Source code for scqubits.core.zeropi

# zeropi.py
#
# This file is part of scqubits: a Python package for superconducting qubits,
# arXiv:2107.08552 (2021). https://arxiv.org/abs/2107.08552
#
#    Copyright (c) 2019 and later, Jens Koch and Peter Groszkowski
#    All rights reserved.
#
#    This source code is licensed under the BSD-style license found in the
#    LICENSE file in the root directory of this source tree.
############################################################################

import os
import warnings

from typing import Any, Dict, List, Optional, Tuple, Union

import numpy as np

from matplotlib.axes import Axes
from matplotlib.figure import Figure
from numpy import ndarray
from scipy import sparse
from scipy.sparse.csc import csc_matrix
from scipy.sparse.dia import dia_matrix

import scqubits.core.central_dispatch as dispatch
import scqubits.core.constants as constants
import scqubits.core.descriptors as descriptors
import scqubits.core.discretization as discretization
import scqubits.core.qubit_base as base
import scqubits.core.storage as storage
import scqubits.io_utils.fileio_serializers as serializers
import scqubits.settings as settings
import scqubits.ui.qubit_widget as ui
import scqubits.utils.plotting as plot
import scqubits.utils.spectrum_utils as spec_utils

from scqubits.core.discretization import Grid1d
from scqubits.core.noise import NoisySystem
from scqubits.core.storage import WaveFunctionOnGrid

