def getBMPSRowOps(GammaC, LambdaC, GammaD, LambdaD, AEnv, BEnv, steps):
convergence = []
envOpAB = bops.permute(bops.multiContraction(AEnv, BEnv, '1', '3'),
[0, 3, 2, 4, 1, 5])
envOpBA = bops.permute(bops.multiContraction(BEnv, AEnv, '1', '3'),
[0, 3, 2, 4, 1, 5])
op = envOpBA
for i in range(steps):
oldGammaC, oldLambdaC, oldGammaD, oldLambdaD = GammaC, LambdaC, GammaD, LambdaD
GammaC, LambdaC, GammaD, LambdaD = bmpsRowStep(GammaC, LambdaC, GammaD,
LambdaD, op)
GammaD, LambdaD, GammaC, LambdaC = bmpsRowStep(GammaD, LambdaD, GammaC,
LambdaC, op)
# if i > 0:
# convergence.append(
# checkConvergence(oldGammaC, oldLambdaC, oldGammaD, oldLambdaD, GammaC, LambdaC, GammaD, LambdaD, 2))
bops.removeState([oldGammaC, oldLambdaC, oldGammaD, oldLambdaD])
# cUp = bops.multiContraction(GammaC, LambdaC, '2', '0', isDiag2=True)
# dUp = bops.multiContraction(GammaD, LambdaD, '2', '0', isDiag2=True)
# GammaC, LambdaC, GammaD, LambdaD = bmpsRowStep(GammaC, LambdaC, GammaD, LambdaD, op)
# cDown = bops.multiContraction(GammaC, LambdaC, '2', '0', isDiag2=True)
# dDown = bops.multiContraction(GammaD, LambdaD, '2', '0', isDiag2=True)
bops.removeState([
GammaC, LambdaC, GammaD, LambdaD, oldGammaC, oldLambdaC, oldGammaD,
oldLambdaD
])
return GammaC, LambdaC, GammaD, LambdaD
def applyHToM(HL, HR, H, M, k):
k1 = k
k2 = k + 1
# Add HL.opSum x h.identity(k1) x h.identity(k2) x I(Right)
# and I(Left) x h.identity(k1) x h.identity(k2) x HR.opSum
Hv = bops.multiContraction(HL.opSum, M, '0', '0')
Hv = bops.addNodes(Hv, bops.multiContraction(M, HR.opSum, '3', '0'))
# Add I(Left) x h.single(k1) x h.identity(k2) x I(Right)
# And I(Left) x h.identity(k1) x h.single(k2) x I(Right)
Hv = bops.addNodes(Hv, \
bops.permute(bops.multiContraction(M, H.singles[k1], '1', '0'), [0, 3, 1, 2]))
Hv = bops.addNodes(Hv, \
bops.permute(bops.multiContraction(M, H.singles[k2], '2', '0'), [0, 1, 3, 2]))
# Add HL.openOp x h.r2l(k1) x h.identity(k2) x I(Right)
# And I(Left) x h.identity(k1) x h.l2r(k2) x HR.openOp
HK1R2L = bops.permute(bops.multiContraction(M, H.r2l[k1], '1', '0'), [0, 4, 3, 1, 2])
Hv = bops.addNodes(Hv, \
bops.multiContraction(HL.openOp, HK1R2L, '02', '01'))
HK2L2R = bops.permute(bops.multiContraction(M, H.l2r[k2], '2', '0'), [0, 1, 3, 4, 2])
Hv = bops.addNodes(Hv, \
bops.multiContraction(HK2L2R, HR.openOp, '43', '02'))
# Add I(Left) x h.l2r(k1) x h.r2l(k2) x I(Right)
HK1K2 = bops.multiContraction(M, H.l2r[k1], '1', '0')
HK1K2 = bops.multiContraction(HK1K2, H.r2l[k2], '14', '02')
HK1K2 = bops.permute(HK1K2, [0, 2, 3, 1])
Hv = bops.addNodes(Hv, HK1K2)
return Hv
def expectationValue(currSites, op):
left = leftRow
for i in range(l):
left = bops.multiContraction(left, cUp, '3', '0', cleanOr1=True)
leftUp = toricCode.applyOpTosite(currSites[0][i * 2], op)
leftDown = toricCode.applyOpTosite(currSites[1][i * 2], op)
left = bops.multiContraction(left, leftUp, '23', '30', cleanOr1=True)
left = bops.multiContraction(left, leftDown, '14', '30', cleanOr1=True)
left = bops.permute(
bops.multiContraction(left, dDown, '04', '21', cleanOr1=True),
[3, 2, 1, 0])
left = bops.multiContraction(left, dUp, '3', '0', cleanOr1=True)
rightUp = toricCode.applyOpTosite(currSites[0][i * 2 + 1], op)
rightDown = toricCode.applyOpTosite(currSites[1][i * 2 + 1], op)
left = bops.multiContraction(left, rightUp, '23', '30', cleanOr1=True)
left = bops.multiContraction(left,
rightDown,
'14',
'30',
cleanOr1=True)
left = bops.permute(
