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In [1]:



    


#import functions
%pylab inline

# from MyUnits import *
from MyFunctions import *
from qutip import *

# from MyQubit import *
# import mpld3
import multiprocessing as mp
import itertools
import datetime



    


















    






Populating the interactive namespace from numpy and matplotlib

















In [2]:



    


%%javascript
IPython.load_extensions('usability/codefolding/main');
IPython.load_extensions('toggle_all_line_number.js');



    


















    



























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import scipy.constants as sc



    











In [4]:



    


import time
import datetime

Standard Hamiltonian

$$ \lambda \left({{b}^\dagger} {\sigma_-} + {b} {\sigma_+} - \frac{g^{2} {{b}^\dagger} {\sigma_-}}{2 \Delta^{2}} - \frac{g^{2} {b} {\sigma_+}}{2 \Delta^{2}} - \frac{g^{2} \left({{c}^\dagger}\right)^{2}}{\Delta^{2}} {\sigma_-} {b} - \frac{g^{2} \left({c}\right)^{2}}{\Delta^{2}} {\sigma_+} {{b}^\dagger}\right) + w_{mr} {{b}^\dagger} {b} + {{c}^\dagger} {c} \left(\omega_{c} + \frac{g^{2} {\sigma_z}}{\Delta} - \frac{g^{2} \lambda}{\Delta^{2}} {{b}^\dagger} {\sigma_-} - \frac{g^{2} \lambda}{\Delta^{2}} {b} {\sigma_+}\right) + {\sigma_z} \left(\frac{w_{q}}{2} + \frac{g^{2}}{2 \Delta} + \frac{g \lambda}{\Delta} {{b}^\dagger} {c} + \frac{g \lambda}{\Delta} {{c}^\dagger} {b}\right) $$ 




In [5]:



    


# Hamiltonians Functions
def Ht(t, args):
    #
    # evaluate the hamiltonian at time t. 
    #
    
    H0 = args['H0']
    c = args['c']
    cDag = args['cDag']
    A = args['A']
    
    w  = args['w']

    return H0 + A * (c + cDag)*cos(w*t) #(a * exp(1j*w*t) + aDag * exp(-1j*w*t))




# Calc Spectrum
def calc_spectrum_6(N,M,P, w_c,w_nr, w_q,L,g,A,w=0, **kwargs):
    
    # dispersive Qubit CPW NR 
    Delta = w_q - w_c
    delta = w_q - w_nr
    # qubit operators
    
    sm = tensor(create(2),qeye(M),qeye(P))
    sz = tensor(sigmaz(),qeye(M),qeye(P))
    sx = tensor(sigmax(),qeye(M),qeye(P))
    nq = sm.dag() * sm
    xq = sm + sm.dag()
    I = tensor(qeye(2), qeye(M),qeye(P))
    
    
    # mechanical resonator operators
    
    b = tensor(qeye(2),destroy(M),qeye(P))
    n_b = b.dag() * b
    x_b = b.dag() + b
    p_b = b - b.dag()
    
    
    # CPW operators
    
    c = tensor(qeye(2),qeye(M),destroy(P))
    n_c = c.dag() * c
    x_c = c.dag() + c
    p_c = c - c.dag()
    
    # Identity
    
    I = tensor(qeye(2),qeye(M),qeye(P))
    
    
#      Hamiltonian
    if 'Full' in kwargs:
        H1 = w_nr * (b.dag() * b + 1/2) + L * sx *(b.dag() + b)

        H2 =   w_c      * (c.dag() * c + 1/2)  + g * (c.dag()*sm + c*sm.dag())
        H2a = (w_c - w) * (c.dag() * c )  + g * (c.dag()*sm + c*sm.dag())

        H3 = -sz *(w_q/2)

        H4 = A * (c.dag() + c)
        
    
    
    
    if 'Disp' in kwargs:
        
       
        H1 = w_nr * (b.dag() * b + 1/2) + L * sx *(b.dag() + b)

        H2 = (c.dag() * c ) * ( w_c + g**2/Delta*sz)
        H2a = (c.dag() * c ) * ( w_c - w + g**2/Delta*sz)

        H3 = sz *(w_q/2 + g**2/2/Delta) 

        H4 = A * (c.dag() + c)
        
        
    if 'Disp-RWA' in kwargs:
        
   
        
        H1 = w_nr * (b.dag() * b + 1/2) + L * (b.dag()*sm + b*sm.dag())

        H2 = (c.dag() * c ) * ( w_c + g**2/Delta*sz)
        H2a = (c.dag() * c ) * ( w_c - w + g**2/Delta*sz)

        H3 = sz *(w_q/2 + g**2/2/Delta) 

        H4 = A * (c.dag() + c)
    
    if '2Disp' in kwargs:
        
        H1 =  b.dag()*b *(w_nr - 2 * g * L**2 /Delta / delta *(sm*c.dag() + sm.dag() *c)) 
        - g*L**2/Delta/delta*(c.dag()*sm+c*sm.dag())
        
        H2 = c.dag()*c *(w_c + g**2/Delta * sz 
                         + (Delta + delta)*(
                         - ((g*L)/(Delta * delta))**2 
                         * ( 1 + sz + 2* b.dag()*b * sz )   
                        ))
        H2a = c.dag()*c *(w_c-w + g**2/Delta * sz 
                         + (Delta + delta)*(
                         - ((g*L)/(Delta * delta))**2 
                         * ( 1 + sz + 2* b.dag()*b * sz )   
                        ))
   
                         
        
        H3 = sz *(w_q/2 + g**2/2/Delta 
                  + b.dag()*b *(L**2/delta - (g*L/Delta/delta)**2*(delta+ Delta) ) 
                  + (L**2/2/delta - (g*L/Delta/delta)**2/2*(delta+Delta) ))
        
