initialMatrix += spinMatrix[m][row] * tensor(matrixMap[m[0]],
matrixMap[m[1]])
initialMatrix /= 4.
# initialMatrix = renderMatrixPhysical(initialMatrix)
import scipy.optimize
# result = scipy.optimize.fmin(probability,parametrizeMatrix(initialMatrix),args = (spinMatrix,row),maxiter = 1000,maxfun = 100000)
# resultMatrix = generateDensityMatrix(result)
resultMatrix = initialMatrix
for a in range(0, 4):
for b in range(0, 4):
datacube.set(**{str(a) + str(b): resultMatrix[a, b]})
datacube.commit()
print trace(resultMatrix), eigh(resultMatrix)[0]
fig = figure(1)
fig.set_size_inches((4, 4))
clf()
plotDensityMatricesContour([resultMatrix, initialMatrix],
style="ellipse",
annotate=False,
labels=["00", "01", "10", "11"])
show()
datacube.savetxt()
import scipy.optimize
result = scipy.optimize.fmin(probability,parametrizeMatrix(initialMatrix),args = (spinMatrix,row),maxiter = 1000,maxfun = 100000)
resultMatrix = generateDensityMatrix(result)
toDatacube(resultMatrix,densityMatrices)
densityMatrices.commit()
print i
fig=figure(1)
fig.set_size_inches((4,4))
clf()
plotDensityMatricesContour([resultMatrix,initialMatrix],style="rectangle",annotate = True,labels=["00","01","10","11"])
show()
densityMatrices.savetxt()
else:
densityMatrices.loadtxt("grover - maximum likelihood density matrices-2")
##Simulate the Grover search algorithm
swap = matrix([[1,0,0,0],[0,0,-1j,0],[0,-1j,0,0],[0,0,0,1]])
step1 = tensor(roty(math.pi/2),roty(math.pi/2))
step2 = swap
step3 = lambda a,b:tensor(rotz(a*math.pi/2),rotz(b*math.pi/2))
y=1.5,
dx=0.8,
dy=0,
zorder=10,
width=2,
fc=(0.7, 0.7, 0.7),
lw=0)
a.set_clip_on(False)
ax.add_artist(a)
figure(11, figsize=(4, 4))
clf()
plotDensityMatricesContour(
[densityMatrix, initialStates[int(i / 2) + offset]],
style="ellipse",
annotate=False,
labels=["00", "01", "10", "11"],
colors=["red", "black"],
showOutline=[False, True])
savefig("input_matrices_%i.pdf" % ((i + offset * 2) / 2))
clf()
plotDensityMatricesContour(
[densityMatrix, outputStates[int(i / 2) + offset]],
style="ellipse",
annotate=False,
labels=["00", "01", "10", "11"],
colors=["red", "black"],
showOutline=[False, True])
savefig("output_matrices_%i.pdf" % ((i + offset * 2) / 2))
figure(10)
print eigh(initialMatrix)[0]
print "Parameters:",parametrizeMatrix(initialMatrix)
reconstructedMatrix = generateDensityMatrix(parametrizeMatrix(initialMatrix))
if not allclose(initialMatrix,reconstructedMatrix):
print "Error parametrizing initial matrix!"
import scipy.optimize
result = scipy.optimize.fmin(probability,parametrizeMatrix(initialMatrix),args = (spinMatrix,row),maxiter = 1000,maxfun = 100000)
resultMatrix = generateDensityMatrix(result)
for a in range(0,4):
for b in range(0,4):
datacube.set(**{str(a)+str(b):resultMatrix[a,b]})
datacube.commit()
print trace(resultMatrix),eigh(resultMatrix)[0]
fig=figure(1)
fig.set_size_inches((4,4))
clf()
plotDensityMatricesContour([resultMatrix,initialMatrix],style="ellipse",annotate = False,labels=["00","01","10","11"])
show()
datacube.savetxt()
(0.03683472221169762 + 0.005920236771060207j),
(-0.035290388800884955 - 0.013034753743398401j),
(0.3696456445542211 + 0j)]])
matrices = [(phiPlusMatrix, phiPlusMatrixIdeal),
(phiMinusMatrix, phiMinusMatrixIdeal),
(psiPlusMatrix, psiPlusMatrixIdeal),
(psiMinusMatrix, psiMinusMatrixIdeal)]
fig = figure(1)
fig.set_size_inches((8, 3))
clf()
i = 1
for matrixPair in matrices:
subplot(1, 4, i)
if i == 1:
annotate = True
else:
annotate = False
plotDensityMatricesContour([matrixPair[0], matrixPair[1]],
style="ellipse",
annotate=annotate,
labels=["00", "01", "10", "11"],
colors=["red", "black"],
showOutline=[False, True])
title("$F_{tr}$ = %.2g %%" %
(traceFidelity(matrixPair[0], matrixPair[1]) * 100))
show()
i += 1
savefig("bell matrices.pdf")
print "Error parametrizing initial matrix!"
