phi):
        """Return potential energy for a given phi."""

        phi_delta_ext = self.params["phi_delta_ext"]
        phi_sum_ext = self.params["phi_sum_ext"]

        V = 0.5 * self.params["El"] * (2 * jnp.pi * phi) ** 2
        V += (
            -2
            * self.params["Ej"]
            * jnp.cos(2 * jnp.pi * (phi + phi_delta_ext))
            * jnp.cos(2 * jnp.pi * phi_sum_ext)
        )
        V += (
            2
            * self.params["dEj"]
            * jnp.sin(2 * jnp.pi * (phi + phi_delta_ext))
            * jnp.sin(2 * jnp.pi * phi_sum_ext)
        )
        V += (
            2
            * self.params["Ej2"]
            * jnp.cos(2 * 2 * jnp.pi * (phi + phi_delta_ext))
            * jnp.cos(2 * 2 * jnp.pi * phi_sum_ext)
        )

        return V

common_ops()

Written in the linear basis.

Source code in jaxquantum/devices/superconducting/ats.py 
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def common_ops(self):
    """Written in the linear basis."""
    ops = {}

    N = self.N_pre_diag
    ops["id"] = identity(N)
    ops["a"] = destroy(N)
    ops["a_dag"] = create(N)
    ops["phi"] = self.phi_zpf() * (ops["a"] + ops["a_dag"])
    ops["n"] = 1j * self.n_zpf() * (ops["a_dag"] - ops["a"])
    return ops

get_H_full()

Return full H in linear basis.

Source code in jaxquantum/devices/superconducting/ats.py 
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def get_H_full(self):
    """Return full H in linear basis."""
    phi_b = self.linear_ops["phi"]
    H_nl = self.get_H_nonlinear(phi_b)
    H = self.get_H_linear() + H_nl
    return H

get_H_linear()

Return linear terms in H.

Source code in jaxquantum/devices/superconducting/ats.py 
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def get_H_linear(self):
    """Return linear terms in H."""
    w = self.get_linear_frequency()
    return w * (
        self.linear_ops["a_dag"] @ self.linear_ops["a"]
        + 0.5 * self.linear_ops["id"]
    )

get_H_nonlinear(phi_op)

Return nonlinear terms in H.

Source code in jaxquantum/devices/superconducting/ats.py 
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def get_H_nonlinear(self, phi_op):
    """Return nonlinear terms in H."""

    Ej = self.params["Ej"]
    dEj = self.params["dEj"]
    Ej2 = self.params["Ej2"]

    phi_sum = self.params["phi_sum_ext"]
    phi_delta = self.params["phi_delta_ext"]

    return ATS.get_H_nonlinear_static(phi_op, Ej, dEj, Ej2, phi_sum, phi_delta)

get_linear_frequency()

Get frequency of linear terms.

Source code in jaxquantum/devices/superconducting/ats.py 
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def get_linear_frequency(self):
    """Get frequency of linear terms."""
    return jnp.sqrt(8 * self.params["El"] * self.params["Ec"])

n_zpf()

Return Charge ZPF.

Source code in jaxquantum/devices/superconducting/ats.py 
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def n_zpf(self):
    """Return Charge ZPF."""
    return (self.params["El"] / (32 * self.params["Ec"])) ** (0.25)

phi_zpf()

Return Phase ZPF.

Source code in jaxquantum/devices/superconducting/ats.py 
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def phi_zpf(self):
    """Return Phase ZPF."""
    return (2 * self.params["Ec"] / self.params["El"]) ** (0.25)

potential(phi)

Return potential energy for a given phi.

Source code in jaxquantum/devices/superconducting/ats.py 
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def potential(self, phi):
    """Return potential energy for a given phi."""

    phi_delta_ext = self.params["phi_delta_ext"]
    phi_sum_ext = self.params["phi_sum_ext"]

    V = 0.5 * self.params["El"] * (2 * jnp.pi * phi) ** 2
    V += (
        -2
        * self.params["Ej"]
        * jnp.cos(2 * jnp.pi * (phi + phi_delta_ext))
        * jnp.cos(2 * jnp.pi * phi_sum_ext)
    )
    V += (
        2
        * self.params["dEj"]
        * jnp.sin(2 * jnp.pi * (phi + phi_delta_ext))
        * jnp.sin(2 * jnp.pi * phi_sum_ext)
    )
    V += (
        2
        * self.params["Ej2"]
        * jnp.cos(2 * 2 * jnp.pi * (phi + phi_delta_ext))
        * jnp.cos(2 * 2 * jnp.pi * phi_sum_ext)
    )

    return V

Device

Bases: ABC

Source code in jaxquantum/devices/base/base.py 
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@struct.dataclass
class Device(ABC):
    DEFAULT_BASIS = BasisTypes.fock
    DEFAULT_HAMILTONIAN = HamiltonianTypes.full

    N: int = struct.field(pytree_node=False)
    N_pre_diag: int = struct.field(pytree_node=False)
    params: Dict[str, Any]
    _label: int = struct.field(pytree_node=False)
    _basis: BasisTypes = struct.field(pytree_node=False)
    _hamiltonian: HamiltonianTypes = struct.field(pytree_node=False)

    @classmethod
    def param_validation(cls, N, N_pre_diag, params, hamiltonian, basis):
        """This can be overridden by subclasses."""
        pass

    @classmethod
    def create(
        cls,
        N,
        params,
        label=0,
        N_pre_diag=None,
        use_linear=False,
        hamiltonian: HamiltonianTypes = None,
        basis: BasisTypes = None,
    ):
        """Create a device.

        Args:
            N (int): dimension of Hilbert space.
            params (dict): parameters of the device.
            label (int, optional): label for the device. Defaults to 0. This is useful when you have multiple of the same device type in the same system.
            N_pre_diag (int, optional): dimension of Hilbert space before diagonalization. Defaults to None, in which case it is set to N. This must be greater than or rqual to N.
            use_linear (bool): whether to use the linearized device. Defaults to False. This will override the hamiltonian keyword argument. This is a bit redundant with hamiltonian, but it is kept for backwards compatibility.
            hamiltonian (HamiltonianTypes, optional): type of Hamiltonian. Defaults to None, in which case the full hamiltonian is used.
            basis (BasisTypes, optional): type of basis. Defaults to None, in which case the fock basis is used.
        """

        if N_pre_diag is None:
            N_pre_diag = N

        assert N_pre_diag >= N, "N_pre_diag must be greater than or equal to N."

        _basis = basis if basis is not None else cls.DEFAULT_BASIS
        _hamiltonian = (
            hamiltonian if hamiltonian is not None else cls.DEFAULT_HAMILTONIAN
        )

        if use_linear:
            _hamiltonian = HamiltonianTypes.linear

        cls.param_validation(N, N_pre_diag, params, _hamiltonian, _basis)

        return cls(N, N_pre_diag, params, label, _basis, _hamiltonian)

    @property
    def basis(self):
        return self._basis

    @property
    def hamiltonian(self):
        return self._hamiltonian

    @property
    def label(self):
        return self.__class__.__name__ + str(self._label)

    @property
    def linear_ops(self):
        return self.common_ops()

    @property
    def original_ops(self):
        return self.common_ops()

    @property
    def ops(self):
        return self.full_ops()

    @abstractmethod
    def common_ops(self) -> Dict[str, Qarray]:
        """Set up common ops in the specified basis."""

    @abstractmethod
    def get_linear_frequency(self):
        """Get frequency of linear terms."""

    @abstractmethod
    def get_H_linear(self):
        """Return linear terms in H."""

    @abstractmethod
    def get_H_full(self):
        """Return full H."""

    def get_H(self):
        """
        Return diagonalized H. Explicitly keep only diagonal elements of matrix.
        """
        return self.get_op_in_H_eigenbasis(
            self._get_H_in_original_basis()
        ).keep_only_diag_elements()

    def _get_H_in_original_basis(self):
        """This returns the Hamiltonian in the original specified basis. This can be overridden by subclasses."""

        if self.hamiltonian == HamiltonianTypes.linear:
            return self.get_H_linear()
        elif self.hamiltonian == HamiltonianTypes.full:
            return self.get_H_full()

    def _calculate_eig_systems(self):
        evs, evecs = jnp.linalg.eigh(self._get_H_in_original_basis().data)  # Hermitian
        idxs_sorted = jnp.argsort(evs)
        return evs[idxs_sorted], evecs[:, idxs_sorted]

    @property
    def eig_systems(self):
        eig_systems = {}
        eig_systems["vals"], eig_systems["vecs"] = self._calculate_eig_systems()

        eig_systems["vecs"] = eig_systems["vecs"]
        eig_systems["vals"] = eig_systems["vals"]
        return eig_systems

    def get_op_in_H_eigenbasis(self, op: Qarray):
        evecs = self.eig_systems["vecs"][:, : self.N]
        dims = [[self.N], [self.N]]
        return get_op_in_new_basis(op, evecs, dims)

    def get_op_data_in_H_eigenbasis(self, op: Array):
        evecs = self.eig_systems["vecs"][:, : self.N]
        return get_op_data_in_new_basis(op, evecs)

    def get_vec_in_H_eigenbasis(self, vec: Qarray):
        evecs = self.eig_systems["vecs"][:, : self.N]
        if vec.qtype == Qtypes.ket:
            dims = [[self.N], [1]]
        else:
            dims = [[1], [self.N]]
        return get_vec_in_new_basis(vec, evecs, dims)

    def get_vec_data_in_H_eigenbasis(self, vec: Array):
        evecs = self.eig_systems["vecs"][:, : self.N]
        return get_vec_data_in_new_basis(vec, evecs)

    def full_ops(self):
        # TODO: use JAX vmap here

        linear_ops = self.linear_ops
        ops = {}
        for name, op in linear_ops.items():
            ops[name] = self.get_op_in_H_eigenbasis(op)

        return ops

common_ops() abstractmethod

Set up common ops in the specified basis.

Source code in jaxquantum/devices/base/base.py 
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@abstractmethod
def common_ops(self) -> Dict[str, Qarray]:
    """Set up common ops in the specified basis."""

create(N, params, label=0, N_pre_diag=None, use_linear=False, hamiltonian=None, basis=None) classmethod

Create a device.

Parameters:

Name Type Description Default
N int

dimension of Hilbert space.

 required
params dict

parameters of the device.

 required
label int

label for the device. Defaults to 0. This is useful when you have multiple of the same device type in the same system.

 0
N_pre_diag int

dimension of Hilbert space before diagonalization. Defaults to None, in which case it is set to N. This must be greater than or rqual to N.

 None
use_linear bool

whether to use the linearized device. Defaults to False. This will override the hamiltonian keyword argument. This is a bit redundant with hamiltonian, but it is kept for backwards compatibility.

 False
hamiltonian HamiltonianTypes

type of Hamiltonian. Defaults to None, in which case the full hamiltonian is used.

 None
basis BasisTypes

type of basis. Defaults to None, in which case the fock basis is used.

 None
Source code in jaxquantum/devices/base/base.py 
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@classmethod
def create(
    cls,
    N,
    params,
    label=0,
    N_pre_diag=None,
    use_linear=False,
    hamiltonian: HamiltonianTypes = None,
    basis: BasisTypes = None,
):
    """Create a device.

    Args:
        N (int): dimension of Hilbert space.
        params (dict): parameters of the device.
        label (int, optional): label for the device. Defaults to 0. This is useful when you have multiple of the same device type in the same system.
        N_pre_diag (int, optional): dimension of Hilbert space before diagonalization. Defaults to None, in which case it is set to N. This must be greater than or rqual to N.
        use_linear (bool): whether to use the linearized device. Defaults to False. This will override the hamiltonian keyword argument. This is a bit redundant with hamiltonian, but it is kept for backwards compatibility.
        hamiltonian (HamiltonianTypes, optional): type of Hamiltonian. Defaults to None, in which case the full hamiltonian is used.
        basis (BasisTypes, optional): type of basis. Defaults to None, in which case the fock basis is used.
    """

    if N_pre_diag is None:
        N_pre_diag = N

    assert N_pre_diag >= N, "N_pre_diag must be greater than or equal to N."

    _basis = basis if basis is not None else cls.DEFAULT_BASIS
    _hamiltonian = (
        hamiltonian if hamiltonian is not None else cls.DEFAULT_HAMILTONIAN
    )

    if use_linear:
        _hamiltonian = HamiltonianTypes.linear

    cls.param_validation(N, N_pre_diag, params, _hamiltonian, _basis)

    return cls(N, N_pre_diag, params, label, _basis, _hamiltonian)

get_H()

Return diagonalized H. Explicitly keep only diagonal elements of matrix.

Source code in jaxquantum/devices/base/base.py 
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def get_H(self):
    """
    Return diagonalized H. Explicitly keep only diagonal elements of matrix.
    """
    return self.get_op_in_H_eigenbasis(
        self._get_H_in_original_basis()
    ).keep_only_diag_elements()

get_H_full() abstractmethod

Return full H.

Source code in jaxquantum/devices/base/base.py 
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@abstractmethod
def get_H_full(self):
    """Return full H."""

get_H_linear() abstractmethod

Return linear terms in H.

Source code in jaxquantum/devices/base/base.py 
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@abstractmethod
def get_H_linear(self):
    """Return linear terms in H."""

get_linear_frequency() abstractmethod

Get frequency of linear terms.

Source code in jaxquantum/devices/base/base.py 
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@abstractmethod
def get_linear_frequency(self):
    """Get frequency of linear terms."""

param_validation(N, N_pre_diag, params, hamiltonian, basis) classmethod

This can be overridden by subclasses.

Source code in jaxquantum/devices/base/base.py 
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@classmethod
def param_validation(cls, N, N_pre_diag, params, hamiltonian, basis):
    """This can be overridden by subclasses."""
    pass

Drive

Bases: ABC

Source code in jaxquantum/devices/superconducting/drive.py 
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@struct.dataclass
class Drive(ABC):
    N: int = struct.field(pytree_node=False)
    fd: float
    _label: int = struct.field(pytree_node=False)

    @classmethod
    def create(cls, M_max, fd, label=0):
        cls.M_max = M_max
        N = 2 * M_max + 1
        return cls(N, fd, label)

    @property
    def label(self):
        return self.__class__.__name__ + str(self._label)

    @property
    def ops(self):
        return self.common_ops()

    def common_ops(self) -> Dict[str, Qarray]:
        ops = {}

        M_max = self.M_max

        # Construct M = ∑ₘ m|m><m| operator in drive charge basis
        ops["M"] = jnp2jqt(jnp.diag(jnp.arange(-M_max, M_max + 1)))

        # Construct Id = ∑ₘ|m><m| in the drive charge basis
        ops["id"] = jnp2jqt(jnp.identity(2 * M_max + 1))

        # Construct M₊ ≡ exp(iθ) and M₋ ≡ exp(-iθ) operators for drive
        ops["M-"] = jnp2jqt(jnp.eye(2 * M_max + 1, k=1))
        ops["M+"] = jnp2jqt(jnp.eye(2 * M_max + 1, k=-1))

        # Construct cos(θ) ≡ 1/2 * [M₊ + M₋] = 1/2 * ∑ₘ|m+1><m| + h.c
        ops["cos(θ)"] = 0.5 * (ops["M+"] + ops["M-"])

        # Construct sin(θ) ≡ -i/2 * [M₊ - M₋] = -i/2 * ∑ₘ|m+1><m| + h.c
        ops["sin(θ)"] = -0.5j * (ops["M+"] - ops["M-"])

        # Construct more general drive operators cos(kθ) and sin(kθ)
        for k in range(2, M_max + 1):
            ops[f"M_+{k}"] = jnp2jqt(jnp.eye(2 * M_max + 1, k=-k))
            ops[f"M_-{k}"] = jnp2jqt(jnp.eye(2 * M_max + 1, k=k))
            ops[f"cos({k}θ)"] = 0.5 * (ops[f"M_+{k}"] + ops[f"M_-{k}"])
            ops[f"sin({k}θ)"] = -0.5j * (ops[f"M_+{k}"] - ops[f"M_-{k}"])

        return ops

    #############################################################

    def get_H(self):
        """
        Bare "drive" Hamiltonian (fd * M) in the extended Hilbert space.
        """
        return self.fd * self.ops["M"]

get_H()

Bare "drive" Hamiltonian (fd * M) in the extended Hilbert space.