bops.multiContraction(left, cDown, '04', '21', cleanOr1=True),
[3, 2, 1, 0])
bops.removeState([leftUp, leftDown, rightDown, rightUp])
return bops.multiContraction(left, rightRow, '0123', '3210').tensor * 1
def XXVar(statesDir: str, outDir: str, NA, theta, phi):
maxBondDim = 100
res = np.zeros(2, dtype=complex)
U = tn.Node(
np.matmul(ru.getUPhi(np.pi * phi / 2, 2),
ru.getUTheta(np.pi * theta / 2, 2)))
with open(statesDir + 'psiXX_NA_' + str(NA) + '_NB_' + str(NA), 'rb') as f:
psi = pickle.load(f)
psiCopy = bops.relaxState(psi, 64)
res[0] = bops.getOverlap(psi, psiCopy)
bops.removeState(psi)
for i in range(NA):
psiCopy[i] = bops.permute(
bops.multiContraction(psiCopy[i], U, '1', '0'), [0, 2, 1])
doublePsi = [None for j in range(len(psiCopy))]
for j in range(len(psiCopy)):
doublePsi[j] = doubleMPSSite(psiCopy[j])
doubleCopy = bops.copyState(doublePsi)
for j in range(NA):
doublePsi[j] = bops.permute(
bops.multiContraction(doublePsi[j], E, '1', '0', cleanOr1=True),
[0, 2, 1])
res[1] = bops.getOverlap(doublePsi, doubleCopy)
with open(
outDir + 'XXVar_NA_' + str(NA) + '_t_' + str(theta) + '_p_' +
str(phi), 'wb') as f:
pickle.dump(res, f)
print(res)
def applyLocalOperators(cUp, dUp, cDown, dDown, leftRow, rightRow, A, B, l,
ops):
left = leftRow
for i in range(l):
left = bops.multiContraction(left, cUp, '3', '0', cleanOr1=True)
leftUp = applyOpTosite(B, ops[i * 4])
leftDown = applyOpTosite(A, ops[i * 4 + 1])
left = bops.multiContraction(left, leftUp, '23', '30', cleanOr1=True)
left = bops.multiContraction(left, leftDown, '14', '30', cleanOr1=True)
left = bops.permute(
bops.multiContraction(left, dDown, '04', '21', cleanOr1=True),
[3, 2, 1, 0])
left = bops.multiContraction(left, dUp, '3', '0', cleanOr1=True)
rightUp = applyOpTosite(A, ops[i * 4 + 2])
rightDown = applyOpTosite(B, ops[i * 4 + 3])
left = bops.multiContraction(left, rightUp, '23', '30', cleanOr1=True)
left = bops.multiContraction(left,
rightDown,
'14',
'30',
cleanOr1=True)
left = bops.permute(
bops.multiContraction(left, cDown, '04', '21', cleanOr1=True),
[3, 2, 1, 0])
bops.removeState([leftUp, leftDown, rightDown, rightUp])
return bops.multiContraction(left, rightRow, '0123', '3210').tensor * 1
def projectS(psi, AEnd):
projector0Tensor = np.zeros((2, 2))
projector0Tensor[0, 0] = 1
projector0 = tn.Node(projector0Tensor, backend=None)
projector1Tensor = np.zeros((2, 2))
projector1Tensor[1, 1] = 1
projector1 = tn.Node(projector1Tensor, backend=None)
for i in range(AEnd + 1):
if i % 2 == 0:
psi[i] = bops.permute(bops.multiContraction(psi[i], projector0, [1], [0]), [0, 2, 1])
else:
psi[i] = bops.permute(bops.multiContraction(psi[i], projector1, [1], [0]), [0, 2, 1])
def horizontalPair(leftSite, rightSite, cleanLeft=True, cleanRight=True):
pair = bops.multiContraction(leftSite,
rightSite,
'1',
'3',
cleanOr1=cleanLeft,
cleanOr2=cleanRight)
pair = bops.multiContraction(pair, ru.getPairUnitary(d), '37', '01')
[left, right, te] = bops.svdTruncation(pair, [0, 1, 2, 6], [3, 4, 5, 7],
'>>',
maxBondDim=16)
return bops.permute(left,
[0, 4, 1, 2, 3]), bops.permute(right, [1, 2, 3, 0, 4])
def stateEnergy(psi: List[tn.Node], H: HOp):
E = 0
for i in range(len(psi)):
psiCopy = bops.copyState(psi)
single_i = bops.copyState([H.singles[i]])[0]
psiCopy[i] = bops.permute(tn.contract(psiCopy[i][1] ^ single_i[0], name=('site' + str(i))), [0, 2, 1])
E += bops.getOverlap(psiCopy, psi)
bops.removeState(psiCopy)
