Skip to content

fluxonium

Fluxonium.

Fluxonium

Bases: FluxDevice

Fluxonium Device.

Source code in jaxquantum/devices/superconducting/fluxonium.py 
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
@struct.dataclass
class Fluxonium(FluxDevice):
    """
    Fluxonium Device.
    """

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

        N = self.N_pre_diag
        ops["id"] = jqt.identity(N)
        ops["a"] = jqt.destroy(N)
        ops["a_dag"] = jqt.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)"] = jqt.cosm(ops["phi"] / 2)
        ops["sin(φ/2)"] = jqt.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_ω(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_ω()
        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 = jqt.cosm(phi_op)
        op_sin_phi = jqt.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 
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
def common_ops(self):
    """Written in the linear basis."""
    ops = {}

    N = self.N_pre_diag
    ops["id"] = jqt.identity(N)
    ops["a"] = jqt.destroy(N)
    ops["a_dag"] = jqt.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)"] = jqt.cosm(ops["phi"] / 2)
    ops["sin(φ/2)"] = jqt.sinm(ops["phi"] / 2)

    return ops

get_H_full()

Return full H in linear basis.

Source code in jaxquantum/devices/superconducting/fluxonium.py 
56
57
58
59
60
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 
48
49
50
51
52
53
54
def get_H_linear(self):
    """Return linear terms in H."""
    w = self.get_linear_ω()
    return w * (
        self.linear_ops["a_dag"] @ self.linear_ops["a"]
        + 0.5 * self.linear_ops["id"]
    )

get_linear_ω()

Get frequency of linear terms.

Source code in jaxquantum/devices/superconducting/fluxonium.py 
44
45
46
def get_linear_ω(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 
40
41
42
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 
73
74
75
76
77
78
79
80
81
82
83
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