Source code in jaxquantum/devices/superconducting/drive.py 
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def get_H(self):
    """
    Bare "drive" Hamiltonian (fd * M) in the extended Hilbert space.
    """
    return self.fd * self.ops["M"]

FluxDevice

Bases: Device

Source code in jaxquantum/devices/superconducting/flux_base.py 
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@struct.dataclass
class FluxDevice(Device):
    @abstractmethod
    def phi_zpf(self):
        """Return Phase ZPF."""

    def _calculate_wavefunctions_fock(self, phi_vals):
        """Calculate wavefunctions at phi_exts."""
        phi_osc = self.phi_zpf() * jnp.sqrt(2)  # length of oscillator
        phi_vals = jnp.array(phi_vals)

        # calculate basis functions
        basis_functions = []
        for n in range(self.N_pre_diag):
            basis_functions.append(
                harm_osc_wavefunction(n, phi_vals, jnp.real(phi_osc))
            )
        basis_functions = jnp.array(basis_functions)

        # transform to better diagonal basis
        basis_functions_in_H_eigenbasis = self.get_vec_data_in_H_eigenbasis(
            basis_functions
        )

        # the below is equivalent to evecs_in_H_eigenbasis @ basis_functions_in_H_eigenbasis
        # since evecs in H_eigenbasis is diagonal, i.e. the identity matrix
        wavefunctions = basis_functions_in_H_eigenbasis
        return wavefunctions

    def _calculate_wavefunctions_charge(self, phi_vals):
        phi_vals = jnp.array(phi_vals)

        # calculate basis functions
        basis_functions = []
        n_labels = jnp.diag(self.original_ops["n"].data)
        for n in n_labels:
            basis_functions.append(
                1 / (jnp.sqrt(2 * jnp.pi)) * jnp.exp(1j * n * (2 * jnp.pi * -1 * phi_vals)) # Added a -1 to work with the SNAIL
            )
        basis_functions = jnp.array(basis_functions)

        # transform to better diagonal basis
        basis_functions_in_H_eigenbasis = self.get_vec_data_in_H_eigenbasis(
            basis_functions
        )

        # the below is equivalent to evecs_in_H_eigenbasis @ basis_functions_in_H_eigenbasis
        # since evecs in H_eigenbasis is diagonal, i.e. the identity matrix
        num_eigenstates = basis_functions_in_H_eigenbasis.shape[0]
        phase_correction_factors = (1j ** (jnp.arange(0, num_eigenstates))).reshape(
            num_eigenstates, 1
        )  # TODO: review why these are needed...
        wavefunctions = basis_functions_in_H_eigenbasis * phase_correction_factors
        return wavefunctions

    @abstractmethod
    def potential(self, phi):
        """Return potential energy as a function of phi."""

    def plot_wavefunctions(self, phi_vals, max_n=None, which=None, ax=None, mode="abs", ylim=None, y_scale_factor=1, zero_potential=False, wavefunction_color=None):
        if self.basis == BasisTypes.fock:
            _calculate_wavefunctions = self._calculate_wavefunctions_fock
        elif self.basis == BasisTypes.charge:
            _calculate_wavefunctions = self._calculate_wavefunctions_charge
        else:
            raise NotImplementedError(
                f"The {self.basis} is not yet supported for plotting wavefunctions."
            )

        """Plot wavefunctions at phi_exts."""
        wavefunctions = _calculate_wavefunctions(phi_vals)
        energy_levels = self.eig_systems["vals"][: self.N]

        potential = self.potential(phi_vals)

        min_potential = 0 if not zero_potential else jnp.min(potential)
        if ax is None:
            fig, ax = plt.subplots(1, 1, figsize=(3.5, 2.5), dpi=1000)
        else:
            fig = ax.get_figure()

        min_val = None
        max_val = None

        assert max_n is None or which is None, "Can't specify both max_n and which"

        max_n = self.N if max_n is None else max_n
        levels = range(max_n) if which is None else which

        for n in levels:
            if mode == "abs":
                wf_vals = jnp.abs(wavefunctions[n, :]) ** 2
            elif mode == "real":
                wf_vals = wavefunctions[n, :].real
            elif mode == "imag":
                wf_vals = wavefunctions[n, :].imag

            wf_vals += energy_levels[n]
            curr_min_val = min(wf_vals)
            curr_max_val = max(wf_vals)

            if min_val is None or curr_min_val < min_val:
                min_val = curr_min_val

            if max_val is None or curr_max_val > max_val:
                max_val = curr_max_val

            extra_kwargs = {}
            if wavefunction_color is not None:
                if isinstance(wavefunction_color, list):
                    extra_kwargs["color"] = wavefunction_color[n]
                else:
                    extra_kwargs["color"] = wavefunction_color

            ax.plot(
                phi_vals, (wf_vals - min_potential)*y_scale_factor, label=f"$|${n}$\\rangle$", linestyle="-", linewidth=1, **extra_kwargs
            )

            ax.fill_between(phi_vals, (energy_levels[n] - min_potential)*y_scale_factor, (wf_vals - min_potential)*y_scale_factor, alpha=0.5, **extra_kwargs)

        ax.plot(
            phi_vals,
            (potential - min_potential)*y_scale_factor,
            label="potential",
            color="black",
            linestyle="-",
            linewidth=1,
        )

        ylim = ylim if ylim is not None else [jnp.min(jnp.array([min_val - 1 - min_potential, jnp.min(potential) - min_potential]))*y_scale_factor, (max_val + 1 - min_potential)*y_scale_factor]
        ax.set_ylim(ylim)
        ax.set_xlabel(r"$\varphi/2\pi$")
        ax.set_ylabel(r"Energy [GHz]")

        if mode == "abs":
            title_str = r"$|\psi_n(\Phi)|^2$"
        elif mode == "real":
            title_str = r"Re($\psi_n(\Phi)$)"
        elif mode == "imag":
            title_str = r"Im($\psi_n(\Phi)$)"

        ax.set_title(f"{title_str}")

        ax.legend(fontsize='xx-small')
        fig.tight_layout()

        return ax

phi_zpf() abstractmethod

Return Phase ZPF.

Source code in jaxquantum/devices/superconducting/flux_base.py 
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@abstractmethod
def phi_zpf(self):
    """Return Phase ZPF."""

potential(phi) abstractmethod

Return potential energy as a function of phi.

Source code in jaxquantum/devices/superconducting/flux_base.py 
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@abstractmethod
def potential(self, phi):
    """Return potential energy as a function of phi."""

Fluxonium

Bases: FluxDevice

Fluxonium Device.

Source code in jaxquantum/devices/superconducting/fluxonium.py 
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@struct.dataclass
class Fluxonium(FluxDevice):
    """
    Fluxonium Device.
    """

    def common_ops(self):
        """Written in the linear basis."""
        ops = {}

        N = self.N_pre_diag
        ops["id"] = identity(N)
        ops["a"] = destroy(N)
        ops["a_dag"] = create(N)
        ops["phi"] = self.phi_zpf() * (ops["a"] + ops["a_dag"])
        ops["n"] = 1j * self.n_zpf() * (ops["a_dag"] - ops["a"])

        ops["cos(φ/2)"] = cosm(ops["phi"] / 2)
        ops["sin(φ/2)"] = sinm(ops["phi"] / 2)

        return ops

    def n_zpf(self):
        n_zpf = (self.params["El"] / (32.0 * self.params["Ec"])) ** (0.25)
        return n_zpf

    def phi_zpf(self):
        """Return Phase ZPF."""
        return (2 * self.params["Ec"] / self.params["El"]) ** (0.25)

    def get_linear_frequency(self):
        """Get frequency of linear terms."""
        return jnp.sqrt(8 * self.params["Ec"] * self.params["El"])

    def get_H_linear(self):
        """Return linear terms in H."""
        w = self.get_linear_frequency()
        return w * (
            self.linear_ops["a_dag"] @ self.linear_ops["a"]
            + 0.5 * self.linear_ops["id"]
        )

    def get_H_full(self):
        """Return full H in linear basis."""

        phi_op = self.linear_ops["phi"]
        return self.get_H_linear() + self.get_H_nonlinear(phi_op)

    def get_H_nonlinear(self, phi_op):
        op_cos_phi = cosm(phi_op)
        op_sin_phi = sinm(phi_op)

        phi_ext = self.params["phi_ext"]
        Hcos = op_cos_phi * jnp.cos(2.0 * jnp.pi * phi_ext) + op_sin_phi * jnp.sin(
            2.0 * jnp.pi * phi_ext
        )
        H_nl = -self.params["Ej"] * Hcos
        return H_nl

    def potential(self, phi):
        """Return potential energy for a given phi."""
        phi_ext = self.params["phi_ext"]
        V_linear = 0.5 * self.params["El"] * (2 * jnp.pi * phi) ** 2

        if self.hamiltonian == HamiltonianTypes.linear:
            return V_linear

        V_nonlinear = -self.params["Ej"] * jnp.cos(2.0 * jnp.pi * (phi - phi_ext))
        if self.hamiltonian == HamiltonianTypes.full:
            return V_linear + V_nonlinear

common_ops()

Written in the linear basis.

Source code in jaxquantum/devices/superconducting/fluxonium.py 
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def common_ops(self):
    """Written in the linear basis."""
    ops = {}

    N = self.N_pre_diag
    ops["id"] = identity(N)
    ops["a"] = destroy(N)
    ops["a_dag"] = create(N)
    ops["phi"] = self.phi_zpf() * (ops["a"] + ops["a_dag"])
    ops["n"] = 1j * self.n_zpf() * (ops["a_dag"] - ops["a"])

    ops["cos(φ/2)"] = cosm(ops["phi"] / 2)
    ops["sin(φ/2)"] = sinm(ops["phi"] / 2)

    return ops

get_H_full()

Return full H in linear basis.

Source code in jaxquantum/devices/superconducting/fluxonium.py 
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def get_H_full(self):
    """Return full H in linear basis."""

    phi_op = self.linear_ops["phi"]
    return self.get_H_linear() + self.get_H_nonlinear(phi_op)

get_H_linear()

Return linear terms in H.

Source code in jaxquantum/devices/superconducting/fluxonium.py 
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def get_H_linear(self):
    """Return linear terms in H."""
    w = self.get_linear_frequency()
    return w * (
        self.linear_ops["a_dag"] @ self.linear_ops["a"]
        + 0.5 * self.linear_ops["id"]
    )

get_linear_frequency()

Get frequency of linear terms.

Source code in jaxquantum/devices/superconducting/fluxonium.py 
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def get_linear_frequency(self):
    """Get frequency of linear terms."""
    return jnp.sqrt(8 * self.params["Ec"] * self.params["El"])

phi_zpf()

Return Phase ZPF.

Source code in jaxquantum/devices/superconducting/fluxonium.py 
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def phi_zpf(self):
    """Return Phase ZPF."""
    return (2 * self.params["Ec"] / self.params["El"]) ** (0.25)

potential(phi)

Return potential energy for a given phi.

Source code in jaxquantum/devices/superconducting/fluxonium.py 
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def potential(self, phi):
    """Return potential energy for a given phi."""
    phi_ext = self.params["phi_ext"]
    V_linear = 0.5 * self.params["El"] * (2 * jnp.pi * phi) ** 2

    if self.hamiltonian == HamiltonianTypes.linear:
        return V_linear

    V_nonlinear = -self.params["Ej"] * jnp.cos(2.0 * jnp.pi * (phi - phi_ext))
    if self.hamiltonian == HamiltonianTypes.full:
        return V_linear + V_nonlinear

IdealQubit

Bases: Device

Ideal qubit Device.

Source code in jaxquantum/devices/superconducting/ideal_qubit.py 
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@struct.dataclass
class IdealQubit(Device):
    """
    Ideal qubit Device.
    """

    @classmethod
    def param_validation(cls, N, N_pre_diag, params, hamiltonian, basis):
        """This can be overridden by subclasses."""
        assert basis == BasisTypes.fock, (
            "IdealQubit is a two-level system defined in the Fock basis."
        )
        assert hamiltonian == HamiltonianTypes.full, (
            "IdealQubit requires a full Hamiltonian."
        )
        assert N == N_pre_diag == 2, "IdealQubit is a two-level system."
        assert "f" in params, "IdealQubit requires a frequency parameter 'f'."

        params["Δ"] = params.get("Δ", 0.0)

    def common_ops(self):
        """Written in the linear basis."""
        ops = {}

        assert self.N_pre_diag == 2
        assert self.N == 2

        N = self.N_pre_diag
        ops["id"] = identity(N)
        ops["sigmaz"] = sigmaz()
        ops["sigmax"] = sigmax()
        ops["sigmay"] = sigmay()
        ops["sigmam"] = sigmam()
        ops["sigmap"] = sigmap()

        return ops

    def get_linear_frequency(self):
        """Get frequency of linear terms."""
        return self.params["f"]

    def get_H_linear(self):
        """Return linear terms in H."""
        w = self.get_linear_frequency()
        return (w / 2) * self.linear_ops["sigmaz"]

    def get_H_full(self):
        """Return full H in linear basis."""

        return self.get_H_linear() + self.params["Δ"] / 2 * self.linear_ops["sigmax"]

common_ops()

Written in the linear basis.

Source code in jaxquantum/devices/superconducting/ideal_qubit.py 
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def common_ops(self):
    """Written in the linear basis."""
    ops = {}

    assert self.N_pre_diag == 2
    assert self.N == 2

    N = self.N_pre_diag
    ops["id"] = identity(N)
    ops["sigmaz"] = sigmaz()
    ops["sigmax"] = sigmax()
    ops["sigmay"] = sigmay()
    ops["sigmam"] = sigmam()
    ops["sigmap"] = sigmap()

    return ops

get_H_full()

Return full H in linear basis.

Source code in jaxquantum/devices/superconducting/ideal_qubit.py 
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def get_H_full(self):
    """Return full H in linear basis."""

    return self.get_H_linear() + self.params["Δ"] / 2 * self.linear_ops["sigmax"]

get_H_linear()

Return linear terms in H.

Source code in jaxquantum/devices/superconducting/ideal_qubit.py 
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def get_H_linear(self):
    """Return linear terms in H."""
    w = self.get_linear_frequency()
    return (w / 2) * self.linear_ops["sigmaz"]

get_linear_frequency()

Get frequency of linear terms.

Source code in jaxquantum/devices/superconducting/ideal_qubit.py 
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def get_linear_frequency(self):
    """Get frequency of linear terms."""
    return self.params["f"]

param_validation(N, N_pre_diag, params, hamiltonian, basis) classmethod

This can be overridden by subclasses.

Source code in jaxquantum/devices/superconducting/ideal_qubit.py 
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@classmethod
def param_validation(cls, N, N_pre_diag, params, hamiltonian, basis):
    """This can be overridden by subclasses."""
    assert basis == BasisTypes.fock, (
        "IdealQubit is a two-level system defined in the Fock basis."
    )
    assert hamiltonian == HamiltonianTypes.full, (
        "IdealQubit requires a full Hamiltonian."
    )
    assert N == N_pre_diag == 2, "IdealQubit is a two-level system."
    assert "f" in params, "IdealQubit requires a frequency parameter 'f'."

    params["Δ"] = params.get("Δ", 0.0)

KNO

Bases: Device

Kerr Nonlinear Oscillator Device.

Source code in jaxquantum/devices/superconducting/kno.py 
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@struct.dataclass
class KNO(Device):
    """
    Kerr Nonlinear Oscillator Device.
    """

    @classmethod
    def param_validation(cls, N, N_pre_diag, params, hamiltonian, basis):
        """This can be overridden by subclasses."""
        assert basis == BasisTypes.fock, (
            "Kerr Nonlinear Oscillator must be defined in the Fock basis."
        )
        assert hamiltonian == HamiltonianTypes.full, (
            "Kerr Nonlinear Oscillator uses a full Hamiltonian."
        )
        assert "f" in params and "α" in params, (
            "Kerr Nonlinear Oscillator requires frequency 'f' and anharmonicity 'α' as parameters."
        )

    def common_ops(self):
        ops = {}

        N = self.N
        ops["id"] = identity(N)
        ops["a"] = destroy(N)
        ops["a_dag"] = create(N)
        ops["phi"] = (ops["a"] + ops["a_dag"]) / jnp.sqrt(2)
        ops["n"] = 1j * (ops["a_dag"] - ops["a"]) / jnp.sqrt(2)
        return ops

    def get_linear_frequency(self):
        """Get frequency of linear terms."""
        return self.params["f"]

    def get_anharm(self):
        """Get anharmonicity."""
        return self.params["α"]

    def get_H_linear(self):
        """Return linear terms in H."""
        w = self.get_linear_frequency()
        return w * self.linear_ops["a_dag"] @ self.linear_ops["a"]

    def get_H_full(self):
        """Return full H in linear basis."""
        α = self.get_anharm()

        return self.get_H_linear() + (α / 2) * (
            self.linear_ops["a_dag"]
            @ self.linear_ops["a_dag"]
            @ self.linear_ops["a"]
            @ self.linear_ops["a"]
        )

get_H_full()

Return full H in linear basis.

Source code in jaxquantum/devices/superconducting/kno.py 
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def get_H_full(self):
    """Return full H in linear basis."""
    α = self.get_anharm()

    return self.get_H_linear() + (α / 2) * (
        self.linear_ops["a_dag"]
        @ self.linear_ops["a_dag"]
        @ self.linear_ops["a"]
        @ self.linear_ops["a"]
    )

get_H_linear()

Return linear terms in H.

Source code in jaxquantum/devices/superconducting/kno.py 
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def get_H_linear(self):
    """Return linear terms in H."""
    w = self.get_linear_frequency()
    return w * self.linear_ops["a_dag"] @ self.linear_ops["a"]

get_anharm()

Get anharmonicity.

Source code in jaxquantum/devices/superconducting/kno.py 
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def get_anharm(self):
    """Get anharmonicity."""
    return self.params["α"]

get_linear_frequency()

Get frequency of linear terms.

Source code in jaxquantum/devices/superconducting/kno.py 
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def get_linear_frequency(self):
    """Get frequency of linear terms."""
    return self.params["f"]

param_validation(N, N_pre_diag, params, hamiltonian, basis) classmethod

This can be overridden by subclasses.

Source code in jaxquantum/devices/superconducting/kno.py 
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@classmethod
def param_validation(cls, N, N_pre_diag, params, hamiltonian, basis):
    """This can be overridden by subclasses."""
    assert basis == BasisTypes.fock, (
        "Kerr Nonlinear Oscillator must be defined in the Fock basis."
    )
    assert hamiltonian == HamiltonianTypes.full, (
        "Kerr Nonlinear Oscillator uses a full Hamiltonian."
    )
    assert "f" in params and "α" in params, (
        "Kerr Nonlinear Oscillator requires frequency 'f' and anharmonicity 'α' as parameters."
    )

Qarray

Bases: Generic[ImplT]

Quantum array with a pluggable storage backend.

Qarray wraps a QarrayImpl together with quantum-mechanical dimension metadata (_qdims) and optional batch dimensions (_bdims). The default backend is dense (DenseImpl); pass implementation="sparse_bcoo" (or QarrayImplType.SPARSE_BCOO) to store data as a JAX BCOO sparse array.

Attributes:

Name Type Description
_impl ImplT

The storage backend holding the raw data.
_qdims Qdims

Quantum dimension metadata (bra/ket structure, Hilbert space sizes).
_bdims tuple[int]

Tuple of batch dimension sizes (empty tuple = non-batched).
Example

import jaxquantum as jqt a = jqt.destroy(10, implementation="sparse_bcoo") a.is_sparse_bcoo True

Source code in jaxquantum/core/qarray.py 
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@struct.dataclass
class Qarray(Generic[ImplT]):
    """Quantum array with a pluggable storage backend.

    ``Qarray`` wraps a ``QarrayImpl`` together with quantum-mechanical
    dimension metadata (``_qdims``) and optional batch dimensions
    (``_bdims``).  The default backend is dense (``DenseImpl``); pass
    ``implementation="sparse_bcoo"`` (or ``QarrayImplType.SPARSE_BCOO``) to
    store data as a JAX BCOO sparse array.

    Attributes:
        _impl: The storage backend holding the raw data.
        _qdims: Quantum dimension metadata (bra/ket structure, Hilbert space
            sizes).
        _bdims: Tuple of batch dimension sizes (empty tuple = non-batched).