tn.remove_node(single_i)
for i in range(len(psi) - 1):
psiCopy = bops.copyState(psi)
r2l = bops.copyState([H.r2l[i+1]])[0]
l2r = bops.copyState([H.l2r[i]])[0]
psiCopy[i][2] ^ psiCopy[i+1][0]
psiCopy[i][1] ^ l2r[0]
r2l[0] ^ psiCopy[i+1][1]
l2r[2] ^ r2l[2]
M = tn.contract_between(psiCopy[i], \
tn.contract_between(l2r, tn.contract_between(r2l, psiCopy[i+1])))
if bops.multiContraction(M, M, '0123', '0123*').tensor != 0:
[psiCopy, te] = bops.assignNewSiteTensors(psiCopy, i, M, '>>')
E += bops.getOverlap(psiCopy, psi)
bops.removeState(psiCopy)
tn.remove_node(r2l)
tn.remove_node(l2r)
return E
def expectationValues(psi: List[tn.Node], vs: List[List[np.array]]):
vs = np.round(vs, 10)
n = len(vs)
NA = len(vs[0])
result = 1
# result = np.eye(2, dtype=complex)
for copy in range(n):
psiCopy = bops.copyState(psi)
for alpha in range(NA - 1, -1, -1):
overlap = np.matmul(vs[copy][alpha],
np.conj(vs[np.mod(copy + 1, n)][alpha]))
toEstimate = np.outer(vs[copy][alpha],
np.conj(vs[np.mod(copy + 1, n)][alpha]))
if np.abs(np.round(overlap, 8)) == 2:
toMeasure = toEstimate
else:
hermitianComponent = np.random.randint(2)
if hermitianComponent:
toMeasure = (toEstimate +
np.conj(np.transpose(toEstimate)))
else:
toMeasure = (toEstimate -
np.conj(np.transpose(toEstimate)))
psiCopy[alpha] = bops.permute(bops.multiContraction(psiCopy[alpha], tn.Node(toMeasure), \
'1', '1'), [0, 2, 1])
psiCopy = bops.shiftWorkingSite(psiCopy, alpha, '<<')
result *= bops.getOverlap(psiCopy, psi)
# result = np.matmul(result, toMeasure)
bops.removeState(psiCopy)
return result
def estimateOp(xRight, xLeft, upRow, downRow, A, ops):
N = len(ops)
curr = xLeft
for i in range(int(N / 2)):
closedA = tn.Node(
np.trace(bops.multiContraction(ops[i * 2], A, '1', '0').tensor,
axis1=0,
axis2=5))
closedB = tn.Node(
np.trace(bops.multiContraction(ops[i * 2 + 1], A, '1', '0').tensor,
axis1=0,
axis2=5))
closed = bops.permute(
bops.multiContraction(closedA, closedB, '1', '3'),
[0, 3, 2, 4, 1, 5])
curr = bops.multiContraction(bops.multiContraction(
bops.multiContraction(curr, upRow, '0', '0'),
closed,
'023',
'201',
cleanOr1=True),
downRow,
'034',
'012',
cleanOr1=True)
return bops.multiContraction(curr, xRight, '012', '012').tensor
def toEnvOperator(op):
result = bops.unifyLegs(
bops.unifyLegs(
bops.unifyLegs(
bops.unifyLegs(bops.permute(op, [0, 4, 1, 5, 2, 6, 3, 7]), 6,
7), 4, 5), 2, 3), 0, 1)
tn.remove_node(op)
return result
def bmpsDensityMatrix(cUp, dUp, cDown, dDown, AEnv, BEnv, A, B, steps):
rightRow = bmpsCols(cUp, dUp, cDown, dDown, AEnv, BEnv, steps, 'right')
leftRow = bmpsCols(cUp, dUp, cDown, dDown, AEnv, BEnv, steps, 'left')
upRow = bops.multiContraction(cUp, dUp, '2', '0')
downRow = bops.multiContraction(cDown, dDown, '2', '0')
circle = bops.multiContraction(
bops.multiContraction(bops.multiContraction(leftRow, upRow, '3', '0'),
rightRow, '5', '0'), downRow, '07', '03')
parityTensor = np.eye(4, dtype=complex)
parityTensor[1, 1] = -1
parityTensor[3, 3] = -1
parity = tn.Node(parityTensor)
if A[0].dimension == 4:
parityA = tn.Node(
np.trace(bops.multiContraction(parity, A, '1', '0').tensor,
axis1=0,
axis2=5))
ABNet = bops.permute(
bops.multiContraction(
bops.multiContraction(parityA, parityA, '1', '3'),
bops.multiContraction(parityA, parityA, '1', '3'),
'15',
'03',
cleanOr1=True,
cleanOr2=True), [5, 1, 0, 2, 3, 6, 4, 7])
p2 = bops.multiContraction(circle, ABNet, '01234567', '01234567')
b = 1
ABNet = bops.permute(