        H4 = A * (c.dag() + c) 
  
    
    
    
    
#     Colapse Operators
    
    c_op_list = []
    
    kappa_n = 0.0005 # cavity
    
    gamma_rel = 0.0001 # qubit
    gamma_dep = 0.002 # qubit
    
    Gamma_m = 0.01 # MR
    
    Ta = 60e-3 #k
    Tb = 60e-3 #k
    Tq = 30e-3 #K
    
    n_th_a = 1/(exp(sc.h*w_q*1e9/(sc.k*Ta)-1))
    
    n_th_q = 1/(exp(sc.h*w_q*1e9/(sc.k*Tq)-1))
    
    if Tb == 0:
         n_th_b = 0
    else:
        
        n_th_b = 1/(exp(sc.h*w_nr*1e9/(sc.k*Tb)-1))
    
    # cavity
    c_op_list = []

    rate = kappa_n * (1 + n_th_a)
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * c)

    rate = kappa_n * n_th_a
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * c.dag())

    rate = gamma_rel * (1 + n_th_q)
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * sm)

    rate = gamma_rel * (n_th_q)
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * sm.dag())

    rate = gamma_dep / 2 * (1 + n_th_q)
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * sz)
        
    rate = Gamma_m * (1 + n_th_b)
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * b)

    rate = Gamma_m * n_th_b
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * b.dag())    
        
    
# Solution Type    
    if 'dispersive' in kwargs:
               
        H0 = H1 + H2a + H3 + H4 #+ H5
        rho = steadystate(H0,c_op_list)
        rho_b = rho*n_b
        rho_a = rho*sz
        rho_c = rho*c
        rho_d = rho*n_c
        
        return rho_c.tr(),rho_a.tr(),rho_b.tr(),rho_d.tr()
    
    
    if 'mapping' in kwargs:
               
        H0 = H1 + H2w + H3 + H4 #+ H5
        rho = steadystate(H0,c_op_list)
        rho_c = rho*c
        return rho_c.tr()
    
    if 'energies'in kwargs:
        H = H1 + H2 + H3
        
        return H.eigenenergies() #+ H4
    
    if 'time'in kwargs:
        
        H0 = H1 + H2 + H3 #+ H4 
        H_args = {'H0': H0, 'c': c, 'cDag': c.dag() , 'A' : A , 'w': w}

    #     rho = steadystate(H,c_op_list)

        T = 2 * pi / w

        U = propagator(Ht, T, c_op_list, H_args)

        rho_ss = propagator_steadystate(U)

        
        rho_b = rho_ss*n_b
        rho_a = rho_ss*sz
        rho_c = rho_ss*c
        rho_d = rho_ss*n_c
        
        return rho_c.tr(),rho_a.tr(),rho_b.tr(),rho_d.tr()



    











In [28]:



    


N = 2
M = 5
P = 5
w_c = 5
w_nr = 3.5
g = 0.1
L = 0.001
Ej = 15
Ec = 0.223
w = 0
w_q_max = sqrt(8 * Ec * Ej) - Ec
w_q = 3.5
print(w_q_max)
d = 0.10
A = 0.00005# field aplitude
kwargs = {'num_cpus':26,'energies':1, 'Disp':1}

E = calc_spectrum_6(N,M,P, w_c,w_nr, w_q,L,g,A,w=0, **kwargs)



    


















    






4.95000686255

















In [29]:



    


E - E[0]



    


















    
Out[29]:








array([  0.        ,   3.4931867 ,   3.50014663,   5.00666667,
         6.993046  ,   7.00028733,   8.48661693,   8.5067164 ,
        10.01333333,  10.49291057,  10.50042276,  11.98656745,
        12.00676589,  13.47997017,  13.51336316,  13.99277991,
        14.00055414,  15.02      ,  15.4865182 ,  15.50681513,
        16.97994039,  17.01339294,  17.49333405,  18.47331206,
        18.52002127,  18.9864692 ,  19.00686485,  20.02666667,
        20.47991067,  20.51342266,  21.9732908 ,  22.02004253,
        22.48666738,  23.46665015,  23.52668318,  23.979881  ,
        24.01345305,  25.47326957,  25.52006377,  26.96663364,
        27.02669969,  27.48000072,  28.97324835,  29.0200857 ,
        30.46661714,  30.52671619,  32.47333405,  33.96660065,
        34.0267334 ,  37.46666739])

















In [82]:



    


N = 2
M = 5
P = 5
w_c = 5
w_nr = 3.5
g = 0.1
L = 0.001
Ej = 15
Ec = 0.223
w = 0
w_q_max = sqrt(8 * Ec * Ej) - Ec
print(w_q_max)
d = 0.10
A = 0.00005# field aplitude

# phi = linspace(0,pi/2,200)
x_i,x_f = 0.3,0.36
phi = pi*linspace(x_i,x_f,100)
x_vec =  sqrt( 8 * Ec * Ej* abs(cos(phi))*sqrt(1+(d*tan(phi))**2) )-Ec
# energies = array([calc_spectrum_6(N,M,P, w_c,w_nr, w_q/2,L,g,A,w,**kwargs)
#                   for w_q in x_vec])
kwargs = {'num_cpus':27,'energies':1, 'Disp':1}



    


















    






4.95000686255

















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In [83]:



    


# Simulate Energies


# variable to count the total number of tasks we need to do; used to create progress bar
task_count =len(x_vec)



# Check number of cpus to be used
if 'num_cpus' in kwargs:
    num_cpu = kwargs['num_cpus']
    if num_cpu == 1:
        print("1 CPU; Serial Simulation")
    else:
        print("Parallel Simulation with %d CPUs " % num_cpu)    
else:
    num_cpu = 1
    print("Serial Simulation")



