def WalkWithExperimentalNoise(U,eps,pairs,refs=(0,0),losses=None,seed=None):
'''Return a unitary with noise applied as Poissonian noise in both
amplitude and phase reconstructions. Function assumes U is a
quantum walk unitary, therefore all elements in real-bordered
form are real and only signs must be deduced from dips. These
signs are determined by taking single point measurements for
classical and quantum coincidences, rather than fitting a full
dip.
U : (ideal) unitary to apply noise to
eps : error in power meter readings for amplitudes
pairs : rate of coincidence counts for Poissonian noise
refs : reference row and column (respectively) for phases
losses : input and output losses
seed : (optional) seed for rng
return : (numpy array) unitary with noise applied'''
# Get the amplitudes
V=numpy.abs(PowerMeterNoise(U,eps,losses,seed))
# Get the phases
nrows,ncols=U.shape
refrow,refcol=refs
rows=range(nrows)
rows.remove(refrow)
cols=range(ncols)
cols.remove(refcol)
for i in rows:
for j in cols:
# Get the phase (sign)
cmean=float(pairs)*(hamiltomo.abs2(U[refrow,refcol]*U[i,j])+\
hamiltomo.abs2(U[refrow,j]*U[i,refcol]))
qmean=float(pairs)*hamiltomo.abs2(U[refrow,refcol]*U[i,j]+\
U[refrow,j]*U[i,refcol])
if cmean<1000:
# Poissonian
classical=numpy.random.poisson(cmean)
else:
# Gaussian approximation
classical=numpy.random.normal(cmean,numpy.sqrt(cmean))
if qmean<1000:
# Poissonian
quantum=numpy.random.poisson(qmean)
else:
# Gaussian approximation
quantum=numpy.random.normal(qmean,numpy.sqrt(qmean))
#if cmean > qmean:
if classical > quantum:
# Dip => negative sign
V[i,j]*=float(-1)
return V
def UnitaryFidelity(U,V): '''Distance measure between two unitary matrices. Uses a trace distance (1/N) Tr(U^V) U : reference matrix (always unitary) V : test matrix (not necessarily unitary) return : (float) trace distance between U and V''' dim=U.shape[0] uv=numpy.dot(U, hamiltomo.dagger(V)) return hamiltomo.abs2((1./dim)*sum(uv.flatten()[0::dim+1]))
def PowerMeterNoise(U,eps,losses=None,seed=None):
'''Return a unitary with noise applied as +-eps on power meter readings
but ideal phases. The total power in each column (i.e. input) is 1.
U : unitary to apply noise to
eps : error on power meter readings
losses : input and output losses
seed : (optional) seed for rng
return : (numpy array) unitary with noise applied'''
dim=U.shape[0] # assume square
amps=hamiltomo.abs2(U)
rng=Random(seed)
if losses is None:
losses=numpy.ones((2,dim))
V=numpy.zeros_like(U)
for i in range(dim):
for j in range(dim):
amp=numpy.sqrt(max(amps[i,j]*losses[0,j]*losses[1,i]+rng.gauss(0,eps),0))
phase=U[i,j]/abs(U[i,j])
V[i,j]=amp*phase
pre,V,post=hamiltomo.Normalise(V,eps=1e-10,maxiter=200)
return V