    Example:
        >>> import jaxquantum as jqt
        >>> a = jqt.destroy(10, implementation="sparse_bcoo")
        >>> a.is_sparse_bcoo
        True
    """

    _impl: ImplT
    _qdims: Qdims = struct.field(pytree_node=False)
    _bdims: tuple[int] = struct.field(pytree_node=False)

    # Initialization ----
    @classmethod
    @overload
    def create(cls, data, dims=None, bdims=None, implementation: Literal[QarrayImplType.DENSE] = QarrayImplType.DENSE) -> "Qarray[DenseImpl]":
        ...

    @classmethod
    @overload
    def create(cls, data, dims=None, bdims=None, implementation: Literal[QarrayImplType.SPARSE_BCOO] = ...) -> "Qarray[SparseBCOOImpl]":
        ...

    @classmethod
    @overload
    def create(cls, data, dims=None, bdims=None, implementation=...) -> "Qarray[DenseImpl]":
        ...

    @classmethod
    def create(cls, data, dims=None, bdims=None, implementation=QarrayImplType.DENSE):
        """Create a ``Qarray`` from raw data.

        Handles shape normalisation, dimension inference, and tidying of small
        values.

        Args:
            data: Input data array (dense array-like or ``sparse.BCOO``).
            dims: Quantum dimensions as ``((row_dims...), (col_dims...))``.
                Inferred from *data* shape when ``None``.
            bdims: Tuple of batch dimension sizes.  Inferred from the leading
                dimensions of *data* when ``None``.
            implementation: Storage backend — ``QarrayImplType.DENSE``
                (default) or ``QarrayImplType.SPARSE_BCOO``, or the equivalent
                string ``"dense"`` / ``"sparse_bcoo"``.

        Returns:
            A new ``Qarray`` backed by the requested implementation.
        """
        # Step 1: Prepare data ----
        data = robust_asarray(data)

        if len(data.shape) == 1 and data.shape[0] > 0:
            data = data.reshape(data.shape[0], 1)

        if len(data.shape) >= 2:
            if data.shape[-2] != data.shape[-1] and not (
                data.shape[-2] == 1 or data.shape[-1] == 1
            ):
                data = data.reshape(*data.shape[:-1], data.shape[-1], 1)

        if bdims is not None:
            if len(data.shape) - len(bdims) == 1:
                data = data.reshape(*data.shape[:-1], data.shape[-1], 1)
        # ----

        # Step 2: Prepare dimensions ----
        if bdims is None:
            bdims = tuple(data.shape[:-2])

        if dims is None:
            dims = ((data.shape[-2],), (data.shape[-1],))

        if not isinstance(dims[0], (list, tuple)):
            # This handles the case where only the hilbert space dimensions are sent in.
            if data.shape[-1] == 1:
                dims = (tuple(dims), tuple([1 for _ in dims]))
            elif data.shape[-2] == 1:
                dims = (tuple([1 for _ in dims]), tuple(dims))
            else:
                dims = (tuple(dims), tuple(dims))
        else:
            dims = (tuple(dims[0]), tuple(dims[1]))

        check_dims(dims, bdims, data.shape)

        qdims = Qdims(dims)

        # NOTE: Constantly tidying up on Qarray creation might be a bit overkill.
        # It increases the compilation time, but only very slightly
        # increased the runtime of the jit compiled function.
        # We could instead use this tidy up where we think we need it.

        impl_class = QarrayImplType(implementation).get_impl_class()
        impl = impl_class.from_data(data)
        impl = impl.tidy_up(SETTINGS["auto_tidyup_atol"])

        return cls(impl, qdims, bdims)

    @classmethod
    @overload
    def from_sparse_bcoo(cls, data, dims=None, bdims=None) -> "Qarray[SparseBCOOImpl]":
        ...

    @classmethod
    def from_sparse_bcoo(cls, data, dims=None, bdims=None):
        """Create a ``Qarray`` directly from a sparse BCOO array without densifying.

        Args:
            data: A ``sparse.BCOO`` or array-like to store as sparse BCOO.
            dims: Quantum dimensions.  Inferred when ``None``.
            bdims: Batch dimensions.  Inferred when ``None``.

        Returns:
            A ``Qarray[SparseBCOOImpl]``.
        """
        return cls.create(data, dims=dims, bdims=bdims, implementation=QarrayImplType.SPARSE_BCOO)

    @classmethod
    def from_sparse_dia(cls, data, dims=None, bdims=None) -> "Qarray":
        """Create a SparseDIA-backed ``Qarray``.

        Accepts either a dense array-like (diagonals are auto-detected) or a
        :class:`~jaxquantum.core.sparse_dia.SparseDiaData` container.

        Args:
            data: Dense array of shape (*batch, n, n) or a ``SparseDiaData``.
            dims: Quantum dimensions ``((row_dims,), (col_dims,))``.
            bdims: Batch dimension sizes.

        Returns:
            A ``Qarray`` backed by ``SparseDiaImpl``.
        """
        return cls.create(data, dims=dims, bdims=bdims, implementation=QarrayImplType.SPARSE_DIA)

    @classmethod
    @overload
    def from_list(cls, qarr_list: List["Qarray[DenseImpl]"]) -> "Qarray[DenseImpl]":
        ...

    @classmethod
    @overload
    def from_list(cls, qarr_list: List["Qarray[SparseBCOOImpl]"]) -> "Qarray[SparseBCOOImpl]":
        ...

    @classmethod
    def from_list(cls, qarr_list: List[Qarray]) -> Qarray:
        """Create a batched ``Qarray`` from a list of same-shaped ``Qarray`` objects.

        The output implementation is determined by the element with the highest
        ``PROMOTION_ORDER``: if all inputs are sparse the result is sparse; if
        any input is dense (or types are mixed) all inputs are promoted to dense
        and the result is dense.

        Args:
            qarr_list: List of ``Qarray`` objects with identical ``dims`` and
                ``bdims``.  May be empty.

        Returns:
            A ``Qarray`` with an extra leading batch dimension of size
            ``len(qarr_list)``.

        Raises:
            ValueError: If the elements have mismatched ``dims`` or ``bdims``.
        """
        if len(qarr_list) == 0:
            dims = ((), ())
            bdims = (0,)
            return cls.create(jnp.array([]), dims=dims, bdims=bdims)

        dims = qarr_list[0].dims
        bdims = qarr_list[0].bdims

        if not all(qarr.dims == dims and qarr.bdims == bdims for qarr in qarr_list):
            raise ValueError("All Qarrays in the list must have the same dimensions.")

        new_bdims = (len(qarr_list),) + bdims

        # Pick the target type: highest PROMOTION_ORDER wins (dense beats sparse).
        target_impl_type = max(
            (q.impl_type for q in qarr_list),
            key=lambda t: t.get_impl_class().PROMOTION_ORDER,
        )

        if target_impl_type == QarrayImplType.SPARSE_DIA:
            # All inputs are SparseDIA — batch without densifying.
            # Compute union of offsets across all operators, then remap each
            # operator's _diags rows into the union shape and stack.
            from jaxquantum.core.sparse_dia import SparseDiaData  # lazy to avoid circular
            union_offsets = tuple(sorted(
                set().union(*[set(q._impl._offsets) for q in qarr_list])
            ))
            union_idx = {k: i for i, k in enumerate(union_offsets)}
            n = qarr_list[0]._impl._diags.shape[-1]
            dtype = jnp.result_type(*[q._impl._diags.dtype for q in qarr_list])
            remapped = []
            for q in qarr_list:
                row = jnp.zeros((len(union_offsets), n), dtype=dtype)
                for i_src, k in enumerate(q._impl._offsets):
                    row = row.at[union_idx[k], :].set(q._impl._diags[i_src, :])
                remapped.append(row)
            stacked = jnp.stack(remapped, axis=0)  # (n_ops, n_union_diags, N)
            raw = SparseDiaData(offsets=union_offsets, diags=stacked)
            return cls.create(raw, dims=dims, bdims=new_bdims, implementation=QarrayImplType.SPARSE_DIA)

        if target_impl_type == QarrayImplType.SPARSE_BCOO:
            # All inputs are sparse BCOO — stack via dense intermediates then re-sparsify.
            data = jnp.array([q.data.todense() for q in qarr_list])
            return cls.create(data, dims=dims, bdims=new_bdims, implementation=QarrayImplType.SPARSE_BCOO)

        # Target is dense: promote any sparse inputs before stacking.
        data = jnp.array([q.to_dense().data for q in qarr_list])
        return cls.create(data, dims=dims, bdims=new_bdims, implementation=QarrayImplType.DENSE)

    @classmethod
    @overload
    def from_array(cls, qarr_arr: "Qarray[DenseImpl]") -> "Qarray[DenseImpl]":
        ...

    @classmethod
    @overload
    def from_array(cls, qarr_arr: "Qarray[SparseBCOOImpl]") -> "Qarray[SparseBCOOImpl]":
        ...

    @classmethod
    def from_array(cls, qarr_arr) -> Qarray:
        """Create a ``Qarray`` from a (possibly nested) list of ``Qarray`` objects.

        Args:
            qarr_arr: A ``Qarray`` (returned as-is) or a nested list of
                ``Qarray`` objects.

        Returns:
            A ``Qarray`` with batch dimensions matching the nesting structure
            of *qarr_arr*.
        """
        if isinstance(qarr_arr, Qarray):
            return qarr_arr

        bdims = ()
        lvl = qarr_arr
        while not isinstance(lvl, Qarray):
            bdims = bdims + (len(lvl),)
            if len(lvl) > 0:
                lvl = lvl[0]
            else:
                break

        def flat(lis):
            flatList = []
            for element in lis:
                if type(element) is list:
                    flatList += flat(element)
                else:
                    flatList.append(element)
            return flatList

        qarr_list = flat(qarr_arr)
        qarr = cls.from_list(qarr_list)
        qarr = qarr.reshape_bdims(*bdims)
        return qarr

    # Properties ----
    @property
    def qtype(self):
        """Quantum type of this array (ket, bra, or operator)."""
        return self._qdims.qtype

    @property
    def dtype(self):
        """Data type of the underlying storage array."""
        return self._impl.dtype()

    @property
    def dims(self):
        """Quantum dimensions as ``((row_dims...), (col_dims...))``."""
        return self._qdims.dims

    @property
    def bdims(self):
        """Tuple of batch dimension sizes (empty tuple = non-batched)."""
        return self._bdims

    @property
    def qdims(self):
        """The ``Qdims`` metadata object for this array."""
        return self._qdims

    @property
    def space_dims(self):
        """Hilbert space dimensions for the relevant side (ket row / bra col)."""
        if self.qtype in [Qtypes.oper, Qtypes.ket]:
            return self.dims[0]
        elif self.qtype == Qtypes.bra:
            return self.dims[1]
        else:
            # TODO: not reached for some reason
            raise ValueError("Unsupported qtype.")

    @property
    def data(self):
        """The raw underlying data (dense ``jnp.ndarray`` or ``sparse.BCOO``)."""
        return self._impl.data

    @property
    def shaped_data(self):
        """Data reshaped to ``bdims + dims[0] + dims[1]``."""
        return self.data.reshape(self.bdims + self.dims[0] + self.dims[1])

    @property
    def shape(self):
        """Shape of the underlying data array."""
        return self.data.shape

    @property
    def is_batched(self):
        """True if this array has one or more batch dimensions."""
        return len(self.bdims) > 0

    @property
    def is_sparse_bcoo(self):
        """True if the storage backend is ``SparseBCOOImpl`` (BCOO)."""
        return self._impl.impl_type == QarrayImplType.SPARSE_BCOO

    @property
    def is_dense(self):
        """True if the storage backend is ``DenseImpl``."""
        return self._impl.impl_type == QarrayImplType.DENSE

    @property
    def is_sparse_dia(self):
        """True if the storage backend is ``SparseDiaImpl``."""
        return self._impl.impl_type == QarrayImplType.SPARSE_DIA

    @property
    def impl_type(self):
        """The ``QarrayImplType`` member of the current storage backend."""
        return self._impl.impl_type

    def to_sparse_bcoo(self) -> "Qarray[SparseBCOOImpl]":
        """Return a BCOO-sparse-backed copy of this array.

        If the array is already sparse BCOO, returns self unchanged.

        Returns:
            A ``Qarray[SparseBCOOImpl]``.
        """
        if self.is_sparse_bcoo:
            return self
        new_impl = self._impl.to_sparse_bcoo()
        return Qarray(new_impl, self._qdims, self._bdims)

    def to_sparse_dia(self) -> "Qarray":
        """Return a SparseDIA-backed copy of this array.

        If the array is already SparseDIA, returns self unchanged.

        Returns:
            A ``Qarray[SparseDiaImpl]``.
        """
        if self.is_sparse_dia:
            return self
        new_impl = self._impl.to_sparse_dia()
        return Qarray(new_impl, self._qdims, self._bdims)

    def to_dense(self) -> "Qarray[DenseImpl]":
        """Return a dense-backed copy of this array.

        If the array is already dense, returns self unchanged.

        Returns:
            A ``Qarray[DenseImpl]``.
        """
        if self.is_dense:
            return self
        new_impl = self._impl.to_dense()
        return Qarray(new_impl, self._qdims, self._bdims)

    def __getitem__(self, index):
        if len(self.bdims) > 0:
            return Qarray.create(
                self.data[index],
                dims=self.dims,
                implementation=self.impl_type,
            )
        else:
            raise ValueError("Cannot index a non-batched Qarray.")

    def reshape_bdims(self, *args):
        """Reshape the batch dimensions of this ``Qarray``.

        Args:
            *args: New batch dimension sizes.

        Returns:
            A new ``Qarray`` with the requested batch shape.
        """
        new_bdims = tuple(args)

        if prod(new_bdims) == 0:
            new_shape = new_bdims
        else:
            new_shape = new_bdims + (prod(self.dims[0]),) + (-1,)

        # Preserve implementation type
        implementation = self.impl_type
        return Qarray.create(
            self.data.reshape(new_shape),
            dims=self.dims,
            bdims=new_bdims,
            implementation=implementation,
        )

    def space_to_qdims(self, space_dims: List[int]):
        """Convert Hilbert space dimensions to full quantum dims tuple.

        Args:
            space_dims: Sequence of per-subsystem Hilbert space sizes, or a
                full ``((row_dims), (col_dims))`` tuple (returned unchanged).

        Returns:
            A ``((row_dims...), (col_dims...))`` tuple.

        Raises:
            ValueError: If ``self.qtype`` is not ket, bra, or oper.
        """
        if isinstance(space_dims[0], (list, tuple)):
            return space_dims

        if self.qtype in [Qtypes.oper, Qtypes.ket]:
            return (tuple(space_dims), tuple([1 for _ in range(len(space_dims))]))
        elif self.qtype == Qtypes.bra:
            return (tuple([1 for _ in range(len(space_dims))]), tuple(space_dims))
        else:
            raise ValueError("Unsupported qtype for space_to_qdims conversion.")

    def reshape_qdims(self, *args):
        """Reshape the quantum dimensions of the Qarray.

        Note that this does not take in qdims but rather the new Hilbert space
        dimensions.

        Args:
            *args: New Hilbert dimensions for the Qarray.

        Returns:
            Qarray: reshaped Qarray.
        """

        new_space_dims = tuple(args)
        current_space_dims = self.space_dims
        assert prod(new_space_dims) == prod(current_space_dims)

        new_qdims = self.space_to_qdims(new_space_dims)
        new_bdims = self.bdims

        # Preserve implementation type
        implementation = self.impl_type
        return Qarray.create(self.data, dims=new_qdims, bdims=new_bdims, implementation=implementation)

    def resize(self, new_shape):
        """Resize the Qarray to a new shape.

        TODO: review and maybe deprecate this method.

        Args:
            new_shape: Target shape tuple.

        Returns:
            A new ``Qarray`` with data resized via ``jnp.resize``.
        """
        dims = self.dims
        data = jnp.resize(self.data, new_shape)
        # Preserve implementation type
        implementation = self.impl_type
        return Qarray.create(
            data,
            dims=dims,
            implementation=implementation,
        )

    def __len__(self):
        """Length along the first batch dimension.

        Returns:
            Size of the leading batch dimension.

        Raises:
            ValueError: If the array is not batched.
        """
        if len(self.bdims) > 0:
            return self.data.shape[0]
        else:
            raise ValueError("Cannot get length of a non-batched Qarray.")

    def __eq__(self, other):
        if not isinstance(other, Qarray):
            raise ValueError("Cannot calculate equality of a Qarray with a non-Qarray.")

        if self.dims != other.dims:
            return False

        if self.bdims != other.bdims:
            return False

        if self.is_sparse_bcoo and other.is_sparse_bcoo:
            # Fast structural path: same sparsity pattern → compare values only (no todense)
            if (self.data.indices.shape == other.data.indices.shape
                    and bool(jnp.all(self.data.indices == other.data.indices))):
                return bool(jnp.allclose(self.data.data, other.data.data))
            # Different patterns: fall back to dense comparison (unavoidable)
            return bool(jnp.all(self.data.todense() == other.data.todense()))

        # At least one dense: convert sparse side to dense for comparison
        self_data  = self.data.todense()  if hasattr(self.data,  'todense') else self.data
        other_data = other.data.todense() if hasattr(other.data, 'todense') else other.data
        return bool(jnp.all(self_data == other_data))

    def __ne__(self, other):
        return not self.__eq__(other)

    # Elementary Math ----
    def __matmul__(self, other):
        if not isinstance(other, Qarray):
            return NotImplemented

        _qdims_new = self._qdims @ other._qdims
        new_impl = self._impl.matmul(other._impl)

        return Qarray.create(
            new_impl.data,
            dims=_qdims_new.dims,
            implementation=new_impl.impl_type,
        )

    def __mul__(self, other):
        if isinstance(other, Qarray):
            return self.__matmul__(other)

        other = other + 0.0j
        if not robust_isscalar(other) and len(other.shape) > 0:  # not a scalar
            other = other.reshape(other.shape + (1, 1))

        new_impl = self._impl.mul(other)
        return Qarray.create(
            new_impl.data,
            dims=self._qdims.dims,
            implementation=new_impl.impl_type,
        )

    def __rmul__(self, other):
        return self.__mul__(other)

    def __neg__(self):
        return self.__mul__(-1)

    def __truediv__(self, other):
        """Divide by a scalar.