## Program to run function in parallel: 

try:
    t_start = time.time() # start time simulation
    time_1 = []
    pool = mp.Pool(processes=num_cpu) #  create the initial pool to run the simulation   
#         manager = mp.Manager()
#         queue = manager.Queue()


#         _update_progress_bar(1)
#     task_args = a,z
    results = [pool.apply_async(calc_spectrum_6,(N,
                                                 M,
                                                 P,
                                                 w_c,
                                                 w_nr,
                                                 a1,
                                                 L,
                                                 g,
                                                 A,
                                                 w),kwargs
                                ,callback=None,error_callback=None) for a1 in x_vec]



    #####N,M,P, w_c,w_nr, w_q,L,g,A,w=0
    while True:
        incomplete_count = sum(1 for x in results if not x.ready())

        if incomplete_count == 0:
            print("[100.0%] of the simulations calculated, Estimated Remaining time: 0.0s", end="\r")
            print( "\nAll done! \nTotal time:%s"%datetime.timedelta(seconds=int(dif_time)))
            break

        else:

            p = float(task_count - incomplete_count) / task_count * 100 

            dif_time = (time.time() - t_start)    

#                 
            if p > 0:
                rem_time = (datetime.timedelta(seconds=int(dif_time*(100-p)/p)))

#                     rem_time_1 = (datetime.timedelta(seconds=int(dif_time/(task_count-incomplete_count))))
                time_1.append(float(dif_time/(task_count-  incomplete_count)))
#                     rem_time_1 = mean(time_1) *task_count
#                     rem_time_1 = (datetime.timedelta( seconds=int(mean(time_1) *task_count)))
                rem_time_1 = time.strftime("%Z - %Y/%m/%d, %H:%M:%S", time.localtime(t_start+mean(time_1) *task_count))
            else:
                rem_time = '?'
                rem_time_1 = 0


            print("[%4.1f%%] of the simulations calculated, Estimated Remaining time: %s, (%s)"
                  %(p,rem_time,rem_time_1) , end="\r")

            time.sleep(.25)


    while not all([ar.ready() for ar in results]):

        for ar in results:    
            ar.wait(timeout=0.1)

    pool.terminate()
    pool.join()

except KeyboardInterrupt as e:
    pool.terminate()
    pool.join()
    raise e




energies_temp = [ar.get() for ar in results]
energies = asarray(energies_temp)



    


















    






Parallel Simulation with 27 CPUs 
[100.0%] of the simulations calculated, Estimated Remaining time: 0.0s
All done! 
Total time:0:00:00

















In [84]:



    


# Plot Energies 
fig, axes = subplots(1,1, figsize=(16,6))
x_inf = -1
x_sup = 10

for n in range(len(energies[0,:])):
    axes.plot(phi/pi, (energies[:,n]-energies[:,0]),'-',linewidth=2)
#     axes.plot(phi/pi, (energies[:,n]-energies[:,0])/2,'--')
    
    if n < 4:
        axes.text(x_i,energies[0,n]-energies[0,0],r'|%s>'%(n),fontsize=20)
    
axes.set_title('Full')
axes.set_ylim(x_inf, x_sup)
axes.set_xlabel(r'$\phi$', fontsize=18)
axes.set_ylabel(r'$E_n-E_0$', fontsize=18)
axes.hlines(w_nr,x_i,x_f,linestyles='dashed',linewidth=3,color='green')
axes.hlines(w_c,x_i,x_f,linestyles='dashed',linewidth=3)
axes.vlines(0.33,0,10,linestyles='dashed',linewidth=3)



    


















    
Out[84]:








<matplotlib.collections.LineCollection at 0x7f3ca6848518>










    
























In [6]:



    


y_i,y_f = 4.95,5.05
y_vec = linspace(y_i,y_f,50) 
a , b = zip(*itertools.product(x_vec,y_vec))
kwargs = {'num_cpus':27,'dispersive':1, 'Disp':1}



    


















    






---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-6-f9117e8a753a> in <module>()
      1 y_i,y_f = 4.95,5.05
      2 y_vec = linspace(y_i,y_f,50)
----> 3 a , b = zip(*itertools.product(x_vec,y_vec))
      4 kwargs = {'num_cpus':27,'dispersive':1, 'Disp':1}

NameError: name 'x_vec' is not defined
















In [ ]:



    


# Run Spectrum
# Create from the original vectors the new vector with the correct number copies
a , b = zip(*itertools.product(x_vec,y_vec))
# variable to count the total number of tasks we need to do; used to create progress bar
task_count =len(x_vec)*len(y_vec)

# Check number of cpus to be used
if 'num_cpus' in kwargs:
    num_cpu = kwargs['num_cpus']
    if num_cpu == 1:
        print("1 CPU; Serial Simulation")
    else:
        print("Parallel Simulation with %d CPUs " % num_cpu)    
else:
    num_cpu = 1
    print("Serial Simulation")



## Program to run function in parallel: 
t_start = time.time() # start time simulation
time_1 = []
try:
    pool = mp.Pool(processes=num_cpu) #  create the initial pool to run the simulation   
#         manager = mp.Manager()
#         queue = manager.Queue()


#         _update_progress_bar(1)
#     task_args = a,z
    results = [pool.apply_async(calc_spectrum_6,(N,
                                                 M,
                                                 P,
                                                 w_c,
                                                 w_nr,
                                                 a1,
                                                 L,
                                                 g,
                                                 A,
                                                 b1),kwargs
                                ,callback=None,error_callback=None) for a1,b1 in zip(a,b)]



