pdc-quantum

Keybase proof

I hereby claim:

• I am pierredc on github.
• I am pierredc (https://keybase.io/pierredc) on keybase.
• I have a public key ASB9VnZNw9mP3CqUh3-Ck40NjzqcsaWezeVpNldjh57BLAo

To claim this, I am signing this object:

pdc-quantum

x = np.array([ 
   [1,29,57,85,113,141,169,197,225,253,1,29,57,85,113,141,169,197,225,253],
   [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
   [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] ])

counts = np.array([ 
   [966,675,542,406,362,355,296,284,238,244,960,503,322,342,291,252,245,267,256,250],
   [943,608,487,404,310,276,290,248,250,248,951,623,429,337,279,248,248,251,268,252],
   [971,687,550,391,372,293,278,264,259,260,940,596,424,320,285,251,249,231,253,253],
   [961,660,501,416,316,294,299,268,253,239,966,632,413,339,269,265,276,241,254,262],

pdc-quantum

from scipy.optimize import curve_fit

def gsp(x, a, alpha, alpha_c, b):
    return    x[1] * (a * alpha ** x[0] + b) \
            + x[2] * (a * (alpha * alpha_c) ** x[0] + b)

pdc-quantum

# curve fit
popt, pcov = curve_fit(f = gsp, xdata = x,
                       ydata = np.mean(counts, axis = 0) / shots,
                       sigma = np.std(counts, axis = 0) / shots / np.sqrt(num_samples),
                       absolute_sigma = True,
                       bounds = ([scale - .1, .9, .9, (1. - scale) - .1],
                                 [scale + .1, 1., 1., (1. - scale) + .1]))

# statistical error on pararameters
perr = np.sqrt(np.diag(pcov))

pdc-quantum

import pymc3 as pm
h_model = pm.Model()

pdc-quantum

with h_model:
    BoundedUniform = pm.Bound(pm.Uniform,
                              lower=np.fmax(popt-0.1, np.full(popt.shape, 1.e-9)),
                              upper=np.fmin(popt+0.1, np.full(popt.shape, 1.-1.e-9)))
    
    pi = BoundedUniform("π", testval = popt, shape = popt.shape)
 
    EPC = pm.Deterministic('EPC', scale * (1 - pi[2]) ) 

pdc-quantum

with h_model:        
    GSP = pi[0] * ( x[1] * pi[1] ** x[0] + \
                    x[2] * (pi[1] * pi[2] ) ** x[0] ) +  pi[3]  

pdc-quantum

with h_model:
    BoundedGamma = pm.Bound(pm.Gamma,
                            lower= 0.0005,
                            upper= 0.004 + 0.001 * (N - 1) )
    sigma = BoundedGamma("σ_Beta",
                           alpha = 10 - 5 * (N - 1), 
                           beta = 10000 - 8000 * (N - 1),
                           testval = 0.001 + 0.0015 * (N - 1), 
                           shape = counts.shape[1])

pdc-quantum

with h_model:
    theta = pm.Beta('θ', mu = GSP, sigma = sigma,
                         shape = counts.shape[1])  

pdc-quantum

with h_model:      
    p = pm.Binomial("Counts", p = theta, observed = counts, n = shots)