import scipy.optimize
result = scipy.optimize.fmin(probability,
parametrizeMatrix(initialMatrix),
args=(spinMatrix, row),
maxiter=1000,
maxfun=100000)
resultMatrix = generateDensityMatrix(result)
for a in range(0, 4):
for b in range(0, 4):
densityMatrices.set(**{str(a) + str(b): resultMatrix[a, b]})
densityMatrices.commit()
print trace(resultMatrix), eigh(resultMatrix)[0]
fig = figure(1)
fig.set_size_inches((4, 4))
clf()
plotDensityMatricesContour([resultMatrix],
showOutline=[False],
annotate=False,
labels=[])
savefig("matrices/matrix_%d.pdf" % (i + 1))
show()
densityMatrices.savetxt()
print eigh(initialMatrix)[0]
print "Parameters:",parametrizeMatrix(initialMatrix)
reconstructedMatrix = generateDensityMatrix(parametrizeMatrix(initialMatrix))
if not allclose(initialMatrix,reconstructedMatrix):
print "Error parametrizing initial matrix!"
import scipy.optimize
result = scipy.optimize.fmin(probability,parametrizeMatrix(initialMatrix),args = (spinMatrix,row),maxiter = 1000,maxfun = 100000)
resultMatrix = generateDensityMatrix(result)
for a in range(0,4):
for b in range(0,4):
densityMatrices.set(**{str(a)+str(b):resultMatrix[a,b]})
densityMatrices.commit()
print trace(resultMatrix),eigh(resultMatrix)[0]
fig=figure(1)
fig.set_size_inches((4,4))
clf()
plotDensityMatricesContour([resultMatrix],showOutline = [False],annotate = False,labels=["00","01","10","11"])
savefig("matrices/matrix_%d.pdf" % i)
show()
spinMatrix.savetxt()
args=(spinMatrix, row),
maxiter=1000,
maxfun=100000)
resultMatrix = generateDensityMatrix(result)
toDatacube(resultMatrix, densityMatrices)
densityMatrices.commit()
print i
fig = figure(1)
fig.set_size_inches((4, 4))
clf()
plotDensityMatricesContour([resultMatrix, initialMatrix],
style="rectangle",
annotate=True,
labels=["00", "01", "10", "11"])
show()
densityMatrices.savetxt()
else:
densityMatrices.loadtxt("grover - maximum likelihood density matrices-2")
##Simulate the Grover search algorithm
swap = matrix([[1, 0, 0, 0], [0, 0, -1j, 0], [0, -1j, 0, 0], [0, 0, 0, 1]])
step1 = tensor(roty(math.pi / 2), roty(math.pi / 2))
step2 = swap
step3 = lambda a, b: tensor(rotz(a * math.pi / 2), rotz(b * math.pi / 2))
for j in range(0,d):
densityMatrix[i,j] = cube[str(i)+str(j)][row]
return densityMatrix
detector1 = matrix([[0.9515,1-0.8843],[1-0.9515,0.8843]])
detector2 = matrix([[0.9563,1-0.8737],[1-0.9563,0.8737]])
detector = tensor(detector1,detector2)
detectorReal = matrix(groverSingleRunData.parameters()["qubit1"]["detectorFunction"])
import matplotlib.gridspec as gridspec
figure(12)
clf()
plotDensityMatricesContour([detector,detectorReal],style="rectangle",annotate = annotate,labels=["00","01","10","11"])
show()
fig = figure(10)
subplot(441)
rc('font',size = 12)
rc('axes', edgecolor=(0.5,0.5,0.5),facecolor = 'white')
fig.set_size_inches((12,3))
gs = gridspec.GridSpec(1, 4)
for state in range(0,4):
densityMatrix = fromDatacube(densityMatrices,4+5*state)
print densityMatrix
measuredProbs = map(lambda i:float(groverSingleRunData.children()[state]["zzp"+i][0]),["00","01","10","11"])
probs = matrix(map(lambda i:float(densityMatrix[i,i]),range(0,4)))
densityMatrix = fromDatacube(densityMatrices,i+offset*2,order = order)