        #####
    while True:
        incomplete_count = sum(1 for x in results if not x.ready())

        if incomplete_count == 0:
            print("[100.0%] of the simulations calculated, Estimated Remaining time: 0.0s", end="\r")
            print( "\nAll done! \nMean time:%f"%(dif_time/task_count))
            print( "\nTotal time:%s"%datetime.timedelta(seconds=int(dif_time)))
            break

        else:

            p = float(task_count - incomplete_count) / task_count * 100 

            dif_time = (time.time() - t_start)    

#                 
            if p > 0:
                rem_time = (datetime.timedelta(seconds=int(dif_time*(100-p)/p)))

#                     rem_time_1 = (datetime.timedelta(seconds=int(dif_time/(task_count-incomplete_count))))
                time_1.append(float(dif_time/(task_count -  incomplete_count)))
#                     rem_time_1 = mean(time_1) *task_count
#                     rem_time_1 = (datetime.timedelta( seconds=int(mean(time_1) *task_count)))
                rem_time_1 = time.strftime("%Z - %Y/%m/%d, %H:%M:%S", time.localtime(t_start+mean(time_1) *task_count))
            else:
                rem_time = '?'
                rem_time_1 = 0


            print("[%4.1f%%] of the simulations calculated, Estimated Remaining time: %s, (%s)"
                  %(p,rem_time,rem_time_1) , end="\r")

            time.sleep(.25)


    while not all([ar.ready() for ar in results]):

        for ar in results:    
            ar.wait(timeout=0.1)

    pool.terminate()
    pool.join()

except KeyboardInterrupt as e:
    pool.terminate()
    pool.join()
    raise e




results = [ar.get() for ar in results]



    











In [87]:



    


# Reshape Results
#results = qload('Two_Dispersive_Simulation')
results_1 = asarray(results)
# qsave(results,name='One_Dispersive_Simulation_200x300')
#qsave(results,name='Two_Dispersive_Simulation')
# qsave(results,name='ThirtytyVolts')

tr_c = reshape(results_1[:,0],(-1,len(y_vec+1)))
tr_a = reshape(results_1[:,1],(-1,len(y_vec+1)))
tr_b = reshape(results_1[:,2],(-1,len(y_vec+1)))
tr_d = reshape(results_1[:,3],(-1,len(y_vec+1)))



    











In [88]:



    


# Plot Graphics
fig, ax = subplots(4,1, figsize=(16,20))



im = ax[0].pcolor(phi/pi,y_vec,transpose(log10(abs(tr_c))))#,vmin=0, vmax=1)
fig.colorbar(im, ax=ax[0])
# ax[0,0].set_xlim(4.27,4.39)
# ax[0,0].set_ylim(P_i,P_f)
ax[0].set_ylabel(r'Probe Frequency (GHz)',fontsize=20)
# ax[0].set_xlabel(r'Qubit Tone Frequency (GHz)',fontsize=10)
ax[0].set_title(r'$Tr[\rho c]$',fontsize=20)


im = ax[1].pcolor(phi/pi,y_vec,transpose((abs(tr_a))))#,vmin=0, vmax=1)
fig.colorbar(im, ax=ax[1])
# ax[0,0].set_xlim(4.27,4.39)
# ax[0,0].set_ylim(P_i,P_f)
ax[1].set_ylabel(r'Probe Frequency (GHz)',fontsize=20)
# ax[1].set_xlabel(r'Qubit Tone Frequency (GHz)',fontsize=10)
ax[1].set_title(r'$Tr[\rho \sigma_z]$',fontsize=20)

im = ax[2].pcolor(phi/pi,y_vec,transpose(log10(abs(tr_b))))#,vmin=0, vmax=1)
fig.colorbar(im, ax=ax[2])
# ax[0,0].set_xlim(4.27,4.39)
# ax[0,0].set_ylim(P_i,P_f)
ax[2].set_ylabel(r'Probe Frequency (GHz)',fontsize=20)
# ax[2].set_xlabel(r'Qubit Tone Frequency (GHz)',fontsize=10)
ax[2].set_title(r'$Tr[\rho b^\dagger  b]$',fontsize=20)

im = ax[3].pcolor(phi/pi,y_vec,transpose((abs(tr_d))))#,vmin=0, vmax=1)
fig.colorbar(im, ax=ax[3])
# ax[0,0].set_xlim(4.27,4.39)
# ax[0,0].set_ylim(P_i,P_f)
ax[3].set_ylabel(r'Probe Frequency (GHz)',fontsize=20)
ax[3].set_xlabel(r'Flux ($\Phi_0$)',fontsize=20)
ax[3].set_title(r'$Tr[\rho c^\dagger c]$',fontsize=20)



    


















    
Out[88]:








<matplotlib.text.Text at 0x7f3ca650c6d8>










    
























In [89]:



    


# Plot Graphic II
fig, axes = subplots(1,1, figsize=(16,10))
y_inf = y_i
y_sup = y_f
x_inf = x_i
x_sup = x_f

for n in range(len(energies[0,:])):
    axes.plot(phi/pi, (energies[:,n]-energies[:,0]),'-',linewidth=1)
    axes.plot(phi/pi, (energies[:,n]-energies[:,0])/2,'--')
    