bops.multiContraction(bops.multiContraction(B, A, '2', '4'),
bops.multiContraction(A, B, '2', '4'),
'28',
'16',
cleanOr1=True,
cleanOr2=True),
[2, 10, 9, 13, 14, 5, 1, 6, 0, 4, 8, 12, 3, 7, 11, 15])
dm = bops.multiContraction(circle,
ABNet,
'23140567',
'01234567',
cleanOr1=True,
cleanOr2=True)
ordered = np.round(np.reshape(dm.tensor, [16, 16]), 13)
ordered = ordered / np.trace(ordered)
return dm
def trotterSweep(trotterGates, psi, startSite, endSite, maxBondDim=1024):
psiCopy = bops.copyState(psi)
truncErr = 0
N = len(psi)
for k in [endSite - i for i in range(startSite, endSite)]:
M = bops.multiContraction(psiCopy[k - 1], psiCopy[k], [2], [0])
M = bops.permute(
bops.multiContraction(M, trotterGates[k - 1], [1, 2], [0, 1]),
[0, 2, 3, 1])
[l, r, currTruncErr] = bops.svdTruncation(M,
M[:2],
M[2:],
'<<',
maxBondDim,
leftName='site' + str(k - 1),
rightName='site' + str(k),
edgeName='v' + str(k))
if currTruncErr > truncErr:
truncErr = currTruncErr
psiCopy[k] = r
psiCopy[k - 1] = l
bops.multiContraction(r, r, [1, 2], [1, 2, '*'])
for k in range(startSite, endSite):
M = bops.multiContraction(psiCopy[k], psiCopy[k + 1], [2], [0])
M = bops.permute(
bops.multiContraction(M, trotterGates[k], [1, 2], [0, 1]),
[0, 2, 3, 1])
[l, r,
currTruncErr] = bops.svdTruncation(M,
M[:2],
M[2:],
'>>',
maxBondDim,
leftName='site' + str(k),
rightName='site' + str(k + 1),
edgeName='v' + str(k + 1))
if currTruncErr > truncErr:
truncErr = currTruncErr
psiCopy[k] = l
psiCopy[k + 1] = r
# For imaginary time propagation, renormalize state.
norm = bops.getOverlap(psiCopy, psiCopy)
psiCopy[N - 1].tensor = psiCopy[N - 1].tensor / math.sqrt(abs(norm))
return psiCopy, truncErr
def exactPurity(l, xRight, xLeft, upRow, downRow, A, filename, d=2):
curr = xLeft
pair = bops.permute(bops.multiContraction(A, A, '2', '4'),
[1, 6, 3, 7, 2, 8, 0, 5, 4, 9])
for i in range(int(l / 2)):
curr = bops.multiContraction(
bops.multiContraction(curr, upRow, '0', '0'), downRow, '1', '0')
curr = bops.multiContraction(
curr, pair, [0, i * 4 + 1, i * 4 + 2, i * 4 + 4, i * 4 + 5],
'20145')
curr = bops.permute(curr, [i * 4, i * 4 + 2, i * 4 + 1] +
list(range(i * 2)) + [i * 4 + 3, i * 4 + 4] +
list(range(i * 2, i * 4)) + [i * 4 + 5, i * 4 + 6])
dm = bops.multiContraction(curr, xRight, '012', '012')
ordered = np.reshape(dm.tensor, [d**l, d**l]) / np.trace(
np.reshape(dm.tensor, [d**l, d**l]))
purity = sum(np.linalg.eigvalsh(np.matmul(ordered, ordered)))
with open(filename + '_l_' + str(l), 'wb') as f:
pickle.dump(purity, f)
return purity
def applyH(psi: List[tn.Node], H: HOp):
psiCopy = bops.copyState(psi)
single_0 = bops.copyState([H.singles[0]])[0]
psiCopy[0] = bops.permute(tn.contract(psiCopy[0][1] ^ single_0[0], name=('site' + str(0))), [0, 2, 1])
result = psiCopy
for i in range(1, len(psi)):
psiCopy = bops.copyState(psi)
single_i = bops.copyState([H.singles[i]])[0]
psiCopy[i] = bops.permute(tn.contract(psiCopy[i][1] ^ single_i[0], name=('site' + str(i))), [0, 2, 1])
result = bops.addStates(result, psiCopy)
for i in range(len(psi) - 1):
psiCopy = bops.copyState(psi)
r2l = bops.copyState([H.r2l[i+1]])[0]
l2r = bops.copyState([H.l2r[i]])[0]
psiCopy[i][2] ^ psiCopy[i+1][0]
psiCopy[i][1] ^ l2r[0]
r2l[0] ^ psiCopy[i+1][1]
l2r[2] ^ r2l[2]
M = tn.contract_between(psiCopy[i], \
tn.contract_between(l2r, tn.contract_between(r2l, psiCopy[i+1])))
[psiCopy, te] = bops.assignNewSiteTensors(psiCopy, i, M, '>>')
