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transmon

Transmon.

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_ω(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_ω()
        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_ω()
    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_ω()

Get frequency of linear terms.

Source code in jaxquantum/devices/superconducting/transmon.py 
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def get_linear_ω(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