def singleProjectorSample(args):
(P, L, seed) = args # unpack arguments (easier for parallel code)
(phases, xs, zs) = P
t = len(xs[0])
# init seed
np.random.seed(seed)
# sample random theta
theta = StabilizerState.randomStabilizerState(t)
# project random state to P
projfactor = 1
for g in range(len(phases)):
res = theta.measurePauli(phases[g], zs[g], xs[g])
projfactor *= res
if res == 0: return 0 # theta annihilated by P
total = 0
if L is None: # exact decomposition
size = int(np.ceil(t / 2))
for i in range(0, 2**size):
phi = prepH(i, t)
total += StabilizerState.innerProduct(theta, phi)
else: # approximate decomposition
size = len(L)
for i in range(0, 2**size):
phi = prepL(i, t, L)
total += StabilizerState.innerProduct(theta, phi)
return 2**t * np.abs(projfactor * total)**2
def prepL(i, t, L):
# compute bitstring by adding rows of l
Lbits = list(np.binary_repr(i, width=len(L)))
bitstring = np.zeros(t)
for idx in range(len(Lbits)):
if Lbits[idx] == '1':
bitstring += L[idx]
bitstring = bitstring.astype(int) % 2
# Stabilizer state is product of |0> and |+>
# 1's in bitstring indicate positions of |+>
# initialize stabilizer state
phi = StabilizerState(t, t)
# construct state using shrink
for xtildeidx in range(t):
if bitstring[xtildeidx] == 0:
vec = np.zeros(t)
vec[xtildeidx] = 1
phi.shrink(vec, 0)
# |0> at index, inner prod with 1 is 0
# |+> at index -> do nothing
return phi
def exactThread(args):
(P, L, i) = args
(phases, xs, zs) = P
t = len(xs[0])
if L is None: size = int(np.ceil(t/2))
else: size = len(L)
total = 0
if L is None: theta = prepH(i, t)
else: theta = prepL(i, t, L)
projfactor = 1
for g in range(len(phases)):
res = theta.measurePauli(phases[g], zs[g], xs[g])
projfactor *= res
if res == 0: return 0 # theta annihilated by P
for j in range(0, 2**size):
if L is None: phi = prepH(j, t)
else: phi = prepL(j, t, L)
inner = StabilizerState.innerProduct(theta, phi)
total += inner * projfactor
return total
def load(psi):
state = StabilizerState(psi["n"], psi["k"])
state.G = np.array(psi["G"])
state.Gbar = np.array(psi["Gbar"])
state.h = np.array(psi["h"])
if "D" in psi:
state.D = np.array(psi["D"])[:state.k]
state.J = np.array(psi["J"])[:state.k, :state.k] * 4
state.Q = psi["Q"]
return state
def evalHcomponent(args):
(i, _, theta, t) = args # unpack arguments (easier for parallel code)
size = int(np.ceil(t/2))
odd = t % 2 == 1
bits = list(np.binary_repr(i, width=size))
# initialize stabilizer state
phi = StabilizerState(t, t)
for idx in range(size):
bit = int(bits[idx])
if bit == 0 and not (odd and idx == size-1):
# phi.J = np.array([[0, 4], [4, 0]])
phi.J[idx*2+1, idx*2] = 4
phi.J[idx*2, idx*2+1] = 4
for idx in range(size):
bit = int(bits[idx])
vec = np.zeros(t)
if odd and idx == size-1:
vec[t-1] = 1
# last qubit: |H> = (1/2v)(|0> + |+>)
if bit == 0:
phi.measurePauli(0, vec, np.zeros(t)) # |0>, measure Z
else:
phi.measurePauli(0, np.zeros(t), vec) # |+>, measure X
continue
if bit == 0: continue
vec[idx*2+1] = 1
vec[idx*2] = 1
phi.measurePauli(0, np.zeros(t), vec) # measure XX
phi.measurePauli(0, vec, np.zeros(t)) # measure ZZ
return StabilizerState.innerProduct(theta, phi)
def evalLcomponent(args):
(i, L, theta, t) = args # unpack arguments (easier for parallel code)
# compute bitstring by adding rows of l
Lbits = list(np.binary_repr(i, width=len(L)))
bitstring = np.zeros(t)
for idx in range(len(Lbits)):
if Lbits[idx] == '1':
bitstring += L[idx]
bitstring = bitstring.astype(int) % 2
# Stabilizer state is product of |0> and |+>
# 1's in bitstring indicate positions of |+>
# initialize stabilizer state
phi = StabilizerState(t, t)
# construct state by measuring paulis
for xtildeidx in range(t):
vec = np.zeros(t)
vec[xtildeidx] = 1
if bitstring[xtildeidx] == 1:
# |+> at index, so measure X
phi.measurePauli(0, np.zeros(t), vec)
else:
# |0> at index, so measure Z
phi.measurePauli(0, vec, np.zeros(t))
return StabilizerState.innerProduct(theta, phi)
def sampleProjector(args):
(P, L, seed, parallel) = args # unpack arguments (easier for parallel code)
(phases, xs, zs) = P
# empty projector
if len(phases) == 0:
return 1
t = len(xs[0])
# clifford circuit
if t == 0:
lookup = {0: 1, 2: -1}
generators = [1] # include identity
for phase in phases: generators.append(lookup[phase])
# calculate sum of all permutations of generators
return sum(generators)/len(generators)