result = bops.addStates(result, psiCopy)
return result
def makeMeasurement(psi, site, toProject):
localDM = bops.multiContraction(psi[site], psi[site], '02', '02*').tensor
projectionProbability = np.trace(np.matmul(localDM,
toProject)) / np.trace(localDM)
# Project to the measured vector
if np.random.uniform(0, 1) < projectionProbability:
psi[site] = bops.permute(
bops.multiContraction(psi[site],
tn.Node(toProject),
'1',
'1',
cleanOr1=True,
cleanOr2=True), [0, 2, 1])
res = 1
else:
psi[site] = bops.permute(
bops.multiContraction(psi[site],
tn.Node(np.eye(d) - toProject),
'1',
'1',
cleanOr1=True,
cleanOr2=True), [0, 2, 1])
res = 0
return res
def bmpsCols(upRow: tn.Node,
downRow: tn.Node,
AEnv: tn.Node,
BEnv: tn.Node,
steps,
option='right',
X=None):
envOpAB = bops.permute(bops.multiContraction(AEnv, BEnv, '1', '3'),
[0, 3, 2, 4, 1, 5])
envOpBA = bops.permute(bops.multiContraction(BEnv, AEnv, '1', '3'),
[0, 3, 2, 4, 1, 5])
if X is None:
if option == 'right':
X = tn.Node(
np.ones((upRow[3].dimension, envOpBA[3].dimension,
envOpAB[3].dimension, downRow[0].dimension),
dtype=complex))
else:
X = tn.Node(
np.ones((downRow[0].dimension, envOpAB[2].dimension,
envOpBA[2].dimension, upRow[0].dimension),
dtype=complex))
for i in range(steps):
if option == 'right':
X = bops.multiContraction(upRow, X, '3', '0')
X = bops.multiContraction(X, envOpBA, '123', '013', cleanOr1=True)
X = bops.multiContraction(X, envOpAB, '451', '013', cleanOr1=True)
X = bops.multiContraction(X, downRow, '154', '012', cleanOr1=True)
else:
X = bops.multiContraction(downRow, X, '3', '0')
X = bops.multiContraction(X, envOpAB, '321', '245', cleanOr1=True)
X = bops.multiContraction(X, envOpBA, '134', '245', cleanOr1=True)
X = bops.multiContraction(X, upRow, '134', '012', cleanOr1=True)
norm = np.sqrt(bops.multiContraction(X, X, '0123', '0123*').tensor)
X = bops.multNode(X, 1 / norm)
return X
def get2ByNExplicit(l: int):
with open('results/toricBoundaries', 'rb') as f:
[upRow, downRow, leftRow, rightRow, openA, openB, A,
B] = pickle.load(f)
left = bops.multiContraction(
downRow, bops.multiContraction(leftRow, upRow, '3', '0'), '3', '0')
for i in range(1, l):
left = bops.multiContraction(
downRow,
bops.multiContraction(left, upRow, [3 + 4 * i], '0',
cleanOr1=True), '3', '0')
circle = bops.multiContraction(left, downRow, [3 + 4 * l, 0], '03')
openA = tn.Node(
np.transpose(
np.reshape(np.kron(A.tensor, A.tensor),
[d**2, d**2, d**2, d**2, d, d]), [4, 0, 1, 2, 3, 5]))
openB = tn.Node(
np.transpose(
np.reshape(np.kron(B.tensor, B.tensor),
[d**2, d**2, d**2, d**2, d, d]), [4, 0, 1, 2, 3, 5]))
ABNet = bops.permute(
bops.multiContraction(bops.multiContraction(openB, openA, '2', '4'),
bops.multiContraction(openA, openB, '2', '4'),
'28',
'16',
cleanOr1=True,
cleanOr2=True),
[1, 5, 6, 13, 14, 9, 10, 2, 0, 4, 8, 12, 3, 7, 11, 15])
if l == 2:
curr = bops.multiContraction(circle, ABNet, '234567', '456701')
res = bops.permute(
bops.multiContraction(curr, ABNet, '23450176', '01234567'),
[0, 1, 2, 3, 8, 9, 10, 11, 4, 5, 6, 7, 12, 13, 14, 15])
rdm = np.reshape(res.tensor, [2**8, 2**8])
rdm = rdm / np.trace(rdm)
return rdm
def twoCopiesEntanglement(circle, A, B):
doubleCircle = tn.Node(np.kron(circle.tensor, circle.tensor))
doubleA = tn.Node(np.kron(A.tensor, A.tensor))
doubleB = tn.Node(np.kron(B.tensor, B.tensor))
AEnv = tn.Node(np.trace(A.get_tensor(), axis1=0, axis2=5))
BEnv = tn.Node(np.trace(B.get_tensor(), axis1=0, axis2=5))