        Args:
            other: Scalar divisor.

        Returns:
            A new ``Qarray`` with all elements divided by *other*.

        Raises:
            ValueError: If *other* is a ``Qarray``.
        """
        if isinstance(other, Qarray):
            raise ValueError("Cannot divide a Qarray by another Qarray.")

        return self.__mul__(1 / other)

    def __add__(self, other):
        if isinstance(other, Qarray):
            if self.dims != other.dims:
                msg = (
                    "Dimensions are incompatible: "
                    + repr(self.dims)
                    + " and "
                    + repr(other.dims)
                )
                raise ValueError(msg)
            new_impl = self._impl.add(other._impl)
            return Qarray.create(
                new_impl.data,
                dims=self.dims,
                implementation=new_impl.impl_type,
            )

        if robust_isscalar(other) and other == 0:
            return self.copy()

        if self.data.shape[-2] == self.data.shape[-1]:
            other = other + 0.0j
            if not robust_isscalar(other) and len(other.shape) > 0:  # not a scalar
                other = other.reshape(other.shape + (1, 1))
            eye_data = self._impl._eye_data(self.data.shape[-2], dtype=self.data.dtype)
            other = Qarray.create(
                other * eye_data,
                dims=self.dims,
                implementation=self.impl_type
            )
            return self.__add__(other)

        return NotImplemented

    def __radd__(self, other):
        return self.__add__(other)

    def __sub__(self, other):
        if isinstance(other, Qarray):
            if self.dims != other.dims:
                msg = (
                    "Dimensions are incompatible: "
                    + repr(self.dims)
                    + " and "
                    + repr(other.dims)
                )
                raise ValueError(msg)
            new_impl = self._impl.sub(other._impl)
            return Qarray.create(
                new_impl.data,
                dims=self.dims,
                implementation=new_impl.impl_type,
            )

        if robust_isscalar(other) and other == 0:
            return self.copy()

        if self.data.shape[-2] == self.data.shape[-1]:
            other = other + 0.0j

            if not robust_isscalar(other) and len(other.shape) > 0:  # not a scalar
                other = other.reshape(other.shape + (1, 1))
            eye_data = self._impl._eye_data(self.data.shape[-2], dtype=self.data.dtype)
            other = Qarray.create(
                other * eye_data,
                dims=self.dims,
                implementation=self.impl_type
            )
            return self.__sub__(other)

        return NotImplemented

    def __rsub__(self, other):
        return self.__neg__().__add__(other)

    def __xor__(self, other):
        if not isinstance(other, Qarray):
            return NotImplemented
        return tensor(self, other)

    def __rxor__(self, other):
        if not isinstance(other, Qarray):
            return NotImplemented
        return tensor(other, self)

    def __pow__(self, other):
        if not isinstance(other, int):
            return NotImplemented

        return powm(self, other)

    # String Representation ----
    def _str_header(self):
        """Build the one-line header string for ``__str__`` and ``__repr__``."""
        impl_type = self.impl_type.value
        out = ", ".join(
            [
                "Quantum array: dims = " + str(self.dims),
                "bdims = " + str(self.bdims),
                "shape = " + str(self.data.shape),
                "type = " + str(self.qtype),
                "impl = " + impl_type,
            ]
        )
        return out

    def __str__(self):
        return self._str_header() + "\nQarray data =\n" + str(self.data)

    @property
    def header(self):
        """One-line header string describing dimensions, shape, and backend."""
        return self._str_header()

    def __repr__(self):
        return self.__str__()

    # Utilities ----
    def copy(self, memo=None):
        """Return a deep copy of this ``Qarray``.

        Args:
            memo: Optional memo dict forwarded to ``deepcopy``.

        Returns:
            A new ``Qarray`` with independent copies of all data.
        """
        return self.__deepcopy__(memo)

    def __deepcopy__(self, memo):
        """Need to override this when defining __getattr__."""

        return Qarray(
            _impl=deepcopy(self._impl, memo=memo),
            _qdims=deepcopy(self._qdims, memo=memo),
            _bdims=deepcopy(self._bdims, memo=memo),
        )

    def __getattr__(self, method_name):
        if "__" == method_name[:2]:
            # NOTE: we return NotImplemented for binary special methods logic in python, plus things like __jax_array__
            return lambda *args, **kwargs: NotImplemented

        modules = [jnp, jnp.linalg, jsp, jsp.linalg]

        method_f = None
        for mod in modules:
            method_f = getattr(mod, method_name, None)
            if method_f is not None:
                break

        if method_f is None:
            raise NotImplementedError(
                f"Method {method_name} does not exist. No backup method found in {modules}."
            )

        def func(*args, **kwargs):
            # For operations that might not be supported in sparse, convert to dense
            if self.is_sparse_bcoo:
                dense_self = self.to_dense()
                res = method_f(dense_self.data, *args, **kwargs)
            else:
                res = method_f(self.data, *args, **kwargs)

            if getattr(res, "shape", None) is None or res.shape != self.data.shape:
                return res
            else:
                # Preserve implementation type
                return Qarray.create(res, dims=self._qdims.dims, implementation=self.impl_type)

        return func

    # Conversions / Reshaping ----
    def dag(self):
        """Conjugate transpose of this array."""
        return dag(self)

    def to_dm(self):
        """Convert a ket to a density matrix via outer product."""
        return ket2dm(self)

    def is_dm(self):
        """Return True if this array is an operator (density-matrix type)."""
        return self.qtype == Qtypes.oper

    def is_vec(self):
        """Return True if this array is a ket or bra."""
        return self.qtype == Qtypes.ket or self.qtype == Qtypes.bra

    def to_ket(self):
        """Convert a bra to a ket (no-op for kets)."""
        return to_ket(self)

    def transpose(self, *args):
        """Transpose subsystem indices."""
        return transpose(self, *args)

    def keep_only_diag_elements(self):
        """Zero out all off-diagonal elements."""
        return keep_only_diag_elements(self)

    # Math Functions ----
    def unit(self):
        """Return the normalised (unit-norm) version of this array."""
        return unit(self)

    def norm(self):
        """Compute the norm of this array."""
        return norm(self)

    def frobenius_norm(self):
        """Compute the Frobenius norm directly from the implementation.

        Returns:
            The Frobenius norm as a scalar.
        """
        return self._impl.frobenius_norm()

    def real(self):
        """Element-wise real part.

        Returns:
            A new ``Qarray`` containing the real parts of each element.
        """
        new_impl = self._impl.real()
        return Qarray.create(
            new_impl.data,
            dims=self.dims,
            implementation=new_impl.impl_type,
        )

    def imag(self):
        """Element-wise imaginary part.

        Returns:
            A new ``Qarray`` containing the imaginary parts of each element.
        """
        new_impl = self._impl.imag()

        return Qarray.create(
            new_impl.data,
            dims=self.dims,
            implementation=new_impl.impl_type,
        )

    def conj(self):
        """Element-wise complex conjugate.

        Returns:
            A new ``Qarray`` containing the complex-conjugated elements.
        """
        new_impl = self._impl.conj()
        return Qarray.create(
            new_impl.data,
            dims=self.dims,
            implementation=new_impl.impl_type,
        )

    def expm(self):
        """Matrix exponential."""
        return expm(self)

    def powm(self, n):
        """Matrix power.

        Args:
            n: Exponent (integer or float).

        Returns:
            This array raised to the *n*-th matrix power.
        """
        return powm(self, n)

    def cosm(self):
        """Matrix cosine."""
        return cosm(self)

    def sinm(self):
        """Matrix sine."""
        return sinm(self)

    def tr(self, **kwargs):
        """Full trace."""
        return tr(self, **kwargs)

    def trace(self, **kwargs):
        """Full trace (alias for :meth:`tr`)."""
        return tr(self, **kwargs)

    def ptrace(self, indx):
        """Partial trace over subsystem *indx*.

        Args:
            indx: Index of the subsystem to trace out.

        Returns:
            Reduced density matrix.
        """
        return ptrace(self, indx)

    def eigenstates(self):
        """Eigenvalues and eigenstates of this operator."""
        return eigenstates(self)

    def eigenenergies(self):
        """Eigenvalues of this operator."""
        return eigenenergies(self)

    def eigenvalues(self):
        """Eigenvalues of this operator (alias for :meth:`eigenenergies`)."""
        return eigenenergies(self)

    def collapse(self, mode="sum"):
        """Collapse batch dimensions.

        Args:
            mode: Collapse strategy — currently only ``"sum"`` is supported.

        Returns:
            A non-batched ``Qarray``.
        """
        return collapse(self, mode=mode)

bdims property

Tuple of batch dimension sizes (empty tuple = non-batched).

data property

The raw underlying data (dense jnp.ndarray or sparse.BCOO).

dims property

Quantum dimensions as ((row_dims...), (col_dims...)).

dtype property

Data type of the underlying storage array.

header property

One-line header string describing dimensions, shape, and backend.

impl_type property

The QarrayImplType member of the current storage backend.

is_batched property

True if this array has one or more batch dimensions.

is_dense property

True if the storage backend is DenseImpl.

is_sparse_bcoo property

True if the storage backend is SparseBCOOImpl (BCOO).

is_sparse_dia property

True if the storage backend is SparseDiaImpl.

qdims property

The Qdims metadata object for this array.

qtype property

Quantum type of this array (ket, bra, or operator).

shape property

Shape of the underlying data array.

shaped_data property

Data reshaped to bdims + dims[0] + dims[1].

space_dims property

Hilbert space dimensions for the relevant side (ket row / bra col).

__deepcopy__(memo)

Need to override this when defining getattr.

Source code in jaxquantum/core/qarray.py 
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def __deepcopy__(self, memo):
    """Need to override this when defining __getattr__."""

    return Qarray(
        _impl=deepcopy(self._impl, memo=memo),
        _qdims=deepcopy(self._qdims, memo=memo),
        _bdims=deepcopy(self._bdims, memo=memo),
    )

__len__()

Length along the first batch dimension.

Returns:

Type Description

Size of the leading batch dimension.

Raises:

Type Description
ValueError

If the array is not batched.
Source code in jaxquantum/core/qarray.py 
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def __len__(self):
    """Length along the first batch dimension.

    Returns:
        Size of the leading batch dimension.

    Raises:
        ValueError: If the array is not batched.
    """
    if len(self.bdims) > 0:
        return self.data.shape[0]
    else:
        raise ValueError("Cannot get length of a non-batched Qarray.")

__truediv__(other)

Divide by a scalar.

Parameters:

Name Type Description Default
other

Scalar divisor.

 required

Returns:

Type Description

A new Qarray with all elements divided by other.

Raises:

Type Description
ValueError

If other is a Qarray.
Source code in jaxquantum/core/qarray.py 
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def __truediv__(self, other):
    """Divide by a scalar.

    Args:
        other: Scalar divisor.

    Returns:
        A new ``Qarray`` with all elements divided by *other*.

    Raises:
        ValueError: If *other* is a ``Qarray``.
    """
    if isinstance(other, Qarray):
        raise ValueError("Cannot divide a Qarray by another Qarray.")

    return self.__mul__(1 / other)

collapse(mode='sum')

Collapse batch dimensions.

Parameters:

Name Type Description Default
mode

Collapse strategy — currently only "sum" is supported.

 'sum'

Returns:

Type Description

A non-batched Qarray.
Source code in jaxquantum/core/qarray.py 
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def collapse(self, mode="sum"):
    """Collapse batch dimensions.

    Args:
        mode: Collapse strategy — currently only ``"sum"`` is supported.

    Returns:
        A non-batched ``Qarray``.
    """
    return collapse(self, mode=mode)

conj()

Element-wise complex conjugate.

Returns:

Type Description

A new Qarray containing the complex-conjugated elements.
Source code in jaxquantum/core/qarray.py 
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def conj(self):
    """Element-wise complex conjugate.

    Returns:
        A new ``Qarray`` containing the complex-conjugated elements.
    """
    new_impl = self._impl.conj()
    return Qarray.create(
        new_impl.data,
        dims=self.dims,
        implementation=new_impl.impl_type,
    )

copy(memo=None)

Return a deep copy of this Qarray.

Parameters:

Name Type Description Default
memo

Optional memo dict forwarded to deepcopy.

 None

Returns:

Type Description

A new Qarray with independent copies of all data.
Source code in jaxquantum/core/qarray.py 
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def copy(self, memo=None):
    """Return a deep copy of this ``Qarray``.

    Args:
        memo: Optional memo dict forwarded to ``deepcopy``.

    Returns:
        A new ``Qarray`` with independent copies of all data.
    """
    return self.__deepcopy__(memo)

cosm()

Matrix cosine.

Source code in jaxquantum/core/qarray.py 
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def cosm(self):
    """Matrix cosine."""
    return cosm(self)

create(data, dims=None, bdims=None, implementation=QarrayImplType.DENSE) classmethod 

create(data, dims=None, bdims=None, implementation: Literal[QarrayImplType.DENSE] = QarrayImplType.DENSE) -> 'Qarray[DenseImpl]'

create(data, dims=None, bdims=None, implementation: Literal[QarrayImplType.SPARSE_BCOO] = ...) -> 'Qarray[SparseBCOOImpl]'

create(data, dims=None, bdims=None, implementation=...) -> 'Qarray[DenseImpl]'

Create a Qarray from raw data.

Handles shape normalisation, dimension inference, and tidying of small values.

Parameters:

Name Type Description Default
data

Input data array (dense array-like or sparse.BCOO).

 required
dims

Quantum dimensions as ((row_dims...), (col_dims...)). Inferred from data shape when None.

 None
bdims

Tuple of batch dimension sizes. Inferred from the leading dimensions of data when None.

 None
implementation

Storage backend — QarrayImplType.DENSE (default) or QarrayImplType.SPARSE_BCOO, or the equivalent string "dense" / "sparse_bcoo".

 DENSE

Returns:

Type Description

A new Qarray backed by the requested implementation.
Source code in jaxquantum/core/qarray.py 
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@classmethod
def create(cls, data, dims=None, bdims=None, implementation=QarrayImplType.DENSE):
    """Create a ``Qarray`` from raw data.

    Handles shape normalisation, dimension inference, and tidying of small
    values.

    Args:
        data: Input data array (dense array-like or ``sparse.BCOO``).
        dims: Quantum dimensions as ``((row_dims...), (col_dims...))``.
            Inferred from *data* shape when ``None``.
        bdims: Tuple of batch dimension sizes.  Inferred from the leading
            dimensions of *data* when ``None``.
        implementation: Storage backend — ``QarrayImplType.DENSE``
            (default) or ``QarrayImplType.SPARSE_BCOO``, or the equivalent
            string ``"dense"`` / ``"sparse_bcoo"``.

    Returns:
        A new ``Qarray`` backed by the requested implementation.
    """
    # Step 1: Prepare data ----
    data = robust_asarray(data)

    if len(data.shape) == 1 and data.shape[0] > 0:
        data = data.reshape(data.shape[0], 1)

    if len(data.shape) >= 2:
        if data.shape[-2] != data.shape[-1] and not (
            data.shape[-2] == 1 or data.shape[-1] == 1
        ):
            data = data.reshape(*data.shape[:-1], data.shape[-1], 1)

    if bdims is not None:
        if len(data.shape) - len(bdims) == 1:
            data = data.reshape(*data.shape[:-1], data.shape[-1], 1)
    # ----

    # Step 2: Prepare dimensions ----
    if bdims is None:
        bdims = tuple(data.shape[:-2])

    if dims is None:
        dims = ((data.shape[-2],), (data.shape[-1],))

    if not isinstance(dims[0], (list, tuple)):
        # This handles the case where only the hilbert space dimensions are sent in.
        if data.shape[-1] == 1:
            dims = (tuple(dims), tuple([1 for _ in dims]))
        elif data.shape[-2] == 1:
            dims = (tuple([1 for _ in dims]), tuple(dims))
        else:
            dims = (tuple(dims), tuple(dims))
    else:
        dims = (tuple(dims[0]), tuple(dims[1]))

    check_dims(dims, bdims, data.shape)

    qdims = Qdims(dims)

    # NOTE: Constantly tidying up on Qarray creation might be a bit overkill.
    # It increases the compilation time, but only very slightly
    # increased the runtime of the jit compiled function.
    # We could instead use this tidy up where we think we need it.

    impl_class = QarrayImplType(implementation).get_impl_class()
    impl = impl_class.from_data(data)
    impl = impl.tidy_up(SETTINGS["auto_tidyup_atol"])

    return cls(impl, qdims, bdims)

dag()

Conjugate transpose of this array.

Source code in jaxquantum/core/qarray.py 
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def dag(self):
    """Conjugate transpose of this array."""
    return dag(self)

eigenenergies()

Eigenvalues of this operator.

Source code in jaxquantum/core/qarray.py 
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def eigenenergies(self):
    """Eigenvalues of this operator."""
    return eigenenergies(self)

eigenstates()

Eigenvalues and eigenstates of this operator.

Source code in jaxquantum/core/qarray.py 
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def eigenstates(self):
    """Eigenvalues and eigenstates of this operator."""
    return eigenstates(self)

eigenvalues()

Eigenvalues of this operator (alias for :meth:eigenenergies).

Source code in jaxquantum/core/qarray.py 
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def eigenvalues(self):
    """Eigenvalues of this operator (alias for :meth:`eigenenergies`)."""
    return eigenenergies(self)

expm()

Matrix exponential.

Source code in jaxquantum/core/qarray.py 
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def expm(self):
    """Matrix exponential."""
    return expm(self)

frobenius_norm()

Compute the Frobenius norm directly from the implementation.

Returns:

Type Description

The Frobenius norm as a scalar.
Source code in jaxquantum/core/qarray.py 
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def frobenius_norm(self):
    """Compute the Frobenius norm directly from the implementation.

    Returns:
        The Frobenius norm as a scalar.
    """
    return self._impl.frobenius_norm()

from_array(qarr_arr) classmethod 

from_array(qarr_arr: 'Qarray[DenseImpl]') -> 'Qarray[DenseImpl]'

from_array(qarr_arr: 'Qarray[SparseBCOOImpl]') -> 'Qarray[SparseBCOOImpl]'

Create a Qarray from a (possibly nested) list of Qarray objects.