# - ZeroPi noise class


class NoisyZeroPi(NoisySystem):
    pass


# -Symmetric 0-pi qubit, phi discretized, theta in charge basis---------------------------------------------------------


[docs]class ZeroPi(base.QubitBaseClass, serializers.Serializable, NoisyZeroPi): r"""Zero-Pi Qubit | [1] Brooks et al., Physical Review A, 87(5), 052306 (2013). http://doi.org/10.1103/PhysRevA.87.052306 | [2] Dempster et al., Phys. Rev. B, 90, 094518 (2014). http://doi.org/10.1103/PhysRevB.90.094518 | [3] Groszkowski et al., New J. Phys. 20, 043053 (2018). https://doi.org/10.1088/1367-2630/aab7cd Zero-Pi qubit without coupling to the `zeta` mode, i.e., no disorder in `EC` and `EL`, see Eq. (4) in Groszkowski et al., New J. Phys. 20, 043053 (2018), .. math:: H &= -2E_\text{CJ}\partial_\phi^2+2E_{\text{C}\Sigma}(i\partial_\theta-n_g)^2 +2E_{C\Sigma}dC_J\,\partial_\phi\partial_\theta -2E_\text{J}\cos\theta\cos(\phi-\varphi_\text{ext}/2)+E_L\phi^2\\ &\qquad +2E_\text{J} + E_J dE_J \sin\theta\sin(\phi-\phi_\text{ext}/2). Formulation of the Hamiltonian matrix proceeds by discretization of the `phi` variable, and using charge basis for the `theta` variable. Parameters ---------- EJ: mean Josephson energy of the two junctions EL: inductive energy of the two (super-)inductors ECJ: charging energy associated with the two junctions EC: charging energy of the large shunting capacitances; set to `None` if `ECS` is provided instead dEJ: relative disorder in EJ, i.e., (EJ1-EJ2)/EJavg dCJ: relative disorder of the junction capacitances, i.e., (CJ1-CJ2)/CJavg ng: offset charge associated with theta flux: magnetic flux through the circuit loop, measured in units of flux quanta (h/2e) grid: specifies the range and spacing of the discretization lattice ncut: charge number cutoff for `n_theta`, `n_theta = -ncut, ..., ncut` ECS: total charging energy including large shunting capacitances and junction capacitances; may be provided instead of EC truncated_dim: desired dimension of the truncated quantum system; expected: truncated_dim > 1 id_str: optional string by which this instance can be referred to in `HilbertSpace` and `ParameterSweep`. If not provided, an id is auto-generated. """ EJ = descriptors.WatchedProperty(float, "QUANTUMSYSTEM_UPDATE") EL = descriptors.WatchedProperty(float, "QUANTUMSYSTEM_UPDATE") ECJ = descriptors.WatchedProperty(float, "QUANTUMSYSTEM_UPDATE") EC = descriptors.WatchedProperty(float, "QUANTUMSYSTEM_UPDATE") dEJ = descriptors.WatchedProperty(float, "QUANTUMSYSTEM_UPDATE") dCJ = descriptors.WatchedProperty(float, "QUANTUMSYSTEM_UPDATE") ng = descriptors.WatchedProperty(float, "QUANTUMSYSTEM_UPDATE") ncut = descriptors.WatchedProperty(int, "QUANTUMSYSTEM_UPDATE") def __init__( self, EJ: float, EL: float, ECJ: float, EC: Optional[float], ng: float, flux: float, grid: Grid1d, ncut: int, dEJ: float = 0.0, dCJ: float = 0.0, ECS: float = None, truncated_dim: int = 6, id_str: Optional[str] = None, ) -> None: base.QuantumSystem.__init__(self, id_str=id_str) self.EJ = EJ self.EL = EL self.ECJ = ECJ if EC is None and ECS is None: raise ValueError("Argument missing: must either provide EC or ECS") if EC and ECS: raise ValueError("Argument error: can only provide either EC or ECS") if EC: self.EC = EC elif ECS: self.EC = 1 / (1 / ECS - 1 / self.ECJ) self.dEJ = dEJ self.dCJ = dCJ self.ng = ng self.flux = flux self.grid = grid self.ncut = ncut self.truncated_dim = truncated_dim self._evec_dtype = np.complex_ # _default_grid is for *theta*, needed for plotting wavefunction self._default_grid = discretization.Grid1d(-np.pi / 2, 3 * np.pi / 2, 200) self._init_params.remove( "ECS" ) # used in for file Serializable purposes; remove ECS as init parameter self._image_filename = os.path.join( os.path.dirname(os.path.abspath(__file__)), "qubit_img/zeropi.jpg" ) dispatch.CENTRAL_DISPATCH.register("GRID_UPDATE", self)
[docs] @staticmethod def default_params() -> Dict[str, Any]: return { "EJ": 10.0, "EL": 0.04, "ECJ": 20.0, "EC": 0.04, "dEJ": 0.0, "dCJ": 0.0, "ng": 0.1, "flux": 0.23, "ncut": 30, "truncated_dim": 10, }
[docs] @classmethod def create(cls) -> "ZeroPi": phi_grid = discretization.Grid1d(-19.0, 19.0, 200) init_params = cls.default_params() init_params["grid"] = phi_grid zeropi = cls(**init_params) zeropi.widget() return zeropi
[docs] @classmethod def supported_noise_channels(cls) -> List[str]: """Return a list of supported noise channels""" return [ "tphi_1_over_f_cc", "tphi_1_over_f_flux", "t1_flux_bias_line", # 't1_capacitive', "t1_inductive", ]