ABNet = bops.permute(
bops.multiContraction(bops.multiContraction(BEnv, AEnv, '1', '3'),
bops.multiContraction(AEnv, BEnv, '1', '3'),
'15', '03'), [5, 1, 0, 2, 3, 6, 4, 7])
n = bops.multiContraction(circle, ABNet, '01234567', '01234567').tensor
p2 = bops.multiContraction(doubleCircle, ABNet, '01234567',
'01234567').tensor
return p2
def verticalPair(topSite, bottomSite, cleanTop=True, cleanBottom=True):
pair = bops.multiContraction(topSite,
bottomSite,
'2',
'0',
cleanOr1=cleanTop,
cleanOr2=cleanBottom)
pair = bops.multiContraction(pair,
ru.getPairUnitary(d),
'37',
'01',
cleanOr1=True,
cleanOr2=True)
[top, bottom, te] = bops.svdTruncation(pair, [0, 1, 2, 6], [3, 4, 5, 7],
'>>',
maxBondDim=16)
return bops.permute(top, [0, 1, 4, 2, 3]), bottom
def bmpsSides(cUp: tn.Node,
dUp: tn.Node,
cDown: tn.Node,
dDown: tn.Node,
AEnv: tn.Node,
BEnv: tn.Node,
steps,
option='right'):
envOpAB = bops.permute(bops.multiContraction(AEnv, BEnv, '1', '3'),
[0, 3, 2, 4, 1, 5])
upRow = bops.multiContraction(cUp, dUp, '2', '0')
downRow = bops.multiContraction(cDown, dDown, '2', '0')
if option == 'right':
X = tn.Node(
np.ones((upRow[3].dimension, envOpAB[3].dimension,
downRow[3].dimension),
dtype=complex))
else:
X = tn.Node(
np.ones((upRow[0].dimension, envOpAB[2].dimension,
downRow[0].dimension),
dtype=complex))
for i in range(steps):
if option == 'right':
X = bops.multiContraction(
bops.multiContraction(bops.multiContraction(
X, upRow, '0', '3'),
envOpAB,
'340',
'013',
cleanOr1=True), downRow, '034', '312')
else:
X = bops.multiContraction(bops.multiContraction(
bops.multiContraction(X, upRow, '0', '0'),
envOpAB,
'023',
'201',
cleanOr1=True),
downRow,
'034',
'012',
cleanOr1=True)
norm = np.sqrt(bops.multiContraction(X, X, '012', '012*').tensor)
X = bops.multNode(X, 1 / norm)
return X
def getDMRGH(N, onsiteTerms, neighborTerms, d=2):
hSingles = [None] * N
for i in range(N):
hSingles[i] = tn.Node(onsiteTerms[i], name=('single' + str(i)), axis_names=['s' + str(i) + '*', 's' + str(i)])
hr2l = [None] * (N)
hl2r = [None] * (N)
for i in range(N-1):
if d == 2:
neighborTerm = np.reshape(neighborTerms[i], (2, 2, 2, 2))
elif d == 3:
neighborTerm = np.reshape(neighborTerms[i], (3, 3, 3, 3))
pairOp = tn.Node(neighborTerm, \
axis_names=['s' + str(i) + '*', 's' + str(i+1) + '*', 's' + str(i), 's' + str(i+1)])
splitted = tn.split_node(pairOp, [pairOp[0], pairOp[2]], [pairOp[1], pairOp[3]], \
left_name=('l2r' + str(i)), right_name=('r2l' + str(i) + '*'), edge_name='m')
hr2l[i+1] = bops.permute(splitted[1], [1, 2, 0])
hl2r[i] = splitted[0]
return HOp(hSingles, hr2l, hl2r)
def localVecsEstimate(psi: List[tn.Node],
vs: List[List[np.array]],
half='left'):
vs = np.round(vs, 10)
n = len(vs)
result = 1
for copy in range(n):
if half == 'left':
NA = len(vs[0])
curr = bops.multiContraction(psi[NA], psi[NA], '12', '12*')
sites = range(NA - 1, -1, -1)
elif half == 'right':
NA = len(psi) - len(vs[0])
curr = bops.multiContraction(psi[len(psi) - NA - 1],
psi[len(psi) - NA - 1], '01', '01*')
sites = range(NA, len(psi))
psiCopy = bops.copyState(psi)
for alpha in sites:
toEstimate = np.outer(vs[copy][alpha - NA],
np.conj(vs[np.mod(copy + 1, n)][alpha - NA]))
psiCopy[alpha] = bops.permute(bops.multiContraction(psiCopy[alpha], tn.Node(toEstimate), \
'1', '1'), [0, 2, 1])
if half == 'left':
curr = bops.multiContraction(bops.multiContraction(
psiCopy[alpha], curr, '2', '0', cleanOr2=True),
psi[alpha],