#     if n < 4:
#         axes.text(.2,energies[0,n]-energies[0,0],r'|%s>'%(n),fontsize=20)
    
axes.set_title('Full')
axes.set_ylim(y_inf, y_sup)
axes.set_xlim(x_inf,x_sup)


axes.set_xlabel(r'$\phi$', fontsize=18)
axes.set_ylabel(r'Cavity Tone Frequency GHz', fontsize=18)
axes.hlines(w_nr,x_i,x_f,linestyles='dashed')
axes.hlines(w_c,x_i,x_f,linestyles='dashed')
# axes.vlines(0.245,0,10,linestyles='dashed',linewidth=3)
axes.vlines(0.33,0,10,linestyles='dashed')

im = axes.pcolor(phi/pi,y_vec,transpose(log10(abs(tr_c))))#axes.pcolor(phi/pi,y_vec,transpose((abs(tr))))#,vmin=0, vmax=1)
fig.colorbar(im, ax=axes)
# ax[0,0].set_xlim(4.27,4.39)
# ax[0,0].set_ylim(P_i,P_f)
# axes.set_ylabel(r'Qubit Tone Power(dBm)',fontsize=10)
# axes.set_xlabel(r'Qubit Tone Frequency (GHz)',fontsize=10)
# axes.set_title(r'$Tr[\rho\sigma_z]$',fontsize=20)



    


















    
Out[89]:








<matplotlib.colorbar.Colorbar at 0x7f3ca5bb0048>

Scan Coupling





In [397]:



    


phi = 0.33 * pi
w_q = sqrt( 8 * Ec * Ej* abs(cos(phi))*sqrt(1+(d*tan(phi))**2) )-Ec


x_i,x_f = 0.0,0.005
x_vec= linspace(x_i,x_f,60)

y_i,y_f = 4.98,5.02
y_vec = linspace(y_i,y_f,30) 

a , b = zip(*itertools.product(x_vec,y_vec))
kwargs = {'num_cpus':26,'dispersive':1, 'sc':1}



    











In [398]:



    


# Run Spectrum
# Create from the original vectors the new vector with the correct number copies
a , b = zip(*itertools.product(x_vec,y_vec))
# variable to count the total number of tasks we need to do; used to create progress bar
task_count =len(x_vec)*len(y_vec)

# Check number of cpus to be used
if 'num_cpus' in kwargs:
    num_cpu = kwargs['num_cpus']
    if num_cpu == 1:
        print("1 CPU; Serial Simulation")
    else:
        print("Parallel Simulation with %d CPUs " % num_cpu)    
else:
    num_cpu = 1
    print("Serial Simulation")



## Program to run function in parallel: 
t_start = time.time() # start time simulation
time_1 = []
try:
    pool = mp.Pool(processes=num_cpu) #  create the initial pool to run the simulation   
#         manager = mp.Manager()
#         queue = manager.Queue()


#         _update_progress_bar(1)
#     task_args = a,z
    results = [pool.apply_async(calc_spectrum_6,(N,
                                                 M,
                                                 P,
                                                 w_c,
                                                 w_nr,
                                                 w_q,
                                                 a1,
                                                 g,
                                                 A,
                                                 b1),kwargs
                                ,callback=None,error_callback=None) for a1,b1 in zip(a,b)]



        #####calc_spectrum_6(N,M,P, w_c,w_nr, w_q,L,g,A,w=0, **kwargs)
    while True:
        incomplete_count = sum(1 for x in results if not x.ready())

        if incomplete_count == 0:
            print("[100.0%] of the simulations calculated, Estimated Remaining time: 0.0s", end="\r")
            print( "\nAll done! \nMean time:%f"%(dif_time/task_count))
            print( "\nTotal time:%s"%datetime.timedelta(seconds=int(dif_time)))
            break

        else:

            p = float(task_count - incomplete_count) / task_count * 100 

            dif_time = (time.time() - t_start)    

#                 
            if p > 0:
                rem_time = (datetime.timedelta(seconds=int(dif_time*(100-p)/p)))

#                     rem_time_1 = (datetime.timedelta(seconds=int(dif_time/(task_count-incomplete_count))))
                time_1.append(float(dif_time/(task_count -  incomplete_count)))
#                     rem_time_1 = mean(time_1) *task_count
#                     rem_time_1 = (datetime.timedelta( seconds=int(mean(time_1) *task_count)))
                rem_time_1 = time.strftime("%Z - %Y/%m/%d, %H:%M:%S", time.localtime(t_start+mean(time_1) *task_count))
            else:
                rem_time = '?'
                rem_time_1 = 0


            print("[%4.1f%%] of the simulations calculated, Estimated Remaining time: %s, (%s)"
                  %(p,rem_time,rem_time_1) , end="\r")

            time.sleep(.25)


    while not all([ar.ready() for ar in results]):

        for ar in results:    
            ar.wait(timeout=0.1)

    pool.terminate()
    pool.join()

except KeyboardInterrupt as e:
    pool.terminate()
    pool.join()
    raise e




results = [ar.get() for ar in results]



    


















    






Parallel Simulation with 26 CPUs 
[100.0%] of the simulations calculated, Estimated Remaining time: 0.0s
All done! 
Mean time:0.114948

Total time:0:03:26

















In [399]:



    


#results = qload('Two_Dispersive_Simulation')
results_2 = asarray(results)
# qsave(results,name='One_Dispersive_Simulation_200x300')
#qsave(results,name='Two_Dispersive_Simulation')
# qsave(results,name='ThirtytyVolts')

tr_c = reshape(results_2[:,0],(-1,len(y_vec+1)))
tr_a = reshape(results_2[:,1],(-1,len(y_vec+1)))
tr_b = reshape(results_2[:,2],(-1,len(y_vec+1)))
tr_d = reshape(results_2[:,3],(-1,len(y_vec+1)))



    











In [400]:



    