def widget(self, params: Dict[str, Any] = None) -> None: init_params = params or self.get_initdata() init_params.pop("id_str", None) del init_params["grid"] init_params["grid_max_val"] = self.grid.max_val init_params["grid_min_val"] = self.grid.min_val init_params["grid_pt_count"] = self.grid.pt_count ui.create_widget( self.set_params, init_params, image_filename=self._image_filename )
[docs] def set_params(self, **kwargs) -> None: phi_grid = discretization.Grid1d( kwargs.pop("grid_min_val"), kwargs.pop("grid_max_val"), kwargs.pop("grid_pt_count"), ) self.grid = phi_grid for param_name, param_val in kwargs.items(): setattr(self, param_name, param_val)
def receive(self, event: str, sender: object, **kwargs): if sender is self.grid: self.broadcast("QUANTUMSYSTEM_UPDATE") def _evals_calc(self, evals_count: int) -> ndarray: hamiltonian_mat = self.hamiltonian() evals = sparse.linalg.eigsh( hamiltonian_mat, k=evals_count, sigma=0.0, which="LM", return_eigenvectors=False, v0=settings.RANDOM_ARRAY[: self.hilbertdim()], ) return np.sort(evals) def _esys_calc(self, evals_count: int) -> Tuple[ndarray, ndarray]: hamiltonian_mat = self.hamiltonian() evals, evecs = sparse.linalg.eigsh( hamiltonian_mat, k=evals_count, sigma=0.0, which="LM", return_eigenvectors=True, v0=settings.RANDOM_ARRAY[: self.hilbertdim()], ) evals, evecs = spec_utils.order_eigensystem(evals, evecs) return evals, evecs def get_ECS(self) -> float: return 1 / (1 / self.EC + 1 / self.ECJ) def set_ECS(self, value) -> None: warnings.warn( "It is not possible to directly set ECS (except in initialization)." " Instead, set EC or ECJ, or use set_EC_via_ECS() to update EC indirectly.", Warning, ) ECS = property(get_ECS, set_ECS)
[docs] def set_EC_via_ECS(self, ECS: float) -> None: """Helper function to set `EC` by providing `ECS`, keeping `ECJ` constant.""" self.EC = 1 / (1 / ECS - 1 / self.ECJ)
[docs] def hilbertdim(self) -> int: """Returns Hilbert space dimension""" return self.grid.pt_count * (2 * self.ncut + 1)
[docs] def potential(self, phi: ndarray, theta: ndarray) -> ndarray: """ Returns ------- value of the potential energy evaluated at phi, theta """ return ( -2.0 * self.EJ * np.cos(theta) * np.cos(phi - 2.0 * np.pi * self.flux / 2.0) + self.EL * phi ** 2 + 2.0 * self.EJ + self.EJ * self.dEJ * np.sin(theta) * np.sin(phi - 2.0 * np.pi * self.flux / 2.0) )
[docs] def sparse_kinetic_mat(self) -> csc_matrix: """ Kinetic energy portion of the Hamiltonian. Returns ------- matrix representing the kinetic energy operator """ pt_count = self.grid.pt_count dim_theta = 2 * self.ncut + 1 identity_phi = sparse.identity(pt_count, format="csc") identity_theta = sparse.identity(dim_theta, format="csc") kinetic_matrix_phi = self.grid.second_derivative_matrix( prefactor=-2.0 * self.ECJ ) diag_elements = ( 2.0 * self.ECS * np.square(np.arange(-self.ncut + self.ng, self.ncut + 1 + self.ng)) ) kinetic_matrix_theta = sparse.dia_matrix( (diag_elements, [0]), shape=(dim_theta, dim_theta) ).tocsc() kinetic_matrix = sparse.kron( kinetic_matrix_phi, identity_theta, format="csc" ) + sparse.kron(identity_phi, kinetic_matrix_theta, format="csc") if self.dCJ != 0: kinetic_matrix -= ( 2.0 * self.ECS * self.dCJ * self.i_d_dphi_operator() * self.n_theta_operator() ) return kinetic_matrix
[docs] def sparse_potential_mat(self) -> csc_matrix: """ Potential energy portion of the Hamiltonian. Returns ------- matrix representing the potential energy operator """ pt_count = self.grid.pt_count grid_linspace = self.grid.make_linspace() dim_theta = 2 * self.ncut + 1 phi_inductive_vals = self.EL * np.square(grid_linspace) phi_inductive_potential = sparse.dia_matrix( (phi_inductive_vals, [0]), shape=(pt_count, pt_count) ).tocsc() phi_cos_vals = np.cos(grid_linspace - 2.0 * np.pi * self.flux / 2.0) phi_cos_potential = sparse.dia_matrix( (phi_cos_vals, [0]), shape=(pt_count, pt_count) ).tocsc() phi_sin_vals = np.sin(grid_linspace - 2.0 * np.pi * self.flux / 2.0) phi_sin_potential = sparse.dia_matrix( (phi_sin_vals, [0]), shape=(pt_count, pt_count) ).tocsc() theta_cos_potential = ( -self.EJ * ( sparse.dia_matrix( ([1.0] * dim_theta, [-1]), shape=(dim_theta, dim_theta) ) + sparse.dia_matrix( ([1.0] * dim_theta, [1]), shape=(dim_theta, dim_theta) ) ) ).tocsc() potential_mat = ( sparse.kron(phi_cos_potential, theta_cos_potential, format="csc") + sparse.kron(phi_inductive_potential, self._identity_theta(), format="csc") + 2 * self.EJ * sparse.kron(self._identity_phi(), self._identity_theta(), format="csc") ) if self.dEJ != 0: potential_mat += ( self.EJ * self.dEJ * sparse.kron(phi_sin_potential, self._identity_theta(), format="csc") * self.sin_theta_operator() ) return potential_mat