Parameters:

Name Type Description Default
qarr_arr

A Qarray (returned as-is) or a nested list of Qarray objects.

 required

Returns:

Type Description
Qarray

A Qarray with batch dimensions matching the nesting structure
Qarray

of qarr_arr.
Source code in jaxquantum/core/qarray.py 
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@classmethod
def from_array(cls, qarr_arr) -> Qarray:
    """Create a ``Qarray`` from a (possibly nested) list of ``Qarray`` objects.

    Args:
        qarr_arr: A ``Qarray`` (returned as-is) or a nested list of
            ``Qarray`` objects.

    Returns:
        A ``Qarray`` with batch dimensions matching the nesting structure
        of *qarr_arr*.
    """
    if isinstance(qarr_arr, Qarray):
        return qarr_arr

    bdims = ()
    lvl = qarr_arr
    while not isinstance(lvl, Qarray):
        bdims = bdims + (len(lvl),)
        if len(lvl) > 0:
            lvl = lvl[0]
        else:
            break

    def flat(lis):
        flatList = []
        for element in lis:
            if type(element) is list:
                flatList += flat(element)
            else:
                flatList.append(element)
        return flatList

    qarr_list = flat(qarr_arr)
    qarr = cls.from_list(qarr_list)
    qarr = qarr.reshape_bdims(*bdims)
    return qarr

from_list(qarr_list) classmethod 

from_list(qarr_list: List['Qarray[DenseImpl]']) -> 'Qarray[DenseImpl]'

from_list(qarr_list: List['Qarray[SparseBCOOImpl]']) -> 'Qarray[SparseBCOOImpl]'

Create a batched Qarray from a list of same-shaped Qarray objects.

The output implementation is determined by the element with the highest PROMOTION_ORDER: if all inputs are sparse the result is sparse; if any input is dense (or types are mixed) all inputs are promoted to dense and the result is dense.

Parameters:

Name Type Description Default
qarr_list List[Qarray]

List of Qarray objects with identical dims and bdims. May be empty.

 required

Returns:

Type Description
Qarray

A Qarray with an extra leading batch dimension of size
Qarray

len(qarr_list).

Raises:

Type Description
ValueError

If the elements have mismatched dims or bdims.
Source code in jaxquantum/core/qarray.py 
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@classmethod
def from_list(cls, qarr_list: List[Qarray]) -> Qarray:
    """Create a batched ``Qarray`` from a list of same-shaped ``Qarray`` objects.

    The output implementation is determined by the element with the highest
    ``PROMOTION_ORDER``: if all inputs are sparse the result is sparse; if
    any input is dense (or types are mixed) all inputs are promoted to dense
    and the result is dense.

    Args:
        qarr_list: List of ``Qarray`` objects with identical ``dims`` and
            ``bdims``.  May be empty.

    Returns:
        A ``Qarray`` with an extra leading batch dimension of size
        ``len(qarr_list)``.

    Raises:
        ValueError: If the elements have mismatched ``dims`` or ``bdims``.
    """
    if len(qarr_list) == 0:
        dims = ((), ())
        bdims = (0,)
        return cls.create(jnp.array([]), dims=dims, bdims=bdims)

    dims = qarr_list[0].dims
    bdims = qarr_list[0].bdims

    if not all(qarr.dims == dims and qarr.bdims == bdims for qarr in qarr_list):
        raise ValueError("All Qarrays in the list must have the same dimensions.")

    new_bdims = (len(qarr_list),) + bdims

    # Pick the target type: highest PROMOTION_ORDER wins (dense beats sparse).
    target_impl_type = max(
        (q.impl_type for q in qarr_list),
        key=lambda t: t.get_impl_class().PROMOTION_ORDER,
    )

    if target_impl_type == QarrayImplType.SPARSE_DIA:
        # All inputs are SparseDIA — batch without densifying.
        # Compute union of offsets across all operators, then remap each
        # operator's _diags rows into the union shape and stack.
        from jaxquantum.core.sparse_dia import SparseDiaData  # lazy to avoid circular
        union_offsets = tuple(sorted(
            set().union(*[set(q._impl._offsets) for q in qarr_list])
        ))
        union_idx = {k: i for i, k in enumerate(union_offsets)}
        n = qarr_list[0]._impl._diags.shape[-1]
        dtype = jnp.result_type(*[q._impl._diags.dtype for q in qarr_list])
        remapped = []
        for q in qarr_list:
            row = jnp.zeros((len(union_offsets), n), dtype=dtype)
            for i_src, k in enumerate(q._impl._offsets):
                row = row.at[union_idx[k], :].set(q._impl._diags[i_src, :])
            remapped.append(row)
        stacked = jnp.stack(remapped, axis=0)  # (n_ops, n_union_diags, N)
        raw = SparseDiaData(offsets=union_offsets, diags=stacked)
        return cls.create(raw, dims=dims, bdims=new_bdims, implementation=QarrayImplType.SPARSE_DIA)

    if target_impl_type == QarrayImplType.SPARSE_BCOO:
        # All inputs are sparse BCOO — stack via dense intermediates then re-sparsify.
        data = jnp.array([q.data.todense() for q in qarr_list])
        return cls.create(data, dims=dims, bdims=new_bdims, implementation=QarrayImplType.SPARSE_BCOO)

    # Target is dense: promote any sparse inputs before stacking.
    data = jnp.array([q.to_dense().data for q in qarr_list])
    return cls.create(data, dims=dims, bdims=new_bdims, implementation=QarrayImplType.DENSE)

from_sparse_bcoo(data, dims=None, bdims=None) classmethod 

from_sparse_bcoo(data, dims=None, bdims=None) -> 'Qarray[SparseBCOOImpl]'

Create a Qarray directly from a sparse BCOO array without densifying.

Parameters:

Name Type Description Default
data

A sparse.BCOO or array-like to store as sparse BCOO.

 required
dims

Quantum dimensions. Inferred when None.

 None
bdims

Batch dimensions. Inferred when None.

 None

Returns:

Type Description

A Qarray[SparseBCOOImpl].
Source code in jaxquantum/core/qarray.py 
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@classmethod
def from_sparse_bcoo(cls, data, dims=None, bdims=None):
    """Create a ``Qarray`` directly from a sparse BCOO array without densifying.

    Args:
        data: A ``sparse.BCOO`` or array-like to store as sparse BCOO.
        dims: Quantum dimensions.  Inferred when ``None``.
        bdims: Batch dimensions.  Inferred when ``None``.

    Returns:
        A ``Qarray[SparseBCOOImpl]``.
    """
    return cls.create(data, dims=dims, bdims=bdims, implementation=QarrayImplType.SPARSE_BCOO)

from_sparse_dia(data, dims=None, bdims=None) classmethod

Create a SparseDIA-backed Qarray.

Accepts either a dense array-like (diagonals are auto-detected) or a :class:~jaxquantum.core.sparse_dia.SparseDiaData container.

Parameters:

Name Type Description Default
data

Dense array of shape (*batch, n, n) or a SparseDiaData.

 required
dims

Quantum dimensions ((row_dims,), (col_dims,)).

 None
bdims

Batch dimension sizes.

 None

Returns:

Type Description
'Qarray'

A Qarray backed by SparseDiaImpl.
Source code in jaxquantum/core/qarray.py 
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@classmethod
def from_sparse_dia(cls, data, dims=None, bdims=None) -> "Qarray":
    """Create a SparseDIA-backed ``Qarray``.

    Accepts either a dense array-like (diagonals are auto-detected) or a
    :class:`~jaxquantum.core.sparse_dia.SparseDiaData` container.

    Args:
        data: Dense array of shape (*batch, n, n) or a ``SparseDiaData``.
        dims: Quantum dimensions ``((row_dims,), (col_dims,))``.
        bdims: Batch dimension sizes.

    Returns:
        A ``Qarray`` backed by ``SparseDiaImpl``.
    """
    return cls.create(data, dims=dims, bdims=bdims, implementation=QarrayImplType.SPARSE_DIA)

imag()

Element-wise imaginary part.

Returns:

Type Description

A new Qarray containing the imaginary parts of each element.
Source code in jaxquantum/core/qarray.py 
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def imag(self):
    """Element-wise imaginary part.

    Returns:
        A new ``Qarray`` containing the imaginary parts of each element.
    """
    new_impl = self._impl.imag()

    return Qarray.create(
        new_impl.data,
        dims=self.dims,
        implementation=new_impl.impl_type,
    )

is_dm()

Return True if this array is an operator (density-matrix type).

Source code in jaxquantum/core/qarray.py 
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def is_dm(self):
    """Return True if this array is an operator (density-matrix type)."""
    return self.qtype == Qtypes.oper

is_vec()

Return True if this array is a ket or bra.

Source code in jaxquantum/core/qarray.py 
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def is_vec(self):
    """Return True if this array is a ket or bra."""
    return self.qtype == Qtypes.ket or self.qtype == Qtypes.bra

keep_only_diag_elements()

Zero out all off-diagonal elements.

Source code in jaxquantum/core/qarray.py 
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def keep_only_diag_elements(self):
    """Zero out all off-diagonal elements."""
    return keep_only_diag_elements(self)

norm()

Compute the norm of this array.

Source code in jaxquantum/core/qarray.py 
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def norm(self):
    """Compute the norm of this array."""
    return norm(self)

powm(n)

Matrix power.

Parameters:

Name Type Description Default
n

Exponent (integer or float).

 required

Returns:

Type Description

This array raised to the n-th matrix power.
Source code in jaxquantum/core/qarray.py 
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def powm(self, n):
    """Matrix power.

    Args:
        n: Exponent (integer or float).

    Returns:
        This array raised to the *n*-th matrix power.
    """
    return powm(self, n)

ptrace(indx)

Partial trace over subsystem indx.

Parameters:

Name Type Description Default
indx

Index of the subsystem to trace out.

 required

Returns:

Type Description

Reduced density matrix.
Source code in jaxquantum/core/qarray.py 
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def ptrace(self, indx):
    """Partial trace over subsystem *indx*.

    Args:
        indx: Index of the subsystem to trace out.

    Returns:
        Reduced density matrix.
    """
    return ptrace(self, indx)

real()

Element-wise real part.

Returns:

Type Description

A new Qarray containing the real parts of each element.
Source code in jaxquantum/core/qarray.py 
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def real(self):
    """Element-wise real part.

    Returns:
        A new ``Qarray`` containing the real parts of each element.
    """
    new_impl = self._impl.real()
    return Qarray.create(
        new_impl.data,
        dims=self.dims,
        implementation=new_impl.impl_type,
    )

reshape_bdims(*args)

Reshape the batch dimensions of this Qarray.

Parameters:

Name Type Description Default
*args

New batch dimension sizes.

 ()

Returns:

Type Description

A new Qarray with the requested batch shape.
Source code in jaxquantum/core/qarray.py 
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def reshape_bdims(self, *args):
    """Reshape the batch dimensions of this ``Qarray``.

    Args:
        *args: New batch dimension sizes.

    Returns:
        A new ``Qarray`` with the requested batch shape.
    """
    new_bdims = tuple(args)

    if prod(new_bdims) == 0:
        new_shape = new_bdims
    else:
        new_shape = new_bdims + (prod(self.dims[0]),) + (-1,)

    # Preserve implementation type
    implementation = self.impl_type
    return Qarray.create(
        self.data.reshape(new_shape),
        dims=self.dims,
        bdims=new_bdims,
        implementation=implementation,
    )

reshape_qdims(*args)

Reshape the quantum dimensions of the Qarray.

Note that this does not take in qdims but rather the new Hilbert space dimensions.

Parameters:

Name Type Description Default
*args

New Hilbert dimensions for the Qarray.

 ()

Returns:

Name Type Description
Qarray

reshaped Qarray.
Source code in jaxquantum/core/qarray.py 
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def reshape_qdims(self, *args):
    """Reshape the quantum dimensions of the Qarray.

    Note that this does not take in qdims but rather the new Hilbert space
    dimensions.

    Args:
        *args: New Hilbert dimensions for the Qarray.

    Returns:
        Qarray: reshaped Qarray.
    """

    new_space_dims = tuple(args)
    current_space_dims = self.space_dims
    assert prod(new_space_dims) == prod(current_space_dims)

    new_qdims = self.space_to_qdims(new_space_dims)
    new_bdims = self.bdims

    # Preserve implementation type
    implementation = self.impl_type
    return Qarray.create(self.data, dims=new_qdims, bdims=new_bdims, implementation=implementation)

resize(new_shape)

Resize the Qarray to a new shape.

TODO: review and maybe deprecate this method.

Parameters:

Name Type Description Default
new_shape

Target shape tuple.

 required

Returns:

Type Description

A new Qarray with data resized via jnp.resize.
Source code in jaxquantum/core/qarray.py 
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def resize(self, new_shape):
    """Resize the Qarray to a new shape.

    TODO: review and maybe deprecate this method.

    Args:
        new_shape: Target shape tuple.

    Returns:
        A new ``Qarray`` with data resized via ``jnp.resize``.
    """
    dims = self.dims
    data = jnp.resize(self.data, new_shape)
    # Preserve implementation type
    implementation = self.impl_type
    return Qarray.create(
        data,
        dims=dims,
        implementation=implementation,
    )

sinm()

Matrix sine.

Source code in jaxquantum/core/qarray.py 
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def sinm(self):
    """Matrix sine."""
    return sinm(self)

space_to_qdims(space_dims)

Convert Hilbert space dimensions to full quantum dims tuple.

Parameters:

Name Type Description Default
space_dims List[int]

Sequence of per-subsystem Hilbert space sizes, or a full ((row_dims), (col_dims)) tuple (returned unchanged).

 required

Returns:

Type Description

A ((row_dims...), (col_dims...)) tuple.

Raises:

Type Description
ValueError

If self.qtype is not ket, bra, or oper.
Source code in jaxquantum/core/qarray.py 
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def space_to_qdims(self, space_dims: List[int]):
    """Convert Hilbert space dimensions to full quantum dims tuple.

    Args:
        space_dims: Sequence of per-subsystem Hilbert space sizes, or a
            full ``((row_dims), (col_dims))`` tuple (returned unchanged).

    Returns:
        A ``((row_dims...), (col_dims...))`` tuple.

    Raises:
        ValueError: If ``self.qtype`` is not ket, bra, or oper.
    """
    if isinstance(space_dims[0], (list, tuple)):
        return space_dims

    if self.qtype in [Qtypes.oper, Qtypes.ket]:
        return (tuple(space_dims), tuple([1 for _ in range(len(space_dims))]))
    elif self.qtype == Qtypes.bra:
        return (tuple([1 for _ in range(len(space_dims))]), tuple(space_dims))
    else:
        raise ValueError("Unsupported qtype for space_to_qdims conversion.")

to_dense()

Return a dense-backed copy of this array.

If the array is already dense, returns self unchanged.

Returns:

Type Description
'Qarray[DenseImpl]'

A Qarray[DenseImpl].
Source code in jaxquantum/core/qarray.py 
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def to_dense(self) -> "Qarray[DenseImpl]":
    """Return a dense-backed copy of this array.

    If the array is already dense, returns self unchanged.

    Returns:
        A ``Qarray[DenseImpl]``.
    """
    if self.is_dense:
        return self
    new_impl = self._impl.to_dense()
    return Qarray(new_impl, self._qdims, self._bdims)

to_dm()

Convert a ket to a density matrix via outer product.

Source code in jaxquantum/core/qarray.py 
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def to_dm(self):
    """Convert a ket to a density matrix via outer product."""
    return ket2dm(self)

to_ket()

Convert a bra to a ket (no-op for kets).

Source code in jaxquantum/core/qarray.py 
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def to_ket(self):
    """Convert a bra to a ket (no-op for kets)."""
    return to_ket(self)

to_sparse_bcoo()

Return a BCOO-sparse-backed copy of this array.

If the array is already sparse BCOO, returns self unchanged.

Returns:

Type Description
'Qarray[SparseBCOOImpl]'

A Qarray[SparseBCOOImpl].
Source code in jaxquantum/core/qarray.py 
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def to_sparse_bcoo(self) -> "Qarray[SparseBCOOImpl]":
    """Return a BCOO-sparse-backed copy of this array.

    If the array is already sparse BCOO, returns self unchanged.

    Returns:
        A ``Qarray[SparseBCOOImpl]``.
    """
    if self.is_sparse_bcoo:
        return self
    new_impl = self._impl.to_sparse_bcoo()
    return Qarray(new_impl, self._qdims, self._bdims)

to_sparse_dia()

Return a SparseDIA-backed copy of this array.

If the array is already SparseDIA, returns self unchanged.

Returns:

Type Description
'Qarray'

A Qarray[SparseDiaImpl].
Source code in jaxquantum/core/qarray.py 
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def to_sparse_dia(self) -> "Qarray":
    """Return a SparseDIA-backed copy of this array.

    If the array is already SparseDIA, returns self unchanged.

    Returns:
        A ``Qarray[SparseDiaImpl]``.
    """
    if self.is_sparse_dia:
        return self
    new_impl = self._impl.to_sparse_dia()
    return Qarray(new_impl, self._qdims, self._bdims)

tr(**kwargs)

Full trace.

Source code in jaxquantum/core/qarray.py 
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def tr(self, **kwargs):
    """Full trace."""
    return tr(self, **kwargs)

trace(**kwargs)

Full trace (alias for :meth:tr).

Source code in jaxquantum/core/qarray.py 
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def trace(self, **kwargs):
    """Full trace (alias for :meth:`tr`)."""
    return tr(self, **kwargs)

transpose(*args)

Transpose subsystem indices.

Source code in jaxquantum/core/qarray.py 
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def transpose(self, *args):
    """Transpose subsystem indices."""
    return transpose(self, *args)

unit()

Return the normalised (unit-norm) version of this array.

Source code in jaxquantum/core/qarray.py 
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def unit(self):
    """Return the normalised (unit-norm) version of this array."""
    return unit(self)

Resonator

Bases: FluxDevice

Resonator Device.