'12',
'12*',
cleanOr1=True)
elif half == 'right':
curr = bops.multiContraction(bops.multiContraction(
curr, psiCopy[alpha], '0', '0', cleanOr2=True),
psi[alpha],
'01',
'01*',
cleanOr1=True)
# psiCopy = bops.shiftWorkingSite(psiCopy, alpha, '<<')
result *= np.trace(curr.tensor)
tn.remove_node(curr)
bops.removeState(psiCopy)
return result
def singleHaarEstimation(psi: List[tn.Node], us: List[tn.Node], n: int,
NA: int):
psiCopy = bops.copyState(psi)
projector0 = np.zeros((2, 2))
projector0[0, 0] = 1
projector1 = np.zeros((2, 2))
projector1[1, 1] = 1
measurementResults = np.array(NA)
estimation = 1
for i in range(NA):
psiCopy[i] = bops.permute(
bops.multiContraction(psiCopy[i], us[i], '1', '1', cleanOr1=True),
[0, 2, 1])
measurementResults[i] = makeMeasurement(psiCopy, i, projector0)
if measurementResults:
resultProjector = projector0
else:
resultProjector = projector1
localEstimation = np.matmul(np.matmul(np.conj(np.transpose(us[i].tensor)), resultProjector), us[i].tensor) \
- np.eye(2)
estimation *= np.trace(localEstimation**4)
psiCopy = bops.shiftWorkingSite(psiCopy, i, '<<')
return estimation
def getExplicit2by2(g=0):
if g == 0:
with open('results/toricBoundaries', 'rb') as f:
[upRow, downRow, leftRow, rightRow, openA, openB, A,
B] = pickle.load(f)
else:
with open('results/toricBoundaries_g_' + str(g), 'rb') as f:
[upRow, downRow, leftRow, rightRow, openA, openB, A,
B] = pickle.load(f)
circle = bops.multiContraction(
bops.multiContraction(bops.multiContraction(upRow, rightRow, '3', '0'),
downRow, '5', '0'), leftRow, '70', '03')
ABNet = bops.permute(
bops.multiContraction(bops.multiContraction(openB, openA, '2', '4'),
bops.multiContraction(openA, openB, '2', '4'),
'28',
'16',
cleanOr1=True,
cleanOr2=True),
[1, 5, 6, 13, 14, 9, 10, 2, 0, 4, 8, 12, 3, 7, 11, 15])
dm = bops.multiContraction(circle, ABNet, '01234567', '01234567')
ordered = np.round(np.reshape(dm.tensor, [16, 16]), 14)
ordered /= np.trace(ordered)
return ordered
'3',
'0',
cleanOr1=True),
base,
'4',
'0',
cleanOr1=True)
AEnv = tn.Node(np.trace(A.get_tensor(), axis1=0, axis2=5))
GammaATensor = np.zeros((d, d, d), dtype=complex)
GammaATensor[1, 1, 1] = 1
GammaATensor[0, 0, 0] = 1
GammaBTensor = np.zeros((d, d, d), dtype=complex)
GammaBTensor[1, 1, 1] = 1
GammaBTensor[1, 1, 0] = -1
GammaBTensor[0, 0, 1] = 1
GammaBTensor[0, 0, 0] = 1
LambdaTensor = np.ones(d, dtype=complex)
cUp, dUp, cDown, dDown = peps.getBMPSRowOps(tn.Node(GammaATensor),
tn.Node(LambdaTensor),
tn.Node(GammaBTensor),
tn.Node(LambdaTensor), AEnv, AEnv,
100)
xRight = peps.bmpsSides(cUp, dUp, cUp, dUp, AEnv, AEnv, 100, option='right')
xLeft = peps.bmpsSides(cUp, dUp, cUp, dUp, AEnv, AEnv, 100, option='left')
pair = bops.permute(bops.multiContraction(A, A, '2', '4'),
[1, 6, 3, 7, 2, 8, 0, 5, 4, 9])
upRow = bops.multiContraction(cUp, dUp, '2', '0')
downRow = bops.multiContraction(cDown, dDown, '2', '0')
# origSizes = [T.tensor.shape[0], T.tensor.shape[1]]
# tMatrix = np.round(np.reshape(T.tensor, [origSizes[0] * origSizes[1], origSizes[0] * origSizes[1]]), 14)
# vals, vecs = scipy.sparse.linalg.eigs(tMatrix, k=1)
# # vals = np.round(vals, 6)
# # uVec = vecs[:, list(vals).index(1)]
# uVec = vecs[:, 0]
# uMatrix = np.reshape(uVec, origSizes)
# uMatrix /= np.sqrt(np.trace(np.matmul(uMatrix, np.conj(np.transpose(uMatrix)))) / len(uMatrix))
# print(np.trace(np.matmul(uMatrix, np.conj(uMatrix))) / len(uMatrix))
# U = tn.Node(uMatrix, backend=None)
psiP = bops.copyState(psi, conj=True)
