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devices

Devices.

ATS

Bases: FluxDevice

ATS Device.

Source code in qcsys/devices/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"] = 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"])
        return ops

    def phi_zpf(self):
        """Return Phase ZPF."""
        return (2*self.params["Ec"]/self.params["El"])**(.25)

    def n_zpf(self):
        """Return Charge ZPF."""
        return (self.params["El"]/(32*self.params["Ec"]))**(.25)

    def get_linear_ω(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_ω()
        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 = jqt.cosm(phi_op)
        sin_phi_op = jqt.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."""
        id_op = self.linear_ops["id"]
        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 qcsys/devices/ats.py 
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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"])
    return ops

get_H_full()

Return full H in linear basis.

Source code in qcsys/devices/ats.py 
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def get_H_full(self):
    """Return full H in linear basis."""
    id_op = self.linear_ops["id"]
    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 qcsys/devices/ats.py 
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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_H_nonlinear(phi_op)

Return nonlinear terms in H.

Source code in qcsys/devices/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_ω()

Get frequency of linear terms.

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

n_zpf()

Return Charge ZPF.

Source code in qcsys/devices/ats.py 
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def n_zpf(self):
    """Return Charge ZPF."""
    return (self.params["El"]/(32*self.params["Ec"]))**(.25)

phi_zpf()

Return Phase ZPF.

Source code in qcsys/devices/ats.py 
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def phi_zpf(self):
    """Return Phase ZPF."""
    return (2*self.params["Ec"]/self.params["El"])**(.25)

potential(phi)

Return potential energy for a given phi.

Source code in qcsys/devices/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 qcsys/devices/base.py 
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@struct.dataclass
class Device(ABC):
    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 BasisTypes.fock
        _hamiltonian = hamiltonian if hamiltonian is not None else HamiltonianTypes.full
        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, jqt.Qarray]:
        """Set up common ops in the specified basis."""

    @abstractmethod
    def get_linear_ω(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: jqt.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: jqt.Qarray):
        evecs = self.eig_systems["vecs"][:, : self.N]
        if vec.qtype == jqt.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 qcsys/devices/base.py 
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@abstractmethod
def common_ops(self) -> Dict[str, jqt.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 qcsys/devices/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 BasisTypes.fock
    _hamiltonian = hamiltonian if hamiltonian is not None else HamiltonianTypes.full
    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 qcsys/devices/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 qcsys/devices/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 qcsys/devices/base.py 
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@abstractmethod
def get_H_linear(self):
    """Return linear terms in H."""

get_linear_ω() abstractmethod

Get frequency of linear terms.

Source code in qcsys/devices/base.py 
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@abstractmethod
def get_linear_ω(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 qcsys/devices/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 qcsys/devices/drive.py 
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@struct.dataclass
class Drive(ABC):
    N: int = struct.field(pytree_node=False)
    ωd: float
    _label: int = struct.field(pytree_node=False)

    @classmethod
    def create(cls, M_max, ωd, label=0):
        cls.M_max = M_max
        N = 2 * M_max + 1
        return cls(N, ωd, 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, jqt.Qarray]:
        ops = {}

        M_max = self.M_max

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

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

        # Construct M₊ ≡ exp(iθ) and M₋ ≡ exp(-iθ) operators for drive
        ops["M-"] = jqt.jnp2jqt(jnp.eye(2 * M_max + 1, k=1))
        ops["M+"] = jqt.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}"] = jqt.jnp2jqt(jnp.eye(2 * M_max + 1, k=-k))
            ops[f"M_-{k}"] = jqt.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 (ωd * M) in the extended Hilbert space.
        """
        return self.ωd * self.ops["M"]

get_H()

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

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

FluxDevice

Bases: Device

Source code in qcsys/devices/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_max = (self.N_pre_diag - 1) // 2
        for n in jnp.arange(-n_max, n_max + 1):
            basis_functions.append(
                1/(jnp.sqrt(2*jnp.pi)) * jnp.exp(1j * n * (2*jnp.pi*phi_vals))
            )
        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
        phase_correction_factors =  (1j**(jnp.arange(0,self.N_pre_diag))).reshape(self.N_pre_diag,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"):

        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)

        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

            ax.plot(phi_vals, wf_vals, label=f"$|${n}$\\rangle$", linestyle = '-', linewidth = 1)
            ax.fill_between(phi_vals, energy_levels[n], wf_vals, alpha=0.5)

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

        ax.set_ylim([min_val-1, max_val+1])

        ax.set_xlabel(r"$\Phi/\Phi_0$")
        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}")

        plt.legend(fontsize=6)
        fig.tight_layout()

        return ax

phi_zpf() abstractmethod

Return Phase ZPF.

Source code in qcsys/devices/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 qcsys/devices/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 qcsys/devices/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"] = 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 qcsys/devices/fluxonium.py 
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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 qcsys/devices/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 qcsys/devices/fluxonium.py 
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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 qcsys/devices/fluxonium.py 
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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 qcsys/devices/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 qcsys/devices/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 qcsys/devices/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 "ω" in params, "IdealQubit requires a frequency parameter 'ω'."