Source code in jaxquantum/devices/superconducting/resonator.py 
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@struct.dataclass
class Resonator(FluxDevice):
    """
    Resonator Device.
    """

    def common_ops(self):
        """Written in the linear basis."""
        ops = {}

        N = self.N_pre_diag
        ops["id"] = identity(N)
        ops["a"] = destroy(N)
        ops["a_dag"] = create(N)
        ops["phi"] = self.phi_zpf() * (ops["a"] + ops["a_dag"])
        ops["n"] = 1j * self.n_zpf() * (ops["a_dag"] - ops["a"])

        return ops

    def phi_zpf(self):
        """Return Phase ZPF."""
        return (2 * self.params["Ec"] / self.params["El"]) ** (0.25)

    def n_zpf(self):
        n_zpf = (self.params["El"] / (32.0 * self.params["Ec"])) ** (0.25)
        return n_zpf

    def get_linear_frequency(self):
        """Get frequency of linear terms."""
        return jnp.sqrt(8 * self.params["El"] * self.params["Ec"])

    def get_H_linear(self):
        """Return linear terms in H."""
        w = self.get_linear_frequency()
        return w * (self.linear_ops["a_dag"] @ self.linear_ops["a"] + 1 / 2)

    def get_H_full(self):
        """Return full H in linear basis."""
        return self.get_H_linear()

    def potential(self, phi):
        """Return potential energy for a given phi."""
        return 0.5 * self.params["El"] * (2 * jnp.pi * phi) ** 2

common_ops()

Written in the linear basis.

Source code in jaxquantum/devices/superconducting/resonator.py 
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def common_ops(self):
    """Written in the linear basis."""
    ops = {}

    N = self.N_pre_diag
    ops["id"] = identity(N)
    ops["a"] = destroy(N)
    ops["a_dag"] = create(N)
    ops["phi"] = self.phi_zpf() * (ops["a"] + ops["a_dag"])
    ops["n"] = 1j * self.n_zpf() * (ops["a_dag"] - ops["a"])

    return ops

get_H_full()

Return full H in linear basis.

Source code in jaxquantum/devices/superconducting/resonator.py 
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def get_H_full(self):
    """Return full H in linear basis."""
    return self.get_H_linear()

get_H_linear()

Return linear terms in H.

Source code in jaxquantum/devices/superconducting/resonator.py 
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def get_H_linear(self):
    """Return linear terms in H."""
    w = self.get_linear_frequency()
    return w * (self.linear_ops["a_dag"] @ self.linear_ops["a"] + 1 / 2)

get_linear_frequency()

Get frequency of linear terms.

Source code in jaxquantum/devices/superconducting/resonator.py 
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def get_linear_frequency(self):
    """Get frequency of linear terms."""
    return jnp.sqrt(8 * self.params["El"] * self.params["Ec"])

phi_zpf()

Return Phase ZPF.

Source code in jaxquantum/devices/superconducting/resonator.py 
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def phi_zpf(self):
    """Return Phase ZPF."""
    return (2 * self.params["Ec"] / self.params["El"]) ** (0.25)

potential(phi)

Return potential energy for a given phi.

Source code in jaxquantum/devices/superconducting/resonator.py 
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def potential(self, phi):
    """Return potential energy for a given phi."""
    return 0.5 * self.params["El"] * (2 * jnp.pi * phi) ** 2

SNAIL

Bases: FluxDevice

SNAIL Device.

Source code in jaxquantum/devices/superconducting/snail.py 
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@struct.dataclass
class SNAIL(FluxDevice):
    """
    SNAIL Device.
    """

    DEFAULT_BASIS = BasisTypes.charge
    DEFAULT_HAMILTONIAN = HamiltonianTypes.full

    @classmethod
    def param_validation(cls, N, N_pre_diag, params, hamiltonian, basis):
        """This can be overridden by subclasses."""

        assert params["m"] % 1 == 0, "m must be an integer."
        assert params["m"] >= 2, "m must be greater than or equal to 2."

        if hamiltonian == HamiltonianTypes.linear:
            assert basis == BasisTypes.fock, "Linear Hamiltonian only works with Fock basis."
        elif hamiltonian == HamiltonianTypes.truncated:
            assert basis == BasisTypes.fock, "Truncated Hamiltonian only works with Fock basis."
        elif hamiltonian == HamiltonianTypes.full:
            charge_basis_types = [
                BasisTypes.charge
            ]
            assert basis in charge_basis_types, "Full Hamiltonian only works with Cooper pair charge or single-electron charge bases."

            assert (N_pre_diag - 1) % 2 * (params["m"]) == 0, "(N_pre_diag - 1)/2 must be divisible by m."

        # Set the gate offset charge to zero if not provided
        if "ng" not in params:
            params["ng"] = 0.0

    def common_ops(self):
        """ Written in the specified basis. """

        ops = {}

        N = self.N_pre_diag

        if self.basis == BasisTypes.fock:
            ops["id"] = identity(N)
            ops["a"] = destroy(N)
            ops["a_dag"] = create(N)
            ops["phi"] = self.phi_zpf() * (ops["a"] + ops["a_dag"])
            ops["n"] = 1j * self.n_zpf() * (ops["a_dag"] - ops["a"])

        elif self.basis == BasisTypes.charge:
            """
            Here H = 4 * Ec (n - ng)² - Ej cos(φ) in the Cooper pair charge basis. 
            """
            m = self.params["m"]
            ops["id"] = identity(N)
            ops["cos(φ/m)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=1) + jnp.eye(N, k=-1)))
            ops["sin(φ/m)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=1) - jnp.eye(N, k=-1)))
            ops["cos(φ)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=m) + jnp.eye(N, k=-m)))
            ops["sin(φ)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=m) - jnp.eye(N, k=-m)))

            n_max = (N - 1) // 2
            n_array = jnp.arange(-n_max, n_max + 1) / self.params["m"]
            ops["n"] = jnp2jqt(jnp.diag(n_array))

            n_minus_ng_array = n_array - self.params["ng"] * jnp.ones(N)
            ops["H_charge"] = jnp2jqt(jnp.diag(4 * self.params["Ec"] * n_minus_ng_array**2))

        return ops

    @property
    def Ej(self):
        return self.params["Ej"]

    def phi_zpf(self):
        """Return Phase ZPF."""
        return (2 * self.params["Ec"] / self.Ej) ** (0.25)

    def n_zpf(self):
        """Return Charge ZPF."""
        return (self.Ej / (32 * self.params["Ec"])) ** (0.25)

    def get_linear_frequency(self):
        """Get frequency of linear terms."""
        return jnp.sqrt(8 * self.params["Ec"] * self.Ej)

    def get_H_linear(self):
        """Return linear terms in H."""
        w = self.get_linear_frequency()
        return w * self.original_ops["a_dag"] @ self.original_ops["a"]

    def get_H_full(self):
        """Return full H in specified basis."""

        α = self.params["alpha"]
        m = self.params["m"]
        phi_ext = self.params["phi_ext"]
        Ej = self.Ej

        H_charge = self.original_ops["H_charge"]
        H_inductive = - α * Ej * self.original_ops["cos(φ)"] - m * Ej * (
            jnp.cos(2 * jnp.pi * phi_ext/m) * self.original_ops["cos(φ/m)"] + jnp.sin(2 * jnp.pi * phi_ext/m) * self.original_ops["sin(φ/m)"]
        )
        return H_charge + H_inductive

    def get_H_truncated(self):
        """Return truncated H in specified basis."""
        raise NotImplementedError("Truncated Hamiltonian not implemented for SNAIL.")
        # phi_op = self.original_ops["phi"]  
        # fourth_order_term =  -(1 / 24) * self.Ej * phi_op @ phi_op @ phi_op @ phi_op 
        # sixth_order_term = (1 / 720) * self.Ej * phi_op @ phi_op @ phi_op @ phi_op @ phi_op @ phi_op
        # return self.get_H_linear() + fourth_order_term + sixth_order_term

    def _get_H_in_original_basis(self):
        """ This returns the Hamiltonian in the original specified basis. This can be overridden by subclasses."""

        if self.hamiltonian == HamiltonianTypes.linear:
            return self.get_H_linear()
        elif self.hamiltonian == HamiltonianTypes.full:
            return self.get_H_full()
        elif self.hamiltonian == HamiltonianTypes.truncated:
            return self.get_H_truncated()

    def potential(self, phi):
        """Return potential energy for a given phi."""
        if self.hamiltonian == HamiltonianTypes.linear:
            return 0.5 * self.Ej * (2 * jnp.pi * phi) ** 2
        elif self.hamiltonian == HamiltonianTypes.full:

            α = self.params["alpha"]
            m = self.params["m"]
            phi_ext = self.params["phi_ext"]

            return - α * self.Ej * jnp.cos(2 * jnp.pi * phi) - (
                m * self.Ej * jnp.cos(2 * jnp.pi * (phi_ext - phi) / m)
            )

        elif self.hamiltonian == HamiltonianTypes.truncated:
            raise NotImplementedError("Truncated potential not implemented for SNAIL.")

common_ops()

Written in the specified basis.

Source code in jaxquantum/devices/superconducting/snail.py 
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def common_ops(self):
    """ Written in the specified basis. """

    ops = {}

    N = self.N_pre_diag

    if self.basis == BasisTypes.fock:
        ops["id"] = identity(N)
        ops["a"] = destroy(N)
        ops["a_dag"] = create(N)
        ops["phi"] = self.phi_zpf() * (ops["a"] + ops["a_dag"])
        ops["n"] = 1j * self.n_zpf() * (ops["a_dag"] - ops["a"])

    elif self.basis == BasisTypes.charge:
        """
        Here H = 4 * Ec (n - ng)² - Ej cos(φ) in the Cooper pair charge basis. 
        """
        m = self.params["m"]
        ops["id"] = identity(N)
        ops["cos(φ/m)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=1) + jnp.eye(N, k=-1)))
        ops["sin(φ/m)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=1) - jnp.eye(N, k=-1)))
        ops["cos(φ)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=m) + jnp.eye(N, k=-m)))
        ops["sin(φ)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=m) - jnp.eye(N, k=-m)))

        n_max = (N - 1) // 2
        n_array = jnp.arange(-n_max, n_max + 1) / self.params["m"]
        ops["n"] = jnp2jqt(jnp.diag(n_array))

        n_minus_ng_array = n_array - self.params["ng"] * jnp.ones(N)
        ops["H_charge"] = jnp2jqt(jnp.diag(4 * self.params["Ec"] * n_minus_ng_array**2))

    return ops

get_H_full()

Return full H in specified basis.

Source code in jaxquantum/devices/superconducting/snail.py 
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def get_H_full(self):
    """Return full H in specified basis."""

    α = self.params["alpha"]
    m = self.params["m"]
    phi_ext = self.params["phi_ext"]
    Ej = self.Ej

    H_charge = self.original_ops["H_charge"]
    H_inductive = - α * Ej * self.original_ops["cos(φ)"] - m * Ej * (
        jnp.cos(2 * jnp.pi * phi_ext/m) * self.original_ops["cos(φ/m)"] + jnp.sin(2 * jnp.pi * phi_ext/m) * self.original_ops["sin(φ/m)"]
    )
    return H_charge + H_inductive

get_H_linear()

Return linear terms in H.

Source code in jaxquantum/devices/superconducting/snail.py 
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def get_H_linear(self):
    """Return linear terms in H."""
    w = self.get_linear_frequency()
    return w * self.original_ops["a_dag"] @ self.original_ops["a"]

get_H_truncated()

Return truncated H in specified basis.

Source code in jaxquantum/devices/superconducting/snail.py 
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def get_H_truncated(self):
    """Return truncated H in specified basis."""
    raise NotImplementedError("Truncated Hamiltonian not implemented for SNAIL.")

get_linear_frequency()

Get frequency of linear terms.

Source code in jaxquantum/devices/superconducting/snail.py 
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def get_linear_frequency(self):
    """Get frequency of linear terms."""
    return jnp.sqrt(8 * self.params["Ec"] * self.Ej)

n_zpf()

Return Charge ZPF.

Source code in jaxquantum/devices/superconducting/snail.py 
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def n_zpf(self):
    """Return Charge ZPF."""
    return (self.Ej / (32 * self.params["Ec"])) ** (0.25)

param_validation(N, N_pre_diag, params, hamiltonian, basis) classmethod

This can be overridden by subclasses.

Source code in jaxquantum/devices/superconducting/snail.py 
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@classmethod
def param_validation(cls, N, N_pre_diag, params, hamiltonian, basis):
    """This can be overridden by subclasses."""

    assert params["m"] % 1 == 0, "m must be an integer."
    assert params["m"] >= 2, "m must be greater than or equal to 2."

    if hamiltonian == HamiltonianTypes.linear:
        assert basis == BasisTypes.fock, "Linear Hamiltonian only works with Fock basis."
    elif hamiltonian == HamiltonianTypes.truncated:
        assert basis == BasisTypes.fock, "Truncated Hamiltonian only works with Fock basis."
    elif hamiltonian == HamiltonianTypes.full:
        charge_basis_types = [
            BasisTypes.charge
        ]
        assert basis in charge_basis_types, "Full Hamiltonian only works with Cooper pair charge or single-electron charge bases."

        assert (N_pre_diag - 1) % 2 * (params["m"]) == 0, "(N_pre_diag - 1)/2 must be divisible by m."

    # Set the gate offset charge to zero if not provided
    if "ng" not in params:
        params["ng"] = 0.0

phi_zpf()

Return Phase ZPF.

Source code in jaxquantum/devices/superconducting/snail.py 
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def phi_zpf(self):
    """Return Phase ZPF."""
    return (2 * self.params["Ec"] / self.Ej) ** (0.25)

potential(phi)

Return potential energy for a given phi.

Source code in jaxquantum/devices/superconducting/snail.py 
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def potential(self, phi):
    """Return potential energy for a given phi."""
    if self.hamiltonian == HamiltonianTypes.linear:
        return 0.5 * self.Ej * (2 * jnp.pi * phi) ** 2
    elif self.hamiltonian == HamiltonianTypes.full:

        α = self.params["alpha"]
        m = self.params["m"]
        phi_ext = self.params["phi_ext"]

        return - α * self.Ej * jnp.cos(2 * jnp.pi * phi) - (
            m * self.Ej * jnp.cos(2 * jnp.pi * (phi_ext - phi) / m)
        )

    elif self.hamiltonian == HamiltonianTypes.truncated:
        raise NotImplementedError("Truncated potential not implemented for SNAIL.")

Transmon

Bases: FluxDevice

Transmon Device.

Source code in jaxquantum/devices/superconducting/transmon.py 
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@struct.dataclass
class Transmon(FluxDevice):
    """
    Transmon Device.
    """

    DEFAULT_BASIS = BasisTypes.charge
    DEFAULT_HAMILTONIAN = HamiltonianTypes.full

    @classmethod
    def param_validation(cls, N, N_pre_diag, params, hamiltonian, basis):
        """This can be overridden by subclasses."""
        if hamiltonian == HamiltonianTypes.linear:
            assert basis == BasisTypes.fock, "Linear Hamiltonian only works with Fock basis."
        elif hamiltonian == HamiltonianTypes.truncated:
            assert basis == BasisTypes.fock, "Truncated Hamiltonian only works with Fock basis."
        elif hamiltonian == HamiltonianTypes.full:
            charge_basis_types = [
                BasisTypes.charge,
                BasisTypes.singlecharge,
                BasisTypes.singlecharge_even,
                BasisTypes.singlecharge_odd,
            ]
            assert basis in charge_basis_types, "Full Hamiltonian only works with Cooper pair charge or single-electron charge bases."

        # Set the gate offset charge to zero if not provided
        if "ng" not in params:
            params["ng"] = 0.0

        if basis in [BasisTypes.singlecharge, BasisTypes.singlecharge_even, BasisTypes.singlecharge_odd]:
            assert (N_pre_diag) % 2 == 0, "N_pre_diag must be even for single charge bases."
        else:
            assert (N_pre_diag - 1) % 2 == 0, "N_pre_diag must be odd."

