4mokie / bifluxon

Bifluxon (Aharonov-Casher) Qubit

Intro

This project allows to numerically study Aharonov-Casher qubit, namely calculate wavefunctions and energy levels, visualize energy spectra, evaluate decay rates and etc. The main feature of this objected-oriented code is save time and recources - once the Hamiltonian was solved for certain point, the information about energies and wavefunctions is stored and can be used in futher calculations.

Installation

Download files

wavefunction1d.py
ACstate.py
ACqubit.py

import to your .ipynb or .py file and start playing!

Structure of the code

One can create an instance of ACQubit class, providing the dict of qubit parameters (E_CL, E_L, E_J, E_C, dE_J in GHz)

ACQB15 = ACQubit (E_CL = 15, 
                  E_L = 0.87, 
                  E_J = 33, 
                  E_C = 8,
                  dE_J = 3 )

or

param_dict = {'E_CL': 15,  'E_J' : 33, 'E_C' : 8, 'dE_J' : 3 }
ACQB15 = ACQubit (**param_dict)

Qubit can be set in certain state (n_g and fi_ext), energy and WF of the state are calculated. One the Hamiltonian for certain state was diagonalized, we can use WFs and Es without recalculations.

ACstate methods allow to calculate E, WFs, matrix elements

ACqubit methods are wrappers for interation over range of parameters and plotting.

The Hamiltonian of the qubit can be found in ACstate.py module, calc_WF function

AC qubit methods

• set_state(ng , fi_ext) creates (or retrieves, if was created before) attribute, corresponds to the given gate charge ng (in units of e) and the external flux fi_ext (in rad). Energies and wavefuctions can be calculated for particular state, see more detail in the next section

• iterate_fi( fi_ext_list, ng, get_function, *args) iterates over fi_ext_list for given ng, returns the np.array of results get_function(*args) for each point. List of get_functions see in the next section

• iterate_fi( ng_list, fi_ext, get_function, *args) iterates over ng_ext_list for given fi_ext, returns the np.array of results get_function(*args) for each point. List of get_functions see in the next section

• plot_spectrum( fi_ext_list, ng_list, bands, ax = None ) plots E_0i transitions vs fi_ext_list, for i listed in bands, for gate charges from ng_list on given plt.axis or create new. Returns axis

• plot_bands( ax, fi_ext_list, ng_list, bands ) !! unify all plotting procedures

• plot_chi_i( fi_ext_list, ng_list, i , freq, ax = None )

• plot_fi_ij( fi_ext_list, ng_list, i, j , ax = None )

• plot_n_ij( fi_ext_list, ng_list, i, j , ax = None )

• plot_psi_ij( fi_ext_list, ng_list, i, j )

• plot_bands_Psi( fi_ext_list, ng_list, bands )

AC state methods

• calc_WF( fi_grid , Q_grid ) calculates wavefunctions and energies for given fi_grid = [min_fi, max_fi, N_pts] and Q_grid = [min_Q, max_Q]

• get_WF() checks if wavefunctions and energies are already calculated, and calculates if necessary

• get_E(i) returns energy of i-th level, or array of all levels if i is not given

• get_Psi( band, q) returns 1d wavefunction of fi at the level band, and certain charge variable q (not confuse with induced gate charge!)

  • get_fi_ij( i, j ) returns phase matrix element between states i and j

• get_n_ij( i, j ) returns charge matrix element between states i and j

• get_psi_ij( i, j ) returns overlapping of states i and j

• get_chi_i( i, freq ) !! add coupling returns dispersive shift of the resonator with frequency freq, when qubit is in the state i

• get_T1(fi_ext, ng, i = 0, j = 1) !!kill fiext, ng, add noise ampl