# Plot Graphics
fig, ax = subplots(4,1, figsize=(16,20))



im = ax[0].pcolor(x_vec,y_vec,transpose(log10(abs(tr_c))))#,vmin=0, vmax=1)
fig.colorbar(im, ax=ax[0])
# ax[0,0].set_xlim(4.27,4.39)
# ax[0,0].set_ylim(P_i,P_f)
ax[0].set_ylabel(r'Probe Frequency (GHz)',fontsize=20)
# ax[0].set_xlabel(r'Qubit Tone Frequency (GHz)',fontsize=10)
ax[0].set_title(r'$Tr[\rho c]$',fontsize=20)


im = ax[1].pcolor(x_vec,y_vec,transpose((abs(tr_a))))#,vmin=0, vmax=1)
fig.colorbar(im, ax=ax[1])
# ax[0,0].set_xlim(4.27,4.39)
# ax[0,0].set_ylim(P_i,P_f)
ax[1].set_ylabel(r'Probe Frequency (GHz)',fontsize=20)
# ax[1].set_xlabel(r'Qubit Tone Frequency (GHz)',fontsize=10)
ax[1].set_title(r'$Tr[\rho \sigma_z]$',fontsize=20)

im = ax[2].pcolor(x_vec,y_vec,transpose(log10(abs(tr_b))))#,vmin=0, vmax=1)
fig.colorbar(im, ax=ax[2])
# ax[0,0].set_xlim(4.27,4.39)
# ax[0,0].set_ylim(P_i,P_f)
ax[2].set_ylabel(r'Probe Frequency (GHz)',fontsize=20)
# ax[2].set_xlabel(r'Qubit Tone Frequency (GHz)',fontsize=10)
ax[2].set_title(r'$Tr[\rho b^\dagger  b]$',fontsize=20)

im = ax[3].pcolor(x_vec,y_vec,transpose((abs(tr_d))))#,vmin=0, vmax=1)
fig.colorbar(im, ax=ax[3])
# ax[0,0].set_xlim(4.27,4.39)
# ax[0,0].set_ylim(P_i,P_f)
ax[3].set_ylabel(r'Probe Frequency (GHz)',fontsize=20)
ax[3].set_xlabel(r'$\lambda$ GHz',fontsize=20)
ax[3].set_title(r'$Tr[\rho c^\dagger c]$',fontsize=20)



    


















    
Out[400]:








<matplotlib.text.Text at 0x7f10d711ea20>

Simulation New Hamiltonian

$$ H = -\dfrac{E_{el}}{2}\sigma_x -\dfrac{E_J}{2}\sigma_z +\omega_c c^\dagger c +\omega_{NR} b^\dagger b $$ 




In [515]:



    


def calc_spectrum_7(M,P, w_c,w_nr, E_j,E_c, nac, ndc, g, A, w=0, **kwargs):
    
    # dispersive Qubit CPW NR 
   
    # qubit operators
    
    sm = tensor(destroy(2),qeye(M),qeye(P))
    sz = tensor(sigmaz(),qeye(M),qeye(P))
    sx = tensor(sigmax(),qeye(M),qeye(P))
    nq = sm.dag() * sm
    xq = sm + sm.dag()
    I = tensor(qeye(2), qeye(M),qeye(P))
    
    
    # mechanical resonator operators
    
    b = tensor(qeye(2),destroy(M),qeye(P))
    n_b = b.dag() * b
    x_b = b.dag() + b
    p_b = b - b.dag()
    
    
    # CPW operators
    
    c = tensor(qeye(2),qeye(M),destroy(P))
    n_c = c.dag() * c
    x_c = c.dag() + c
    p_c = c - c.dag()
    
    # Identity
    
    I = tensor(qeye(2),qeye(M),qeye(P))
    
    
    # Hamiltonian
    
    H1 = w_nr * b.dag()*b
    
    H2 = w_c * c.dag()* c
    
    H2a = (w_c-w)*c.dag()*c
    
    ng = I/2 + nac * (c.dag() + c) + ndc * (b.dag() + b)
    Ecx = E_c * (1 + g*x_b)
    
    E_el = 4*Ecx*(1-2*ng)

    
    H3 = - E_el/2 * sx 
    
    H4 = - E_j/2 * sz
    
    H5 = A*x_c
    
    # Time domain
    
    
    
    
    # Colapse Operators
    
    c_op_list = []
    
    kappa_n = 0.0002468 # cavity
    
    gamma_rel = 6.66e-04 # qubit
    gamma_dep = 0.0012 # qubit
    
    Gamma_m = 0.001 # MR
    
    Ta = 60e-3 #k
    Tb = 60e-3 #k
    
    n_th_a = 1/(exp(sc.h*E_j*1e9/(sc.k*Ta)-1))
    n_th_b = 1/(exp(sc.h*w_nr*1e9/(sc.k*Tb)-1))
    
    # cavity
    c_op_list = []

    rate = kappa_n * (1 + n_th_a)
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * c)

    rate = kappa_n * n_th_a
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * c.dag())

    rate = gamma_rel * (1 + n_th_a)
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * sm)

    rate = gamma_rel * (n_th_a)
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * sm.dag())

    rate = gamma_dep / 2 * (1 + n_th_a)
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * sz)
        
    rate = Gamma_m * (1 + n_th_b)
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * b)

    rate = Gamma_m * n_th_b
    if rate > 0.0:
        c_op_list.append(sqrt(rate) * b.dag())    
        
    
    
#     if 'dispersive' in kwargs:
               
#         H0 = H1 + H2b + H4 #+ H5
#         rho = steadystate(H0,c_op_list)
#         rho_c = rho*c
#         return rho_c.tr()
    
    
    if 'mapping' in kwargs:
               