# set unique seed for this calculation
# np.random.seed((seed) % 4294967296)
# sample random theta
theta = StabilizerState.randomStabilizerState(t)
# project random state to P
projfactor = 1
for g in range(len(phases)):
res = theta.measurePauli(phases[g], zs[g], xs[g])
projfactor *= res
# if res == 0: return 0 # theta annihilated by P
if L is None: # use exact decomp into pairs of stabilizer states
func = evalHcomponent
size = int(np.ceil(t/2)) # need one bit for each pair, plus one more if t is odd
else:
func = evalLcomponent
size = len(L)
parallel = False
if parallel: # parallelize for large enough L
pool = Pool()
total = sum(pool.map(func, [(i, L, theta, t) for i in range(0, 2**size)]))
pool.close()
pool.join()
else:
total = sum(map(func, [(i, L, theta, t) for i in range(0, 2**size)]))
return 2**t * np.abs(projfactor*total)**2
def load(psi):
state = StabilizerState(psi["n"], psi["k"])
state.G = np.array(psi["G"])
state.Gbar = np.array(psi["Gbar"])
state.h = np.array(psi["h"])
if "D" in psi:
state.D = np.array(psi["D"])[:state.k]
state.J = np.array(psi["J"])[:state.k, :state.k]*4
state.Q = psi["Q"]
return state
def prepH(i, t):
size = int(np.ceil(t / 2))
odd = t % 2 == 1
bits = list(np.binary_repr(i, width=size))
# initialize stabilizer state
phi = StabilizerState(t, t)
# set J matrix
for idx in range(size):
bit = int(bits[idx])
if bit == 0 and not (odd and idx == size - 1):
# phi.J = np.array([[0, 4], [4, 0]])
phi.J[idx * 2 + 1, idx * 2] = 4
phi.J[idx * 2, idx * 2 + 1] = 4
# truncate affine space using shrink
for idx in range(size):
bit = int(bits[idx])
vec = np.zeros(t)
if odd and idx == size - 1:
# bit = 0 is |+>
# bit = 1 is |0>
if bit == 1:
vec[t - 1] = 1
phi.shrink(vec, 0)
continue
# bit = 1 corresponds to |00> + |11> state
# bit = 0 corresponds to |00> + |01> + |10> - |11>
if bit == 1:
vec[idx * 2] = 1
vec[idx * 2 + 1] = 1
phi.shrink(vec, 0) # only 00 and 11 have inner prod 0 with 11
return phi
def exactProjectorWork(args):
(P, L, l) = args
(phases, xs, zs) = P
t = len(xs[0])
if L is None: size = int(np.ceil(t / 2))
else: size = len(L)
chi = 2**size
i = 0
while l >= chi - i:
l -= chi - i
i += 1
j = l + i
if L is None: theta = prepH(i, t)
else: theta = prepL(i, t, L)
projfactor = 1
for g in range(len(phases)):
res, status = theta.measurePauli(phases[g],
zs[g],
xs[g],
give_status=True)
projfactor *= res
if res == 0: return 0 # theta annihilated by P
if L is None: phi = prepH(j, t)
else: phi = prepL(j, t, L)
inner = StabilizerState.innerProduct(theta, phi)
if i == j:
return inner * projfactor
else:
return 2 * np.real(inner) * projfactor
f = open(directory + "ExponentialSum.txt")
tests = json.loads(f.read())
# tests = []
indexcut = 0
failed = 0
index = 0
starttime = datetime.now()
for test in tests:
index += 1
if index < indexcut: continue
# don't actually depend on n, but need for initialization
k = len(test["D"]["D"])
# k = 4
state = StabilizerState(k, k)
# state.D = np.array(test["D"]["D"])[:4]
state.D = np.array(test["D"]["D"])
# state.J = np.array(test["J"]["J"])[:4, :4]*4
state.J = np.array(test["J"]["J"])*4
state.Q = test["Q"]["Q"]
(eps, p, m) = state.exponentialSum(exact=True)
if eps != test["eps_out"]\
or m != test["m_out"] % 8\
or p != test["p_out"]:
if failed == 0: print("ExponentialSum errors:")
print("ExponentialSum %d (k=%d) failed: (%d,%d,%d) should be (%d,%d,%d)" %
(index, state.k, eps, p, m, test["eps_out"], test["p_out"], test["m_out"]))
failed += 1
# break
f = open(directory + "ExponentialSum.txt")
tests = json.loads(f.read())
tests = []
indexcut = 0
failed = 0
index = 0
starttime = datetime.now()
for test in tests:
index += 1
if index < indexcut: continue
# don't actually depend on n, but need for initialization
k = len(test["D"]["D"])
# k = 4
state = StabilizerState(k, k)
# state.D = np.array(test["D"]["D"])[:4]
state.D = np.array(test["D"]["D"])
# state.J = np.array(test["J"]["J"])[:4, :4]*4
state.J = np.array(test["J"]["J"]) * 4
state.Q = test["Q"]["Q"]
(eps, p, m) = state.exponentialSum(exact=True)
if eps != test["eps_out"]\
or m != test["m_out"] % 8\
or p != test["p_out"]:
if failed == 0: print("ExponentialSum errors:")
print(
"ExponentialSum %d (k=%d) failed: (%d,%d,%d) should be (%d,%d,%d)"
% (index, state.k, eps, p, m, test["eps_out"], test["p_out"],
test["m_out"]))