-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathcomparison_scaling_parameterofdelta_dependingontime.py
167 lines (132 loc) · 5.01 KB
/
comparison_scaling_parameterofdelta_dependingontime.py
1
2
3
4
5
6
7
8
9
10
11
12
13
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
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
# -*- 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=k2/1000 # 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+3*k/10 for k in range(10)]
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 func(t):
return np.exp(-1j*2*delta*(t-T1)*(t>=T1 and t<=T2))
def r(t, args=0):
return np.real(func(t))
def i(t, args=0):
return np.imag(func(t))
def funcA(t, args=0):
val = complex(1-r(t)-i(t))
return val**0.5
def funcB(t, args=0):
val = complex(1-r(t)-i(t))
return val**0.5
def funcApB(t, args=0):
val = complex(r(t))
return val**0.5
def funcApiB(t, args=0):
val = complex(i(t))
return val**0.5
A = k2**0.5*a**2
B = -k2**0.5*alpha_inf_abs**2*Ia
cops = [k1**0.5*a,]
cops.append([A, funcA])
cops.append([B, funcB])
cops.append([A+B, funcApB])
cops.append([A+1j*B, funcApiB])
"Resolution of the equation over time with mesolve"
init_state=C_y_alpha #initial state
tlist = np.linspace(0, T_final, n_t)
res_NOT = qt.mesolve(0*a, 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-step :%.f'%prop)
# 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_TEST_%.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))
#Plot func
fig, ax =plt.subplots()
reslist=[func(t) for t in tlist]
ax.plot(tlist,np.real(reslist),'+')
ax.plot(tlist,np.imag(reslist),'+')