    def common_ops(self):
        """ Written in the specified basis. """

        ops = {}

        N = self.N_pre_diag

        if self.basis == BasisTypes.fock:
            ops["id"] = identity(N)
            ops["a"] = destroy(N)
            ops["a_dag"] = create(N)
            ops["phi"] = self.phi_zpf() * (ops["a"] + ops["a_dag"])
            ops["n"] = 1j * self.n_zpf() * (ops["a_dag"] - ops["a"])

        elif self.basis == BasisTypes.charge:
            """
            Here H = 4 * Ec (n - ng)² - Ej cos(φ) in the Cooper pair charge basis. 
            """
            ops["id"] = identity(N)
            ops["cos(φ)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=1) + jnp.eye(N, k=-1)))
            ops["sin(φ)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=1) - jnp.eye(N, k=-1)))
            ops["cos(2φ)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=2) + jnp.eye(N, k=-2)))
            ops["sin(2φ)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=2) - jnp.eye(N, k=-2)))

            n_max = (N - 1) // 2
            n_array = jnp.arange(-n_max, n_max + 1)
            ops["n"] = jnp2jqt(jnp.diag(n_array))
            n_minus_ng_array = n_array - self.params["ng"] * jnp.ones(N)
            ops["H_charge"] = jnp2jqt(jnp.diag(4 * self.params["Ec"] * n_minus_ng_array**2))

        elif self.basis in [BasisTypes.singlecharge_even, BasisTypes.singlecharge_odd]:
            n_max = N

            if self.basis == BasisTypes.singlecharge_even:
                n_array = jnp.arange(-n_max, n_max, 2)
            elif self.basis == BasisTypes.singlecharge_odd:
                n_array = jnp.arange(-n_max + 1, n_max, 2)

            ops["id"] = identity(n_max)
            ops["cos(φ)"] = 0.5 * (jnp2jqt(jnp.eye(n_max, k=1) + jnp.eye(n_max, k=-1)))
            ops["sin(φ)"] = 0.5j * (jnp2jqt(jnp.eye(n_max, k=1) - jnp.eye(n_max, k=-1)))
            ops["cos(2φ)"] = 0.5 * (jnp2jqt(jnp.eye(n_max, k=2) + jnp.eye(n_max, k=-2)))
            ops["sin(2φ)"] = 0.5j * (jnp2jqt(jnp.eye(n_max, k=2) - jnp.eye(n_max, k=-2)))

            ops["n"] = jnp2jqt(jnp.diag(n_array))
            n_minus_ng_array = n_array - 2 * self.params["ng"] * jnp.ones(n_max)
            ops["H_charge"] = jnp2jqt(jnp.diag(self.params["Ec"] * n_minus_ng_array**2))

        elif self.basis == BasisTypes.singlecharge:
            """
            Here H = Ec (n - 2ng)² - Ej cos(φ) in the single-electron charge basis. Using Eq. (5.36) of Kyle Serniak's
            thesis, we have H = Ec ∑ₙ(n - 2*ng) |n⟩⟨n| - Ej/2 * ∑ₙ|n⟩⟨n+2| + h.c where n counts the number of electrons, 
            not Cooper pairs. Note, we use 2ng instead of ng to match the gate offset charge convention of the transmon 
            (as done in Kyle's thesis).
            """
            n_max = (N) // 2

            ops["id"] = identity(N)
            ops["cos(φ)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=2) + jnp.eye(N, k=-2)))
            ops["sin(φ)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=2) - jnp.eye(N, k=-2)))
            ops["cos(φ/2)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=1) + jnp.eye(N, k=-1)))
            ops["sin(φ/2)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=1) - jnp.eye(N, k=-1)))

            n_array = jnp.arange(-n_max, n_max)
            ops["n"] = jnp2jqt(jnp.diag(n_array))
            n_minus_ng_array = n_array - 2 * self.params["ng"] * jnp.ones(N)
            ops["H_charge"] = jnp2jqt(jnp.diag(self.params["Ec"] * n_minus_ng_array**2))

        return ops

    @property
    def Ej(self):
        return self.params["Ej"]

    def phi_zpf(self):
        """Return Phase ZPF."""
        return (2 * self.params["Ec"] / self.Ej) ** (0.25)

    def n_zpf(self):
        """Return Charge ZPF."""
        return (self.Ej / (32 * self.params["Ec"])) ** (0.25)

    def get_linear_frequency(self):
        """Get frequency of linear terms."""
        return jnp.sqrt(8 * self.params["Ec"] * self.Ej)

    def get_H_linear(self):
        """Return linear terms in H."""
        w = self.get_linear_frequency()
        return w * self.original_ops["a_dag"] @ self.original_ops["a"]

    def get_H_full(self):
        """Return full H in specified basis."""
        return self.original_ops["H_charge"] - self.Ej * self.original_ops["cos(φ)"]

    def get_H_truncated(self):
        """Return truncated H in specified basis."""
        phi_op = self.original_ops["phi"]  
        fourth_order_term =  -(1 / 24) * self.Ej * phi_op @ phi_op @ phi_op @ phi_op 
        sixth_order_term = (1 / 720) * self.Ej * phi_op @ phi_op @ phi_op @ phi_op @ phi_op @ phi_op
        return self.get_H_linear() + fourth_order_term + sixth_order_term

    def _get_H_in_original_basis(self):
        """ This returns the Hamiltonian in the original specified basis. This can be overridden by subclasses."""

        if self.hamiltonian == HamiltonianTypes.linear:
            return self.get_H_linear()
        elif self.hamiltonian == HamiltonianTypes.full:
            return self.get_H_full()
        elif self.hamiltonian == HamiltonianTypes.truncated:
            return self.get_H_truncated()

    def potential(self, phi):
        """Return potential energy for a given phi."""
        if self.hamiltonian == HamiltonianTypes.linear:
            return 0.5 * self.Ej * (2 * jnp.pi * phi) ** 2
        elif self.hamiltonian == HamiltonianTypes.full:
            return - self.Ej * jnp.cos(2 * jnp.pi * phi)
        elif self.hamiltonian == HamiltonianTypes.truncated:
            phi_scaled = 2 * jnp.pi * phi
            second_order = 0.5 * self.Ej * phi_scaled ** 2
            fourth_order =  -(1 / 24) * self.Ej * phi_scaled ** 4
            sixth_order = (1 / 720) * self.Ej * phi_scaled ** 6
            return second_order + fourth_order + sixth_order

    def calculate_wavefunctions(self, phi_vals):
        """Calculate wavefunctions at phi_exts.

        TODO: this is not currently being used for plotting... needs to be updated!
        """

        if self.basis == BasisTypes.fock:
            return super().calculate_wavefunctions(phi_vals)
        elif self.basis == BasisTypes.singlecharge:
            raise NotImplementedError("Wavefunctions for single charge basis not yet implemented.")
        elif self.basis in [BasisTypes.charge, BasisTypes.singlecharge_even, BasisTypes.singlecharge_odd]:
            phi_vals = jnp.array(phi_vals)

            if self.basis in [BasisTypes.singlecharge_even, BasisTypes.singlecharge_odd]:
                n_labels = 1/2 * jnp.diag(self.original_ops["n"].data)
            else:
                n_labels = jnp.diag(self.original_ops["n"].data)

            wavefunctions = []
            for nj in range(self.N_pre_diag):
                wavefunction = []
                for phi in phi_vals:
                    wavefunction.append(
                        (1j ** nj / jnp.sqrt(2*jnp.pi)) * jnp.sum(
                            self.eig_systems["vecs"][:,nj] * jnp.exp(1j * phi * n_labels)
                        )
                    )
                wavefunctions.append(jnp.array(wavefunction))
            return jnp.array(wavefunctions)

calculate_wavefunctions(phi_vals)

Calculate wavefunctions at phi_exts.

TODO: this is not currently being used for plotting... needs to be updated!

Source code in jaxquantum/devices/superconducting/transmon.py 
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def calculate_wavefunctions(self, phi_vals):
    """Calculate wavefunctions at phi_exts.

    TODO: this is not currently being used for plotting... needs to be updated!
    """

    if self.basis == BasisTypes.fock:
        return super().calculate_wavefunctions(phi_vals)
    elif self.basis == BasisTypes.singlecharge:
        raise NotImplementedError("Wavefunctions for single charge basis not yet implemented.")
    elif self.basis in [BasisTypes.charge, BasisTypes.singlecharge_even, BasisTypes.singlecharge_odd]:
        phi_vals = jnp.array(phi_vals)

        if self.basis in [BasisTypes.singlecharge_even, BasisTypes.singlecharge_odd]:
            n_labels = 1/2 * jnp.diag(self.original_ops["n"].data)
        else:
            n_labels = jnp.diag(self.original_ops["n"].data)

        wavefunctions = []
        for nj in range(self.N_pre_diag):
            wavefunction = []
            for phi in phi_vals:
                wavefunction.append(
                    (1j ** nj / jnp.sqrt(2*jnp.pi)) * jnp.sum(
                        self.eig_systems["vecs"][:,nj] * jnp.exp(1j * phi * n_labels)
                    )
                )
            wavefunctions.append(jnp.array(wavefunction))
        return jnp.array(wavefunctions)

common_ops()

Written in the specified basis.

Source code in jaxquantum/devices/superconducting/transmon.py 
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def common_ops(self):
    """ Written in the specified basis. """

    ops = {}

    N = self.N_pre_diag

    if self.basis == BasisTypes.fock:
        ops["id"] = identity(N)
        ops["a"] = destroy(N)
        ops["a_dag"] = create(N)
        ops["phi"] = self.phi_zpf() * (ops["a"] + ops["a_dag"])
        ops["n"] = 1j * self.n_zpf() * (ops["a_dag"] - ops["a"])

    elif self.basis == BasisTypes.charge:
        """
        Here H = 4 * Ec (n - ng)² - Ej cos(φ) in the Cooper pair charge basis. 
        """
        ops["id"] = identity(N)
        ops["cos(φ)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=1) + jnp.eye(N, k=-1)))
        ops["sin(φ)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=1) - jnp.eye(N, k=-1)))
        ops["cos(2φ)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=2) + jnp.eye(N, k=-2)))
        ops["sin(2φ)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=2) - jnp.eye(N, k=-2)))

        n_max = (N - 1) // 2
        n_array = jnp.arange(-n_max, n_max + 1)
        ops["n"] = jnp2jqt(jnp.diag(n_array))
        n_minus_ng_array = n_array - self.params["ng"] * jnp.ones(N)
        ops["H_charge"] = jnp2jqt(jnp.diag(4 * self.params["Ec"] * n_minus_ng_array**2))

    elif self.basis in [BasisTypes.singlecharge_even, BasisTypes.singlecharge_odd]:
        n_max = N

        if self.basis == BasisTypes.singlecharge_even:
            n_array = jnp.arange(-n_max, n_max, 2)
        elif self.basis == BasisTypes.singlecharge_odd:
            n_array = jnp.arange(-n_max + 1, n_max, 2)

        ops["id"] = identity(n_max)
        ops["cos(φ)"] = 0.5 * (jnp2jqt(jnp.eye(n_max, k=1) + jnp.eye(n_max, k=-1)))
        ops["sin(φ)"] = 0.5j * (jnp2jqt(jnp.eye(n_max, k=1) - jnp.eye(n_max, k=-1)))
        ops["cos(2φ)"] = 0.5 * (jnp2jqt(jnp.eye(n_max, k=2) + jnp.eye(n_max, k=-2)))
        ops["sin(2φ)"] = 0.5j * (jnp2jqt(jnp.eye(n_max, k=2) - jnp.eye(n_max, k=-2)))

        ops["n"] = jnp2jqt(jnp.diag(n_array))
        n_minus_ng_array = n_array - 2 * self.params["ng"] * jnp.ones(n_max)
        ops["H_charge"] = jnp2jqt(jnp.diag(self.params["Ec"] * n_minus_ng_array**2))

    elif self.basis == BasisTypes.singlecharge:
        """
        Here H = Ec (n - 2ng)² - Ej cos(φ) in the single-electron charge basis. Using Eq. (5.36) of Kyle Serniak's
        thesis, we have H = Ec ∑ₙ(n - 2*ng) |n⟩⟨n| - Ej/2 * ∑ₙ|n⟩⟨n+2| + h.c where n counts the number of electrons, 
        not Cooper pairs. Note, we use 2ng instead of ng to match the gate offset charge convention of the transmon 
        (as done in Kyle's thesis).
        """
        n_max = (N) // 2

        ops["id"] = identity(N)
        ops["cos(φ)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=2) + jnp.eye(N, k=-2)))
        ops["sin(φ)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=2) - jnp.eye(N, k=-2)))
        ops["cos(φ/2)"] = 0.5 * (jnp2jqt(jnp.eye(N, k=1) + jnp.eye(N, k=-1)))
        ops["sin(φ/2)"] = 0.5j * (jnp2jqt(jnp.eye(N, k=1) - jnp.eye(N, k=-1)))

        n_array = jnp.arange(-n_max, n_max)
        ops["n"] = jnp2jqt(jnp.diag(n_array))
        n_minus_ng_array = n_array - 2 * self.params["ng"] * jnp.ones(N)
        ops["H_charge"] = jnp2jqt(jnp.diag(self.params["Ec"] * n_minus_ng_array**2))

    return ops

get_H_full()

Return full H in specified basis.

Source code in jaxquantum/devices/superconducting/transmon.py 
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def get_H_full(self):
    """Return full H in specified basis."""
    return self.original_ops["H_charge"] - self.Ej * self.original_ops["cos(φ)"]

get_H_linear()

Return linear terms in H.

Source code in jaxquantum/devices/superconducting/transmon.py 
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def get_H_linear(self):
    """Return linear terms in H."""
    w = self.get_linear_frequency()
    return w * self.original_ops["a_dag"] @ self.original_ops["a"]

get_H_truncated()

Return truncated H in specified basis.

Source code in jaxquantum/devices/superconducting/transmon.py 
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def get_H_truncated(self):
    """Return truncated H in specified basis."""
    phi_op = self.original_ops["phi"]  
    fourth_order_term =  -(1 / 24) * self.Ej * phi_op @ phi_op @ phi_op @ phi_op 
    sixth_order_term = (1 / 720) * self.Ej * phi_op @ phi_op @ phi_op @ phi_op @ phi_op @ phi_op
    return self.get_H_linear() + fourth_order_term + sixth_order_term

get_linear_frequency()

Get frequency of linear terms.

Source code in jaxquantum/devices/superconducting/transmon.py 
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def get_linear_frequency(self):
    """Get frequency of linear terms."""
    return jnp.sqrt(8 * self.params["Ec"] * self.Ej)

n_zpf()

Return Charge ZPF.

Source code in jaxquantum/devices/superconducting/transmon.py 
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def n_zpf(self):
    """Return Charge ZPF."""
    return (self.Ej / (32 * self.params["Ec"])) ** (0.25)

param_validation(N, N_pre_diag, params, hamiltonian, basis) classmethod

This can be overridden by subclasses.

Source code in jaxquantum/devices/superconducting/transmon.py 
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@classmethod
def param_validation(cls, N, N_pre_diag, params, hamiltonian, basis):
    """This can be overridden by subclasses."""
    if hamiltonian == HamiltonianTypes.linear:
        assert basis == BasisTypes.fock, "Linear Hamiltonian only works with Fock basis."
    elif hamiltonian == HamiltonianTypes.truncated:
        assert basis == BasisTypes.fock, "Truncated Hamiltonian only works with Fock basis."
    elif hamiltonian == HamiltonianTypes.full:
        charge_basis_types = [
            BasisTypes.charge,
            BasisTypes.singlecharge,
            BasisTypes.singlecharge_even,
            BasisTypes.singlecharge_odd,
        ]
        assert basis in charge_basis_types, "Full Hamiltonian only works with Cooper pair charge or single-electron charge bases."

    # Set the gate offset charge to zero if not provided
    if "ng" not in params:
        params["ng"] = 0.0

    if basis in [BasisTypes.singlecharge, BasisTypes.singlecharge_even, BasisTypes.singlecharge_odd]:
        assert (N_pre_diag) % 2 == 0, "N_pre_diag must be even for single charge bases."
    else:
        assert (N_pre_diag - 1) % 2 == 0, "N_pre_diag must be odd."

phi_zpf()

Return Phase ZPF.

Source code in jaxquantum/devices/superconducting/transmon.py 
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def phi_zpf(self):
    """Return Phase ZPF."""
    return (2 * self.params["Ec"] / self.Ej) ** (0.25)

potential(phi)

Return potential energy for a given phi.

Source code in jaxquantum/devices/superconducting/transmon.py 
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def potential(self, phi):
    """Return potential energy for a given phi."""
    if self.hamiltonian == HamiltonianTypes.linear:
        return 0.5 * self.Ej * (2 * jnp.pi * phi) ** 2
    elif self.hamiltonian == HamiltonianTypes.full:
        return - self.Ej * jnp.cos(2 * jnp.pi * phi)
    elif self.hamiltonian == HamiltonianTypes.truncated:
        phi_scaled = 2 * jnp.pi * phi
        second_order = 0.5 * self.Ej * phi_scaled ** 2
        fourth_order =  -(1 / 24) * self.Ej * phi_scaled ** 4
        sixth_order = (1 / 720) * self.Ej * phi_scaled ** 6
        return second_order + fourth_order + sixth_order

TunableTransmon

Bases: Transmon

Tunable Transmon Device.

Source code in jaxquantum/devices/superconducting/tunable_transmon.py 
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@struct.dataclass
class TunableTransmon(Transmon):
    """
    Tunable Transmon Device.
    """

    @property
    def Ej(self):
        Ejsum = self.params["Ej1"] + self.params["Ej2"]
        phi_ext = 2 * jnp.pi * self.params["phi_ext"]
        gamma = self.params["Ej2"] / self.params["Ej1"]
        d = (gamma - 1) / (gamma + 1)
        external_flux_factor = jnp.abs(
            jnp.sqrt(jnp.cos(phi_ext / 2) ** 2 + d**2 * jnp.sin(phi_ext / 2) ** 2)
        )
        return Ejsum * external_flux_factor

cosm(qarr)

Matrix cosine of a Qarray.

Parameters:

Name Type Description Default
qarr Qarray

Input quantum array (converted to dense internally).

 required

Returns:

Type Description
Qarray

A dense Qarray containing the matrix cosine.
Source code in jaxquantum/core/qarray.py 
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def cosm(qarr: Qarray) -> Qarray:
    """Matrix cosine of a ``Qarray``.

    Args:
        qarr: Input quantum array (converted to dense internally).

    Returns:
        A dense ``Qarray`` containing the matrix cosine.
    """
    dims = qarr.dims
    # Convert to dense for cosm
    dense_data = qarr.to_dense().data
    data = cosm_data(dense_data)
    return Qarray.create(data, dims=dims)

create(N, implementation=QarrayImplType.DENSE)

creation operator

Parameters:

Name Type Description Default
N

Hilbert space size

 required
implementation QarrayImplType

Qarray implementation type, e.g. "sparse" or "dense".

 DENSE

Returns:

Type Description
Qarray

creation operator in Hilber Space of size N
Source code in jaxquantum/core/operators.py 
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def create(N, implementation: QarrayImplType = QarrayImplType.DENSE) -> Qarray:
    """creation operator

    Args:
        N: Hilbert space size
        implementation: Qarray implementation type, e.g. "sparse" or "dense".

    Returns:
        creation operator in Hilber Space of size N
    """
    if QarrayImplType(implementation) == QarrayImplType.SPARSE_DIA:
        # Single subdiagonal at offset -1; Convention A: 1 trailing zero.
        diags = jnp.zeros((1, N), dtype=jnp.float64)
        diags = diags.at[0, :N - 1].set(jnp.sqrt(jnp.arange(1, N, dtype=jnp.float64)))
        return _make_sparsedia(offsets=(-1,), diags=diags)
    return Qarray.create(jnp.diag(jnp.sqrt(jnp.arange(1, N)), k=-1), implementation=implementation)

destroy(N, implementation=QarrayImplType.DENSE)

annihilation operator

Parameters:

Name Type Description Default
N

Hilbert space size

 required
implementation QarrayImplType

Qarray implementation type, e.g. "sparse" or "dense".

 DENSE

Returns:

Type Description
Qarray

annilation operator in Hilber Space of size N
Source code in jaxquantum/core/operators.py 
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def destroy(N, implementation: QarrayImplType = QarrayImplType.DENSE) -> Qarray:
    """annihilation operator

    Args:
        N: Hilbert space size
        implementation: Qarray implementation type, e.g. "sparse" or "dense".