    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"] = jqt.identity(N)
        ops["sigmaz"] = jqt.sigmaz()
        ops["sigmax"] = jqt.sigmax()
        ops["sigmay"] = jqt.sigmay()
        ops["sigmam"] = jqt.sigmam()
        ops["sigmap"] = jqt.sigmap()

        return ops

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

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

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

common_ops()

Written in the linear basis.

Source code in qcsys/devices/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"] = jqt.identity(N)
    ops["sigmaz"] = jqt.sigmaz()
    ops["sigmax"] = jqt.sigmax()
    ops["sigmay"] = jqt.sigmay()
    ops["sigmam"] = jqt.sigmam()
    ops["sigmap"] = jqt.sigmap()

    return ops

get_H_full()

Return full H in linear basis.

Source code in qcsys/devices/ideal_qubit.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 qcsys/devices/ideal_qubit.py 
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def get_H_linear(self):
    """Return linear terms in H."""
    w = self.get_linear_ω()
    return (w / 2) * self.linear_ops["sigma_z"]

get_linear_ω()

Get frequency of linear terms.

Source code in qcsys/devices/ideal_qubit.py 
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def get_linear_ω(self):
    """Get frequency of linear terms."""
    return self.params["ω"]

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

This can be overridden by subclasses.

Source code in qcsys/devices/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 "ω" in params, "IdealQubit requires a frequency parameter 'ω'."

KNO

Bases: Device

Kerr Nonlinear Oscillator Device.

Source code in qcsys/devices/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 "ω" in params and "α" in params, "Kerr Nonlinear Oscillator requires frequency 'ω' and anharmonicity 'α' as parameters."

    def common_ops(self):
        ops = {}

        N = self.N
        ops["id"] = jqt.identity(N)
        ops["a"] = jqt.destroy(N)
        ops["a_dag"] = jqt.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_ω(self):
        """Get frequency of linear terms."""
        return self.params["ω"]

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

    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"]

    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 qcsys/devices/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 qcsys/devices/kno.py 
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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"]

get_anharm()

Get anharmonicity.

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

get_linear_ω()

Get frequency of linear terms.

Source code in qcsys/devices/kno.py 
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def get_linear_ω(self):
    """Get frequency of linear terms."""
    return self.params["ω"]

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

This can be overridden by subclasses.

Source code in qcsys/devices/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 "ω" in params and "α" in params, "Kerr Nonlinear Oscillator requires frequency 'ω' and anharmonicity 'α' as parameters."

Resonator

Bases: FluxDevice

Resonator Device.

Source code in qcsys/devices/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"] = 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"])

        return ops

    def phi_zpf(self):
        """Return Phase ZPF."""
        return (2*self.params["Ec"]/self.params["El"])**(.25)

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

    def get_linear_ω(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_ω()
        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 qcsys/devices/resonator.py 
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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"])

    return ops

get_H_full()

Return full H in linear basis.

Source code in qcsys/devices/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 qcsys/devices/resonator.py 
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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"] + 1/2)

get_linear_ω()

Get frequency of linear terms.

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

phi_zpf()

Return Phase ZPF.

Source code in qcsys/devices/resonator.py 
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def phi_zpf(self):
    """Return Phase ZPF."""
    return (2*self.params["Ec"]/self.params["El"])**(.25)

potential(phi)

Return potential energy for a given phi.

Source code in qcsys/devices/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

Transmon

Bases: FluxDevice

Transmon Device.

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

    @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:
            assert basis in [BasisTypes.charge, BasisTypes.single_charge], "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

        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"] = 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"])

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

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

        elif self.basis == BasisTypes.single_charge:
            """
            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 - 1) // 2

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

            n_minus_ng_array = jnp.arange(-n_max, n_max + 1) - 2 * self.params["ng"] * jnp.ones(N)
            ops["H_charge"] = jqt.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."""

        if self.basis == BasisTypes.fock:
            return super().calculate_wavefunctions(phi_vals)
        elif self.basis == BasisTypes.single_charge:
            raise NotImplementedError("Wavefunctions for single charge basis not yet implemented.")
        elif self.basis == BasisTypes.charge:
            phi_vals = jnp.array(phi_vals)

            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.

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

    if self.basis == BasisTypes.fock:
        return super().calculate_wavefunctions(phi_vals)
    elif self.basis == BasisTypes.single_charge:
        raise NotImplementedError("Wavefunctions for single charge basis not yet implemented.")
    elif self.basis == BasisTypes.charge:
        phi_vals = jnp.array(phi_vals)

        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 qcsys/devices/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"] = 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"])

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

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

    elif self.basis == BasisTypes.single_charge:
        """
        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 - 1) // 2

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

        n_minus_ng_array = jnp.arange(-n_max, n_max + 1) - 2 * self.params["ng"] * jnp.ones(N)
        ops["H_charge"] = jqt.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 qcsys/devices/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 qcsys/devices/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 qcsys/devices/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 qcsys/devices/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 qcsys/devices/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 qcsys/devices/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:
        assert basis in [BasisTypes.charge, BasisTypes.single_charge], "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

    assert (N_pre_diag - 1) % 2 == 0, "N_pre_diag must be odd."

phi_zpf()

Return Phase ZPF.

Source code in qcsys/devices/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 qcsys/devices/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 qcsys/devices/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

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 qcsys/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