        H0 = H1 + H2a + H3 + H4 + H5
        rho = steadystate(H0,c_op_list)
        rho_c = rho*c
        return rho_c.tr()
    
    elif 'energies'in kwargs:
        H = H1 + H2 + H3 + H4 #+ H3
        
        return H.eigenenergies() #+ H4
    
#     elif 'time'in kwargs:
        
#         H0 = H1 + H2 + H3 + H4 
#         H_args = {'H0': H0, 'c': c, 'cDag': c.dag() , 'A' : A , 'w': w}

#     #     rho = steadystate(H,c_op_list)

#         T = 1/ w

#         U = propagator(Ht, T, c_op_list, H_args)

#         rho_ss = propagator_steadystate(U)

#         rho_c = rho_ss*c
        
#         return rho_c.tr()



    











In [516]:



    


N,M,P = 2, 3 ,3

# qubit Cavity parameters
Ej_max = 16 
Ej = 4 
Ec = 0.2 
w_nr = 3.5 
w_c = 5  
Cg = 10e-15 
Cc = 1e-12
Cb = 50e-15
Cnr = 2e-17

# mechanical resonator

m = (700e-9)*(65e-9)*(100e-9)*2700 
Xzpm = sqrt(sc.hbar/(2*m*w_nr*2*pi*1e9))
print('X_ZPM =',Xzpm)
d0 = 30e-9 
g0 = Ec/d0 *Cnr/(Cg+Cb+Cnr)*Xzpm*1e9
print('g0 =', g0)

# Cavity effect
n_ac = Cg /2/sc.e * sqrt(sc.h*w_c*2*pi*1e9/2/Cc)
print('N_ac =',n_ac)

V_dc = 10

n_dc = Cnr/d0*V_dc/2/sc.e*Xzpm*100

print('n_dc = ',n_dc)

d = 0.1 # asymetry 

A = 0.0005# field aplitude

w = 5.001
print('E_q =', sqrt(8 * Ec * Ej_max) - Ec)

d = 0.1
A = 0.0003# field aplitude
kwargs = {'energies':12}

# phi = linspace(0,pi/2,200)
x_i,x_f = 0,1
phi = pi*linspace(x_i,x_f,100)
x_vec =  (sqrt(8 * Ec * Ej_max) - Ec) * abs(cos(phi))*sqrt(1+(d*tan(phi))**2)
# energies = array([calc_spectrum_6(N,M,P, w_c,w_nr, w_q/2,L,g,A,w,**kwargs)
#                   for w_q in x_vec])



    


















    






X_ZPM = 1.39704864016e-14
g0 = 0.0310351802769
N_ac = 0.100681009983
n_dc =  0.0290656404686
E_q = 4.85964425627

















In [517]:



    


kwargs = {'num_cpus':12,'energies':1}

# variable to count the total number of tasks we need to do; used to create progress bar
task_count =len(x_vec)



# Check number of cpus to be used
if 'num_cpus' in kwargs:
    num_cpu = kwargs['num_cpus']
    if num_cpu == 1:
        print("1 CPU; Serial Simulation")
    else:
        print("Parallel Simulation with %d CPUs " % num_cpu)    
else:
    num_cpu = 1
    print("Serial Simulation")



## Program to run function in parallel: 

try:
    t_start = time.time() # start time simulation
    time_1 =[]
    pool = mp.Pool(processes=num_cpu) #  create the initial pool to run the simulation   
#         manager = mp.Manager()
#         queue = manager.Queue()


#         _update_progress_bar(1)
#     task_args = a,z
    results = [pool.apply_async(calc_spectrum_7,(M,
                                                 P,
                                                 w_c,
                                                 w_nr,
                                                 a1,
                                                 Ec,
                                                 n_ac,
                                                 n_dc,
                                                 g,
                                                 A,
                                                 w),
                                kwargs
                                ,callback=None,error_callback=None) for a1 in x_vec]



    #####
    while True:
        incomplete_count = sum(1 for x in results if not x.ready())

        if incomplete_count == 0:
            print("[0.0%] of the simulations calculated, Estimated Remaining time: 0.0s", end="\r")
            print( "\nAll done! \nApproximated total time:%s"%datetime.timedelta(seconds=int(dif_time)))
            break

        else:

            p = float(task_count - incomplete_count) / task_count * 100 
            
            dif_time = (time.time() - t_start)    
            if p > 0:

                rem_time = (datetime.timedelta(seconds=int(dif_time*(100-p)/p)))
                time_1.append(float(dif_time/(task_count-  incomplete_count)))
#                     rem_time_1 = mean(time_1) *task_count
                rem_time_1 = (datetime.timedelta(seconds=int(mean(time_1) * task_count)))
            else:
                rem_time = 0
                rem_time_1 = 0

            print("[%4.1f%%] of the simulations calculated, Estimated: Remaining: %s (Total %s)"
                  %(p,rem_time,rem_time_1) , end="\r")

            time.sleep(.25)


    while not all([ar.ready() for ar in results]):

        for ar in results:    
            ar.wait(timeout=0.1)

    pool.terminate()
    pool.join()

except KeyboardInterrupt as e:
    pool.terminate()
    pool.join()
    raise e



energies_temp = [ar.get() for ar in results]
energies = asarray(energies_temp)



    


















    






Parallel Simulation with 12 CPUs 
[0.0%] of the simulations calculated, Estimated Remaining time: 0.0s
All done! 
Approximated total time:0:00:02

















In [518]:



    


fig, axes = subplots(1,1, figsize=(16,6))
x_inf = 0
x_sup = 10

for n in range(len(energies[0,:])):
    axes.plot(phi/pi, (energies[:,n]-energies[:,0]),'-',linewidth=2)
#     axes.plot(phi/pi, (energies[:,n]-energies[:,0])/2,'--')
    