labels = []
if int(i/4) == 0 and i % 4 == 0:
labels = ["00","01","10","11"]
annotate = False
a = Arrow(x = 3.7,y = 1.5,dx = 0.8,dy = 0,zorder = 10,width = 2,fc = (0.7,0.7,0.7),lw = 0)
a.set_clip_on(False)
ax.add_artist(a)
figure(11,figsize = (4,4))
clf()
plotDensityMatricesContour([densityMatrix,initialStates[int(i/2)+offset]],style="ellipse",annotate = False,labels=["00","01","10","11"],colors = ["red","black"],showOutline = [False,True])
savefig("input_matrices_%i.pdf" % ((i+offset*2)/2))
clf()
plotDensityMatricesContour([densityMatrix,outputStates[int(i/2)+offset]],style="ellipse",annotate = False,labels=["00","01","10","11"],colors = ["red","black"],showOutline = [False,True])
savefig("output_matrices_%i.pdf" % ((i+offset*2)/2))
figure(10)
plotDensityMatricesContour([densityMatrix,initialStates[int(i/2)+offset]],style="ellipse",annotate = False,labels=labels,colors = ["red","black"],showOutline = [False,True])
fidelity = traceFidelity(densityMatrix,initialStates[int(i/2)+offset])
title("$F_{tr}$ = %.2g %%" % (fidelity*100))
xlabel("$%s$" % initialStatesLabels[int(i/2)+offset])
ax = subplot(gs[int(i/4),(i) % 4+1])
densityMatrix = fromDatacube(densityMatrices,i+1+offset*2)
from cmath import *
for i in range(1,4):
for j in range(0,i):
for m in [phiMinusMatrix,phiPlusMatrix]:
m[j,i] = m[i,j].conjugate()
psiMinusMatrix = matrix([[(0.46897871228514415+0j), (0.0787538679534797+0j), (-0.01674925247855+0.00172926959478613j), (-0.4297743574491255-0.020974501340607927j)], [(0.0787538679534797+0j), (0.013224847002998141+0j), (0.03992324135304936+0j), (0.04211084712077284+0.016900339646178042j)], [(-0.01674925247855-0.00172926959478613j), (0.03992324135304936+0j), (0.12052050203473001+0j), (0.051750707321192996-0.0020741618904280444j)], [(-0.4297743574491255+0.020974501340607927j), (0.04211084712077284-0.016900339646178042j), (0.051750707321192996+0.0020741618904280444j), (0.39727593867712774+0j)]])
psiPlusMatrix = matrix([[(0.47356299048313577+0j), (0.04603334696364297+0j), (-0.04479988764319459-0.009609979426587522j), (0.40492025330865916+0.07908492432292454j)], [(0.04603334696364297+0j), (0.004474735305039848+0j), (0.026107022049126117+0j), (0.03683472221169762-0.005920236771060207j)], [(-0.04479988764319459+0.009609979426587522j), (0.026107022049126117+0j), (0.15231662965760334+0j), (-0.035290388800884955+0.013034753743398401j)], [(0.40492025330865916-0.07908492432292454j), (0.03683472221169762+0.005920236771060207j), (-0.035290388800884955-0.013034753743398401j), (0.3696456445542211+0j)]])
matrices = [(phiPlusMatrix,phiPlusMatrixIdeal),(phiMinusMatrix,phiMinusMatrixIdeal),(psiPlusMatrix,psiPlusMatrixIdeal),(psiMinusMatrix,psiMinusMatrixIdeal)]
fig=figure(1)
fig.set_size_inches((8,3))
clf()
i = 1
for matrixPair in matrices:
subplot(1,4,i)
if i == 1:
annotate = True
else:
annotate = False
plotDensityMatricesContour([matrixPair[0],matrixPair[1]],style="ellipse",annotate = annotate,labels=["00","01","10","11"],colors = ["red","black"],showOutline = [False,True])
title("$F_{tr}$ = %.2g %%" % (traceFidelity(matrixPair[0],matrixPair[1])*100))
show()
i+=1
savefig("bell matrices.pdf")