[docs] def hamiltonian(self) -> csc_matrix: """Calculates Hamiltonian in basis obtained by discretizing phi and employing charge basis for theta. Returns ------- matrix representing the potential energy operator """ return self.sparse_kinetic_mat() + self.sparse_potential_mat()
[docs] def sparse_d_potential_d_flux_mat(self) -> csc_matrix: r"""Calculates a of the potential energy w.r.t flux, at the current value of flux, as stored in the object. The flux is assumed to be given in the units of the ratio \Phi_{ext}/\Phi_0. So if \frac{\partial U}{ \partial \Phi_{\rm ext}}, is needed, the expr returned by this function, needs to be multiplied by 1/\Phi_0. Returns ------- matrix representing the derivative of the potential energy """ op_1 = sparse.kron( self._sin_phi_operator(x=-2.0 * np.pi * self.flux / 2.0), self._cos_theta_operator(), format="csc", ) op_2 = sparse.kron( self._cos_phi_operator(x=-2.0 * np.pi * self.flux / 2.0), self._sin_theta_operator(), format="csc", ) return -2.0 * np.pi * self.EJ * op_1 - np.pi * self.EJ * self.dEJ * op_2
[docs] def d_hamiltonian_d_flux(self) -> csc_matrix: r"""Calculates a derivative of the Hamiltonian w.r.t flux, at the current value of flux, as stored in the object. The flux is assumed to be given in the units of the ratio \Phi_{ext}/\Phi_0. So if \frac{\partial H}{ \partial \Phi_{\rm ext}}, is needed, the expr returned by this function, needs to be multiplied by 1/\Phi_0. Returns ------- matrix representing the derivative of the Hamiltonian """ return self.sparse_d_potential_d_flux_mat()
[docs] def sparse_d_potential_d_EJ_mat(self) -> csc_matrix: r"""Calculates a of the potential energy w.r.t EJ. Returns ------- matrix representing the derivative of the potential energy """ return -2.0 * sparse.kron( self._cos_phi_operator(x=-2.0 * np.pi * self.flux / 2.0), self._cos_theta_operator(), format="csc", )
[docs] def d_hamiltonian_d_EJ(self) -> csc_matrix: r"""Calculates a derivative of the Hamiltonian w.r.t EJ. Returns ------- matrix representing the derivative of the Hamiltonian """ return self.sparse_d_potential_d_EJ_mat()
[docs] def d_hamiltonian_d_ng(self) -> csc_matrix: r"""Calculates a derivative of the Hamiltonian w.r.t ng. as stored in the object. Returns ------- matrix representing the derivative of the Hamiltonian """ return -8 * self.EC * self.n_theta_operator()
def _identity_phi(self) -> csc_matrix: r""" Identity operator acting only on the `\phi` Hilbert subspace. """ pt_count = self.grid.pt_count return sparse.identity(pt_count, format="csc") def _identity_theta(self) -> csc_matrix: r""" Identity operator acting only on the `\theta` Hilbert subspace. """ dim_theta = 2 * self.ncut + 1 return sparse.identity(dim_theta, format="csc")
[docs] def i_d_dphi_operator(self) -> csc_matrix: r""" Operator :math:`i d/d\phi`. """ return sparse.kron( self.grid.first_derivative_matrix(prefactor=1j), self._identity_theta(), format="csc", )
def _phi_operator(self) -> dia_matrix: r""" Operator :math:`\phi`, acting only on the `\phi` Hilbert subspace. """ pt_count = self.grid.pt_count phi_matrix = sparse.dia_matrix((pt_count, pt_count)) diag_elements = self.grid.make_linspace() phi_matrix.setdiag(diag_elements) return phi_matrix
[docs] def phi_operator(self) -> csc_matrix: r""" Operator :math:`\phi`. """ return sparse.kron(self._phi_operator(), self._identity_theta(), format="csc")
[docs] def n_theta_operator(self) -> csc_matrix: r""" Operator :math:`n_\theta`. """ dim_theta = 2 * self.ncut + 1 diag_elements = np.arange(-self.ncut, self.ncut + 1) n_theta_matrix = sparse.dia_matrix( (diag_elements, [0]), shape=(dim_theta, dim_theta) ).tocsc() return sparse.kron(self._identity_phi(), n_theta_matrix, format="csc")