    Returns:
        annilation operator in Hilber Space of size N
    """
    if QarrayImplType(implementation) == QarrayImplType.SPARSE_DIA:
        # Single superdiagonal at offset +1; Convention A: 1 leading zero.
        diags = jnp.zeros((1, N), dtype=jnp.float64)
        diags = diags.at[0, 1:].set(jnp.sqrt(jnp.arange(1, N, dtype=jnp.float64)))
        return _make_sparsedia(offsets=(1,), diags=diags)
    return Qarray.create(jnp.diag(jnp.sqrt(jnp.arange(1, N)), k=1), implementation=implementation)

harm_osc_wavefunction(n, x, l_osc)

Taken from scqubits... not jit-able

For given quantum number n=0,1,2,... return the value of the harmonic oscillator wave function :math:\psi_n(x) = N H_n(x/l_{osc}) \exp(-x^2/2l_\text{ osc}), N being the proper normalization factor.

Directly uses scipy.special.pbdv (implementation of the parabolic cylinder function) to mitigate numerical stability issues with the more commonly used expression in terms of a Gaussian and a Hermite polynomial factor.

Parameters

n: index of wave function, n=0 is ground state x: coordinate(s) where wave function is evaluated l_osc: oscillator length, defined via <0|x^2|0> = l_osc^2/2

Returns

value of harmonic oscillator wave function
Source code in jaxquantum/devices/common/utils.py 
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def harm_osc_wavefunction(n, x, l_osc):
    r"""
    Taken from scqubits... not jit-able

    For given quantum number n=0,1,2,... return the value of the harmonic
    oscillator wave function :math:`\psi_n(x) = N H_n(x/l_{osc}) \exp(-x^2/2l_\text{
    osc})`, N being the proper normalization factor.

    Directly uses `scipy.special.pbdv` (implementation of the parabolic cylinder
    function) to mitigate numerical stability issues with the more commonly used
    expression in terms of a Gaussian and a Hermite polynomial factor.

    Parameters
    ----------
    n:
        index of wave function, n=0 is ground state
    x:
        coordinate(s) where wave function is evaluated
    l_osc:
        oscillator length, defined via <0|x^2|0> = l_osc^2/2

    Returns
    -------
        value of harmonic oscillator wave function
    """
    x = 2 * jnp.pi * x
    result = pbdv(n, jnp.sqrt(2.0) * x / l_osc)[0]
    result = result / jnp.sqrt(l_osc * jnp.sqrt(jnp.pi) * factorial_approx(n))
    return result

identity(*args, implementation=QarrayImplType.DENSE, **kwargs)

Identity matrix.

Parameters:

Name Type Description Default
implementation QarrayImplType

Qarray implementation type, e.g. "sparse" or "dense".

 DENSE

Returns:

Type Description
Qarray

Identity matrix.
Source code in jaxquantum/core/operators.py 
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def identity(*args, implementation: QarrayImplType = QarrayImplType.DENSE, **kwargs) -> Qarray:
    """Identity matrix.

    Args:
        implementation: Qarray implementation type, e.g. "sparse" or "dense".

    Returns:
        Identity matrix.
    """
    if QarrayImplType(implementation) == QarrayImplType.SPARSE_DIA:
        # jnp.eye(*args) is typically eye(N) or eye(N, N); extract N from args.
        n = args[0] if args else kwargs.get("N", kwargs.get("n", None))
        if n is not None and (len(args) <= 1) and not kwargs:
            diags = jnp.ones((1, int(n)), dtype=jnp.float64)
            return _make_sparsedia(offsets=(0,), diags=diags)
    return Qarray.create(jnp.eye(*args, **kwargs), implementation=implementation)

jnp2jqt(arr, dims=None)

JAX array -> QuTiP state.

Parameters:

Name Type Description Default
jnp_obj

JAX array.

 required
dims Optional[Union[DIMS_TYPE, List[int]]]

Qarray dims.

 None

Returns:

Type Description

QuTiP state.
Source code in jaxquantum/core/conversions.py 
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def jnp2jqt(arr: Array, dims: Optional[Union[DIMS_TYPE, List[int]]] = None):
    """JAX array -> QuTiP state.

    Args:
        jnp_obj: JAX array.
        dims: Qarray dims.

    Returns:
        QuTiP state.
    """
    dims = extract_dims(arr, dims) if dims is not None else None
    return Qarray.create(arr, dims=dims)

run_sweep(params, sweep_params, metrics_func, fixed_kwargs=None, data=None, is_parallel=False, save_file=None, data_save_mode='end', return_errors=False)

Run a sweep over a single parameter, or multiple parameters.

Parameters:

Name Type Description Default
params dict

The base parameters to sweep over.

 required
sweep_params dict

The parameters to sweep over. key: The parameter name. value: The list of values to sweep over.

 required
metrics_func function

The function to evaluate the metrics.

 required
fixed_params dict

The fixed parameters to send into metrics_func. Defaults to None.

 required
data dict

The data to append to. Defaults to None.

 None
is_parallel bool

Whether to sweep through the sweep_params lists in parallel or through their cartesian product. Defaults to False.

 False
save_file str

The file to save the data to. Defaults to None, in which case data is saved to a temporary file, which will be deleted upon closing (e.g. during garbage collection).

 None
data_save_mode str

The mode to save the data. Defaults to None. Options are: "no" - don't save data "end" - save data at the end of the sweep "during" - save data during and at the end of the sweep

 'end'

Returns: dict: The data after the sweep.

Source code in jaxquantum/devices/analysis/sweeps.py 
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def run_sweep(
    params,
    sweep_params,
    metrics_func,
    fixed_kwargs=None,
    data=None,
    is_parallel=False,
    save_file=None,
    data_save_mode="end",
    return_errors=False,
):
    """Run a sweep over a single parameter, or multiple parameters.

    Args:
        params (dict): The base parameters to sweep over.
        sweep_params (dict): The parameters to sweep over.
            key: The parameter name.
            value: The list of values to sweep over.
        metrics_func (function): The function to evaluate the metrics.
        fixed_params (dict, optional): The fixed parameters to send into metrics_func. Defaults to None.
        data (dict, optional): The data to append to. Defaults to None.
        is_parallel (bool, optional): Whether to sweep through the sweep_params lists in parallel or through their cartesian product. Defaults to False.
        save_file (str, optional): The file to save the data to. Defaults to None, in which case data is saved to a temporary file, which will be deleted upon closing (e.g. during garbage collection).
        data_save_mode (str, optional): The mode to save the data. Defaults to None.
            Options are:
                "no" - don't save data
                "end" - save data at the end of the sweep
                "during" - save data during and at the end of the sweep
    Returns:
        dict: The data after the sweep.
    """
    if data is None:
        data = {}
        run = -1
    else:
        run = max(data.keys())

    assert data_save_mode in ["no", "end", "during"], "Invalid data_save_mode."

    if data_save_mode in ["during", "end"]:
        if isinstance(save_file, str):
            print("Saving data to: ", save_file)
            dirname = os.path.dirname(save_file)
            if not os.path.exists(dirname):
                os.makedirs(dirname)
        else:
            save_file = save_file or NamedTemporaryFile()
            print("Saving data to a temporary file: ", save_file.name)

    fixed_kwargs = fixed_kwargs or {}

    if is_parallel:
        sweep_length = len(list(sweep_params.values())[0])
        assert [len(vals) == sweep_length for vals in sweep_params.values()], (
            "Parallel sweep parameters must have the same length."
        )

        errors = []
        try:
            for j in tqdm(range(sweep_length)):
                run += 1
                data[run] = {}
                data[run]["params"] = deepcopy(params)
                sweep_point_info = {
                    "labels": [],
                    "values": [],
                    "indices": [],
                }
                for key, vals in sweep_params.items():
                    data[run]["params"][key] = vals[j]
                    sweep_point_info["labels"].append(key)
                    sweep_point_info["values"].append(vals[j])
                    sweep_point_info["indices"].append(j)
                data[run]["results"] = metrics_func(data[run]["params"], **fixed_kwargs)
                data[run]["sweep_point_info"] = sweep_point_info
                if data_save_mode == "during":
                    jnp.savez(
                        save_file, data=data, sweep_params=sweep_params, params=params
                    )
        except Exception as e:
            errors.append(str(e))
            print("Error during run: ", errors[-1])

        try:
            if data_save_mode in ["during", "end"]:
                jnp.savez(
                    save_file,
                    data=data,
                    sweep_params=sweep_params,
                    params=params,
                    error=None,
                )
        except Exception as e:
            errors.append(str(e))
            print("Error during saving: ", errors[-1])

        if return_errors:
            return data, errors
        else:
            return data
    else:
        # Product Sweep
        sweep_points = list(itertools.product(*list(sweep_params.values())))
        sweep_points_indxs = list(
            itertools.product(
                *[list(range(len(vals))) for vals in list(sweep_params.values())]
            )
        )
        sweep_point_labels = list(sweep_params.keys())

        errors = []

        try:
            with tqdm(total=len(sweep_points)) as pbar:
                for j, sweep_point in enumerate(sweep_points):
                    run += 1
                    data[run] = {}
                    data[run]["params"] = deepcopy(params)
                    sweep_point_info = {
                        "labels": [],
                        "values": [],
                        "indices": [],
                    }
                    for i, key in enumerate(sweep_point_labels):
                        data[run]["params"][key] = sweep_point[i]
                        sweep_point_info["labels"].append(key)
                        sweep_point_info["values"].append(sweep_point[i])
                        sweep_point_info["indices"].append(sweep_points_indxs[j][i])
                    data[run]["results"] = metrics_func(
                        data[run]["params"], **fixed_kwargs
                    )
                    data[run]["sweep_point_info"] = sweep_point_info
                    pbar.update(1)
                    if data_save_mode == "during":
                        jnp.savez(
                            save_file,
                            data=data,
                            sweep_params=sweep_params,
                            params=params,
                        )
        except Exception as e:
            errors.append(str(e))
            print("Error during run: ", errors[-1])

        try:
            if data_save_mode in ["during", "end"]:
                jnp.savez(
                    save_file, data=data, sweep_params=sweep_params, params=params
                )
        except Exception as e:
            errors.append(str(e))
            print("Error during saving: ", errors[-1])

        if return_errors:
            return data, errors
        else:
            return data

sigmam(implementation=QarrayImplType.DENSE)

σ-

Returns:

Type Description
Qarray

σ- Pauli Operator
Source code in jaxquantum/core/operators.py 
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def sigmam(implementation: QarrayImplType = QarrayImplType.DENSE) -> Qarray:
    """σ-

    Returns:
        σ- Pauli Operator
    """
    if QarrayImplType(implementation) == QarrayImplType.SPARSE_DIA:
        diags = jnp.array([[1.0, 0.0]])
        return _make_sparsedia(offsets=(-1,), diags=diags)
    return Qarray.create(jnp.array([[0.0, 0.0], [1.0, 0.0]]), implementation=implementation)

sigmap(implementation=QarrayImplType.DENSE)

σ+

Returns:

Type Description
Qarray

σ+ Pauli Operator
Source code in jaxquantum/core/operators.py 
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def sigmap(implementation: QarrayImplType = QarrayImplType.DENSE) -> Qarray:
    """σ+

    Returns:
        σ+ Pauli Operator
    """
    if QarrayImplType(implementation) == QarrayImplType.SPARSE_DIA:
        diags = jnp.array([[0.0, 1.0]])
        return _make_sparsedia(offsets=(1,), diags=diags)
    return Qarray.create(jnp.array([[0.0, 1.0], [0.0, 0.0]]), implementation=implementation)

sigmax(implementation=QarrayImplType.DENSE)

σx

Parameters:

Name Type Description Default
implementation QarrayImplType

Qarray implementation type, e.g. "sparse" or "dense".

 DENSE

Returns:

Type Description
Qarray

σx Pauli Operator
Source code in jaxquantum/core/operators.py 
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def sigmax(implementation: QarrayImplType = QarrayImplType.DENSE) -> Qarray:
    """σx

    Args:
        implementation: Qarray implementation type, e.g. "sparse" or "dense".

    Returns:
        σx Pauli Operator
    """
    if QarrayImplType(implementation) == QarrayImplType.SPARSE_DIA:
        # Offset -1: valid at [0:1] → diag[0] = A[1,0] = 1.0, diag[1] = 0 (trailing zero)
        # Offset +1: valid at [1:]  → diag[0] = 0 (leading zero), diag[1] = A[0,1] = 1.0
        diags = jnp.array([[1.0, 0.0], [0.0, 1.0]])
        return _make_sparsedia(offsets=(-1, 1), diags=diags)
    return Qarray.create(jnp.array([[0.0, 1.0], [1.0, 0.0]]), implementation=implementation)

sigmay(implementation=QarrayImplType.DENSE)

σy

Returns:

Type Description
Qarray

σy Pauli Operator
Source code in jaxquantum/core/operators.py 
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def sigmay(implementation: QarrayImplType = QarrayImplType.DENSE) -> Qarray:
    """σy

    Returns:
        σy Pauli Operator
    """
    if QarrayImplType(implementation) == QarrayImplType.SPARSE_DIA:
        diags = jnp.array([[1.0j, 0.0], [0.0, -1.0j]])
        return _make_sparsedia(offsets=(-1, 1), diags=diags)
    return Qarray.create(jnp.array([[0.0, -1.0j], [1.0j, 0.0]]), implementation=implementation)

sigmaz(implementation=QarrayImplType.DENSE)

σz

Returns:

Type Description
Qarray

σz Pauli Operator
Source code in jaxquantum/core/operators.py 
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def sigmaz(implementation: QarrayImplType = QarrayImplType.DENSE) -> Qarray:
    """σz

    Returns:
        σz Pauli Operator
    """
    if QarrayImplType(implementation) == QarrayImplType.SPARSE_DIA:
        diags = jnp.array([[1.0, -1.0]])
        return _make_sparsedia(offsets=(0,), diags=diags)
    return Qarray.create(jnp.array([[1.0, 0.0], [0.0, -1.0]]), implementation=implementation)

sinm(qarr)

Matrix sine of a Qarray.

Parameters:

Name Type Description Default
qarr Qarray

Input quantum array (converted to dense internally).

 required

Returns:

Type Description
Qarray

A dense Qarray containing the matrix sine.
Source code in jaxquantum/core/qarray.py 
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def sinm(qarr: Qarray) -> Qarray:
    """Matrix sine of a ``Qarray``.

    Args:
        qarr: Input quantum array (converted to dense internally).

    Returns:
        A dense ``Qarray`` containing the matrix sine.
    """
    dims = qarr.dims
    # Convert to dense for sinm
    dense_data = qarr.to_dense().data
    data = sinm_data(dense_data)
    return Qarray.create(data, dims=dims)

tensor(*args, **kwargs)

Tensor (Kronecker) product of two or more Qarray objects.

Parameters:

Name Type Description Default
*args

Qarray objects to tensor together (left to right).

 ()
**kwargs

Optional keyword arguments. Pass parallel=True to use an einsum-based batched outer product instead of jnp.kron.

 {}

Returns:

Type Description
Qarray

The tensor product as a Qarray. The output implementation is
Qarray

determined by the highest PROMOTION_ORDER among the inputs: all-sparse
Qarray

inputs → sparse output; any dense input → dense output. This holds for
Qarray

both parallel=True and parallel=False.
Note

parallel=True uses an einsum-based batched outer product. The einsum is always computed on dense data for efficiency, but the result is then wrapped in the appropriate backend (sparse when all inputs are sparse, dense otherwise). For the default (parallel=False) path each backend's kron method is used directly.

Source code in jaxquantum/core/qarray.py 
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def tensor(*args, **kwargs) -> Qarray:
    """Tensor (Kronecker) product of two or more ``Qarray`` objects.

    Args:
        *args: ``Qarray`` objects to tensor together (left to right).
        **kwargs: Optional keyword arguments.  Pass ``parallel=True`` to use
            an einsum-based batched outer product instead of ``jnp.kron``.

    Returns:
        The tensor product as a ``Qarray``.  The output implementation is
        determined by the highest ``PROMOTION_ORDER`` among the inputs: all-sparse
        inputs → sparse output; any dense input → dense output.  This holds for
        both ``parallel=True`` and ``parallel=False``.

    Note:
        ``parallel=True`` uses an einsum-based batched outer product.  The
        einsum is always computed on dense data for efficiency, but the result
        is then wrapped in the appropriate backend (sparse when all inputs are
        sparse, dense otherwise).  For the default (``parallel=False``) path
        each backend's ``kron`` method is used directly.
    """
    parallel = kwargs.pop("parallel", False)

    if parallel:
        # Determine target implementation: highest PROMOTION_ORDER wins.
        # All-sparse → sparse; any dense input → dense (same rule as non-parallel).
        target_impl_type = max(
            (arg.impl_type for arg in args),
            key=lambda t: t.get_impl_class().PROMOTION_ORDER,
        )
        # Einsum-based batched outer product (computed on dense data).
        dense_args = [arg.to_dense() for arg in args]
        data = dense_args[0].data
        dims_0 = dense_args[0].dims[0]
        dims_1 = dense_args[0].dims[1]
        for arg in dense_args[1:]:
            a, b = data, arg.data
            if len(a.shape) > len(b.shape):
                batch_dim = a.shape[:-2]
            elif len(a.shape) == len(b.shape):
                batch_dim = a.shape[:-2] if prod(a.shape[:-2]) > prod(b.shape[:-2]) else b.shape[:-2]
            else:
                batch_dim = b.shape[:-2]

            # NOTE: implementation einsum should be used when available
            data = jnp.einsum("...ij,...kl->...ikjl", a, b).reshape(
                *batch_dim, a.shape[-2] * b.shape[-2], -1
            )
            dims_0 = dims_0 + arg.dims[0]
            dims_1 = dims_1 + arg.dims[1]
        return Qarray.create(data, dims=(dims_0, dims_1), implementation=target_impl_type)

    # Non-parallel: delegate to each impl's kron method.
    # All-sparse inputs stay sparse; mixed inputs promote to dense via _coerce.
    current_impl = args[0]._impl
    dims_0 = args[0].dims[0]
    dims_1 = args[0].dims[1]
    for arg in args[1:]:
        current_impl = current_impl.kron(arg._impl)
        dims_0 = dims_0 + arg.dims[0]
        dims_1 = dims_1 + arg.dims[1]
    return Qarray.create(current_impl.data, dims=(dims_0, dims_1),
                         implementation=current_impl.impl_type)