#     if n < 4:
#         axes.text(.2,energies[0,n]-energies[0,0],r'|%s>'%(n),fontsize=20)
    
axes.set_title('Full')
axes.set_ylim(x_inf, x_sup)
axes.set_xlabel(r'$\phi$', fontsize=18)
axes.set_ylabel(r'$E_n-E_0$', fontsize=18)
axes.hlines(w_nr,x_i,x_f,linestyles='dashed',linewidth=3,color='green')
axes.hlines(w_c,x_i,x_f,linestyles='dashed',linewidth=3)
axes.vlines(0.255,0,10,linestyles='dashed',linewidth=3)



    


















    
Out[518]:








<matplotlib.collections.LineCollection at 0x7f9ef8e26f60>










    
























In [519]:



    


y_i,y_f = 4.7,5.3
y_vec = linspace(y_i,y_f,100) 
    
# phi = linspace(0,pi/2,100)

# x_vec =  w_q_max * abs(cos(phi))*sqrt(1+(d*tan(phi))**2)



# a , b = zip(*itertools.product(x_vec,y_vec))
kwargs = {'num_cpus':12,'mapping':1}



    











In [520]:



    


# Create from the original vectors the new vector with the correct number copies
a , b = zip(*itertools.product(x_vec,y_vec))
# variable to count the total number of tasks we need to do; used to create progress bar
task_count =len(x_vec)*len(y_vec)



# Check number of cpus to be used
if 'num_cpus' in kwargs:
    num_cpu = kwargs['num_cpus']
    if num_cpu == 1:
        print("1 CPU; Serial Simulation")
    else:
        print("Parallel Simulation with %d CPUs " % num_cpu)    
else:
    num_cpu = 1
    print("Serial Simulation")



## Program to run function in parallel: 

try:
    t_start = time.time() # start time simulation
    pool = mp.Pool(processes=num_cpu) #  create the initial pool to run the simulation   
#         manager = mp.Manager()
#         queue = manager.Queue()


#         _update_progress_bar(1)
#     task_args = a,z
    results = [pool.apply_async(calc_spectrum_7,(M,
                                                 P,
                                                 w_c,
                                                 w_nr,
                                                 a1,
                                                 n_ac,
                                                 n_dc,
                                                 g,
                                                 A,
                                                 b1),kwargs
                                ,callback=None,error_callback=None) for a1,b1 in zip(a,b)]



    #####
    while True:
        incomplete_count = sum(1 for x in results if not x.ready())

        if incomplete_count == 0:
            print("[0.0%] of the simulations calculated, Estimated Remaining time: 0.0s", end="\r")
            print( "\nAll done! \nApproximated total time:%s"%datetime.timedelta(seconds=int(dif_time)))
            break

        else:

            p = float(task_count - incomplete_count) / task_count * 100 
            
            dif_time = (time.time() - t_start)    
            if p > 0:

                rem_time = (datetime.timedelta(seconds=int(dif_time*(100-p)/p)))
                time_1.append(float(dif_time/(task_count-  incomplete_count)))
#                     rem_time_1 = mean(time_1) *task_count
                rem_time_1 = (datetime.timedelta(seconds=int(mean(time_1) * task_count)))
            else:
                rem_time = 0
                rem_time_1 = 0

            print("[%4.1f%%] of the simulations calculated, Estimated Remaining: %s (Total %s)"
                  %(p,rem_time,rem_time_1) , end="\r")

            time.sleep(.25)


    while not all([ar.ready() for ar in results]):

        for ar in results:    
            ar.wait(timeout=0.1)

    pool.terminate()
    pool.join()

except KeyboardInterrupt as e:
    pool.terminate()
    pool.join()
    raise e



results = [ar.get() for ar in results]



    


















    






Parallel Simulation with 12 CPUs 
[0.0%] of the simulations calculated, Estimated Remaining time: 0.0s
All done! 
Approximated total time:0:08:36

















In [ ]:



    






    











In [521]:



    


tr = reshape(results,(-1,len(y_vec+1)))
shape(tr)



    


















    
Out[521]:








(100, 100)

















In [522]:



    


fig, axes = subplots(1,1, figsize=(16,10))


for n in range(len(energies[0,:])):
    axes.plot(phi/pi, (energies[:,n]-energies[:,0]),'-',linewidth=3)
    axes.plot(phi/pi, (energies[:,n]-energies[:,0])/2,'--')
    
#     if n < 4:
#         axes.text(.2,energies[0,n]-energies[0,0],r'|%s>'%(n),fontsize=20)
    
axes.set_title('Full')
axes.set_ylim(y_i, y_f)
axes.set_xlim(x_i,x_f)


axes.set_xlabel(r'$\phi$', fontsize=18)
axes.set_ylabel(r'Cavity Tone Frequency GHz', fontsize=18)
axes.hlines(w_nr,x_i,x_f,linestyles='dashed')
axes.hlines(w_c,x_i,x_f,linestyles='dashed')
axes.vlines(0.245,0,10,linestyles='dashed',linewidth=3)
# axes.vlines(0.24,0,10,linestyles='dashed')

im = axes.pcolor(phi/pi,y_vec,transpose(log(abs(tr))))#axes.pcolor(phi/pi,y_vec,transpose((abs(tr))))#,vmin=0, vmax=1)
fig.colorbar(im, ax=axes)
# ax[0,0].set_xlim(4.27,4.39)
# ax[0,0].set_ylim(P_i,P_f)
# axes.set_ylabel(r'Qubit Tone Power(dBm)',fontsize=10)
# axes.set_xlabel(r'Qubit Tone Frequency (GHz)',fontsize=10)
# axes.set_title(r'$Tr[\rho\sigma_z]$',fontsize=20)



    


















    
Out[522]:








<matplotlib.colorbar.Colorbar at 0x7f9f0d7e80b8>










    
























In [ ]:



    






    











In [ ]:



    






    











In [ ]:

Content source: rouxinol/HybridSystem

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