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comparison_scaling_parameterofdelta_TEST.py
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# -*- coding: utf-8 -*-
"""
Created on Tue Oct 15 13:22:19 2019
@author: Camille
"""
import qutip as qt
import numpy as np
import matplotlib.pyplot as plt
import scipy.integrate as integrate
plt.close('all')
from qutip.ui.progressbar import TextProgressBar
from compute_Wigner_class import compute_Wigner
"Parameters that will stay fixed"
k2 = 1
k1=1/1000 # single-photon loss rate
alpha=3
alpha_inf_abs=3 #size of the init cat and the stabilization drive
Na=50 #truncature
nbWignerPlot = 15
nbCols=4
check_plots= True
"List to keep the results"
factors_prop_list=[1+k/10 for k in range(30)]
max_fidelity_list=[]
plt.close('all')
for prop in factors_prop_list :
delta=alpha_inf_abs**2*k2/prop
#Times
T=np.pi /delta
T1 =1./2*T
T2 =T1+T
T_final=T2+3*T
n_t = 1001 #number of points from 0 to T_final
#from 0 to T1 : "free" evolution (with 2 photon drive H)
#from T1 to T2 : gate NOT
#from T2 to T_final : "free" evolution (with 2 photon drive H)
"Local Parameters"
Ia = qt.identity(Na) # identity
a = qt.destroy(Na) # lowering operator
n_a = a.dag()*a # photon number
eps_2=alpha_inf_abs**2*k2/2 #cf Mirrahimi NJP 2014
"Catstates"
C_alpha_plus = qt.coherent(Na, alpha)+qt.coherent(Na, -alpha)
C_alpha_plus = C_alpha_plus/C_alpha_plus.norm()
C_alpha_minus = qt.coherent(Na, alpha)-qt.coherent(Na, -alpha)
C_alpha_minus = C_alpha_minus/C_alpha_minus.norm()
C_y_alpha=qt.coherent(Na,alpha)+ 1j* qt.coherent(Na, -alpha)
C_y_alpha=C_y_alpha/C_y_alpha.norm()
"Calculates the coefficient of the hamiltonian time-dependant terms"
def coef_eps(t,args):
return(-1j*eps_2*np.exp(1j*2*delta*(t-T1)*(t>=T1 and t<=T2)))
def coef_eps_conj(t,args):
return(np.conjugate(coef_eps(t,args)))
H_NOT=[[a**2,coef_eps],[a.dag()**2, coef_eps_conj]]
#H=-1j*(a**2*eps_2-a.dag()**2*np.conjugate(eps_2))
cops=[k1**0.5*a,k2**0.5*a**2]
"Resolution of the equation over time with mesolve"
init_state=qt.coherent(Na,alpha) #initial state
tlist = np.linspace(0, T_final, n_t)
res_NOT = qt.mesolve(H_NOT, init_state, tlist, cops, progress_bar=TextProgressBar())
##Wigner
res_NOT_Wigner = compute_Wigner([-6, 6, 51], nbWignerPlot,nbCols, n_t,-1)
res_NOT_Wigner.draw_Wigner(res_NOT.states, title='Simulations with NOT')
# res_free_Wigner= compute_Wigner([-6,6, 51], nbWignerPlot,nbCols, n_t,-1)
# res_free_Wigner.draw_Wigner(res_free.states, title='Simulations without NOT')
"Plot the evolution of fidelity over time"
target_res=[] #to check the Wigner
fidelity_NOT_list=[]
for ii,t in enumerate(tlist):
if t<=T1:
current_theta=0
elif (t>T1) and (t<T2):
current_theta=delta*(t-T1)
else :
current_theta=np.pi
state_rot= (-1j*current_theta*a.dag()*a).expm()*init_state
state_rot=state_rot/state_rot.norm()
target_res.append(state_rot)
fidelity_NOT_list.append(qt.fidelity(res_NOT.states[ii],state_rot))
#Wigner of target res (to check the rotated states does the job)
target_Wigner= compute_Wigner([-6,6,51], nbWignerPlot, nbCols, n_t,-1)
target_Wigner.draw_Wigner(target_res,"Rotated states")
"Look for the maximum "
ind_time_start=int(n_t*T2/T_final) #to optimize we can look after 0.5T
ind_time_max=ind_time_start+np.argmax(np.array(fidelity_NOT_list[ind_time_start:]))
max_fidelity=fidelity_NOT_list[ind_time_max]
max_fidelity_list.append(max_fidelity)
print("Step : " +str(prop)+ ' done')
print('\n')
"Plots saved to check it is ok"
if check_plots:
fig,axs= plt.subplots()
axs.plot(tlist,fidelity_NOT_list,'+')
axs.plot(tlist[ind_time_max],max_fidelity,'or')
path='C:/Users/Camille/Documents/GitHub/CNOT_simus/Images/Optimal_prop_factor_checkings/cat_plus/'
name1='fidelity_opt_prop_alphais%.0f_prop'%(alpha)
name2=str(prop)+'.png'
fig.savefig(path+name1+name2)
plt.close()
"Plotting the results"
prop_max_ind=np.argmax(max_fidelity_list)
fig, ax= plt.subplots()
ax.plot(factors_prop_list,max_fidelity_list,'+')
ax.plot(factors_prop_list[prop_max_ind],max_fidelity_list[prop_max_ind],'+r')
ax.set_xlabel(r'Factors of proportionality for $\Delta$')
ax.set_ylabel('Fidelity max')
ax.set_title(r'$\alpha=%.0f$ ; trunc=%.0f ;$\Delta=\kappa_2*|\alpha|^2*\frac{1}{prop}$ ; $\kappa_1=\frac{\kappa_2}{1000}$ ; coherent'%(alpha,Na))