def _sin_phi_operator(self, x: float = 0) -> csc_matrix: r""" Operator :math:`\sin(\phi + x)`, acting only on the `\phi` Hilbert subspace.x """ pt_count = self.grid.pt_count vals = np.sin(self.grid.make_linspace() + x) sin_phi_matrix = sparse.dia_matrix( (vals, [0]), shape=(pt_count, pt_count) ).tocsc() return sin_phi_matrix def _cos_phi_operator(self, x: float = 0) -> csc_matrix: r""" Operator :math:`\cos(\phi + x)`, acting only on the `\phi` Hilbert subspace. """ pt_count = self.grid.pt_count vals = np.cos(self.grid.make_linspace() + x) cos_phi_matrix = sparse.dia_matrix( (vals, [0]), shape=(pt_count, pt_count) ).tocsc() return cos_phi_matrix def _cos_theta_operator(self) -> csc_matrix: r""" Operator :math:`\cos(\theta)`, acting only on the `\theta` Hilbert subspace. """ dim_theta = 2 * self.ncut + 1 cos_theta_matrix = ( 0.5 * ( sparse.dia_matrix( ([1.0] * dim_theta, [-1]), shape=(dim_theta, dim_theta) ) + sparse.dia_matrix( ([1.0] * dim_theta, [1]), shape=(dim_theta, dim_theta) ) ).tocsc() ) return cos_theta_matrix
[docs] def cos_theta_operator(self) -> csc_matrix: r""" Operator :math:`\cos(\theta)`. """ return sparse.kron( self._identity_phi(), self._cos_theta_operator(), format="csc" )
def _sin_theta_operator(self) -> csc_matrix: r""" Operator :math:`\sin(\theta)`, acting only on the `\theta` Hilbert space. """ dim_theta = 2 * self.ncut + 1 sin_theta_matrix = ( -0.5 * 1j * ( sparse.dia_matrix( ([1.0] * dim_theta, [1]), shape=(dim_theta, dim_theta) ) - sparse.dia_matrix( ([1.0] * dim_theta, [-1]), shape=(dim_theta, dim_theta) ) ).tocsc() ) return sin_theta_matrix
[docs] def sin_theta_operator(self) -> csc_matrix: r""" Operator :math:`\sin(\theta)`. """ return sparse.kron( self._identity_phi(), self._sin_theta_operator(), format="csc" )
[docs] def plot_potential( self, theta_grid: Grid1d = None, contour_vals: Union[List[float], ndarray] = None, **kwargs ) -> Tuple[Figure, Axes]: """Draw contour plot of the potential energy. Parameters ---------- theta_grid: used for setting a custom grid for theta; if None use self._default_grid contour_vals: **kwargs: plotting parameters """ theta_grid = theta_grid or self._default_grid x_vals = self.grid.make_linspace() y_vals = theta_grid.make_linspace() return plot.contours( x_vals, y_vals, self.potential, contour_vals=contour_vals, xlabel=r"$\phi$", ylabel=r"$\theta$", **kwargs )
[docs] def wavefunction( self, esys: Tuple[ndarray, ndarray] = None, which: int = 0, theta_grid: Grid1d = None, ) -> WaveFunctionOnGrid: """Returns a zero-pi wave function in `phi`, `theta` basis Parameters ---------- esys: eigenvalues, eigenvectors which: index of desired wave function (default value = 0) theta_grid: used for setting a custom grid for theta; if None use self._default_grid """ evals_count = max(which + 1, 3) if esys is None: _, evecs = self.eigensys(evals_count=evals_count) else: _, evecs = esys theta_grid = theta_grid or self._default_grid dim_theta = 2 * self.ncut + 1 state_amplitudes = evecs[:, which].reshape(self.grid.pt_count, dim_theta) # Calculate psi_{phi, theta} = sum_n state_amplitudes_{phi, n} A_{n, theta} # where a_{n, theta} = 1/sqrt(2 pi) e^{i n theta} n_vec = np.arange(-self.ncut, self.ncut + 1) theta_vec = theta_grid.make_linspace() a_n_theta = np.exp(1j * np.outer(n_vec, theta_vec)) / (2 * np.pi) ** 0.5 wavefunc_amplitudes = np.matmul(state_amplitudes, a_n_theta).T wavefunc_amplitudes = spec_utils.standardize_phases(wavefunc_amplitudes) grid2d = discretization.GridSpec( np.asarray( [ [self.grid.min_val, self.grid.max_val, self.grid.pt_count], [theta_grid.min_val, theta_grid.max_val, theta_grid.pt_count], ] ) ) return storage.WaveFunctionOnGrid(grid2d, wavefunc_amplitudes)
[docs] def plot_wavefunction( self, esys: Tuple[ndarray, ndarray] = None, which: int = 0, theta_grid: Grid1d = None, mode: str = "abs", zero_calibrate: bool = True, **kwargs ) -> Tuple[Figure, Axes]: """Plots 2d phase-basis wave function. Parameters ---------- esys: eigenvalues, eigenvectors as obtained from `.eigensystem()` which: index of wave function to be plotted (default value = (0) theta_grid: used for setting a custom grid for theta; if None use self._default_grid mode: choices as specified in `constants.MODE_FUNC_DICT` (default value = 'abs_sqr') zero_calibrate: if True, colors are adjusted to use zero wavefunction amplitude as the neutral color in the palette **kwargs: plot options """ theta_grid = theta_grid or self._default_grid amplitude_modifier = constants.MODE_FUNC_DICT[mode] wavefunc = self.wavefunction(esys, theta_grid=theta_grid, which=which) wavefunc.amplitudes = amplitude_modifier(wavefunc.amplitudes) return plot.wavefunction2d( wavefunc, zero_calibrate=zero_calibrate, xlabel=r"$\phi$", ylabel=r"$\theta$", **kwargs )