for i in A1 + A2:
currU = trUnitary(i)
psiP[i] = bops.permute(bops.multiContraction(psiP[i], currU, [1], [0]), [0, 2, 1])
psiConj = bops.copyState(psi, conj=True)
curr = bops.multiContraction(psiP[A1[0]], psiConj[A1[0]], [0, 1], [0, 1])
for i in range(A1[1], A2[-1]-1):
curr = bops.multiContraction(bops.multiContraction(curr, psiP[i], [0], [0]), psiConj[i], [0, 1], [0, 1])
curr = bops.multiContraction(bops.multiContraction(curr, psiP[A2[-1]], [0], [0]), psiConj[A2[-1]], [0, 1, 2], [0, 1, 2])
# pt = getPartiallyTransposed(psi, A1[0], A1[-1], A2[0], A2[-1])
# reg = getStraightDM(psiP, A1[0], A1[-1], A2[0], A2[-1])
b=1
""" This does not give the same result as Poleman-Turner's paper! """
def applySwap(psi, psiP, startInd, endInd):
psiDagger = bops.copyState(psi, conj=True)
psiPDagger = bops.copyState(psi, conj=True)
curr = bops.multiContraction(psi[startInd], psiDagger[startInd], [0], [0])
currP = bops.multiContraction(psiP[startInd], psiPDagger[startInd], [0], [0])
with open(
homedir + '/expected_MPS_NA_' + str(NA) + '_NB_' + str(NB) + '_n_' +
str(n) + '_' + half, 'wb') as f:
pickle.dump(Sn, f)
mySum = 0
M = 1000
if half == 'left':
steps = int(2**(NA * n))
for k in range(len(psi) - 1, NA - 1, -1):
psi = bops.shiftWorkingSite(psi, k, '<<')
sites = range(NA)
else:
steps = int(2**(NB * n))
sites = range(NA, len(psi))
for site in sites:
psi[site] = bops.permute(bops.multiContraction(psi[site], U, '1', '0'),
[0, 2, 1])
for m in range(M * steps):
if half == 'left':
vs = [[np.array([np.exp(1j * np.pi * np.random.randint(4) / 2), np.exp(1j * np.pi * np.random.randint(4) / 2)]) \
for alpha in range(NA)] for copy in range(n)]
else:
vs = [[np.array([np.exp(1j * np.pi * np.random.randint(4) / 2), np.exp(1j * np.pi * np.random.randint(4) / 2)]) \
for alpha in range(NB)] for copy in range(n)]
u = np.matmul(ru.getUTheta(theta, d=2), ru.getUPhi(phi, d=2))
for i in range(len(vs)):
for j in range(len(vs[0])):
vs[i][j] = np.matmul(u, vs[i][j])
currEstimation = localVecsEstimate(psi, vs, half=half)
mySum += currEstimation
if m % M == M - 1:
with open(
'1', '0')
u1 = tn.Node(randomUs.haar_measure(d))
openA1 = bops.multiContraction(u1,
bops.multiContraction(openA, u1, '5', '1*'),
'1', '0')
u2 = tn.Node(randomUs.haar_measure(d))
openA2 = bops.multiContraction(u2,
bops.multiContraction(openA, u2, '5', '1*'),
'1', '0')
u3 = tn.Node(randomUs.haar_measure(d))
openB3 = bops.multiContraction(u3,
bops.multiContraction(openB, u3, '5', '1*'),
'1', '0')
env123 = bops.multiContraction(circle, BEnv, '12', '03')
env23 = bops.multiContraction(env123, AEnv, '126', '013')
env3 = bops.permute(bops.multiContraction(env23, AEnv, '430', '023'),
[2, 0, 1, 3])
us[m] = [u0.tensor, u1.tensor, u2.tensor, u3.tensor]
rho3 = bops.multiContraction(env3, openB3, '0123', '1234')
ks[m][3] = randomMeas(rho3.tensor / np.trace(rho3.tensor))
if ks[m][3] == 0:
B3 = tn.Node(openB3.tensor[0, :, :, :, :, 0])
else:
B3 = tn.Node(openB3.tensor[1, :, :, :, :, 1])
env2 = bops.permute(bops.multiContraction(env23, B3, '512', '012'),
[2, 3, 1, 0])
rho2 = bops.multiContraction(env2, openA2, '0123', '1234')
ks[m][2] = randomMeas(rho2.tensor / np.trace(rho2.tensor))
if ks[m][2] == 0:
A2 = tn.Node(openA2.tensor[0, :, :, :, :, 0])
AEnv = toEnvOperator(bops.multiContraction(A, A, '4', '4*'))
BEnv = toEnvOperator(bops.multiContraction(B, B, '4', '4*'))
chi = 32
nonPhysicalLegs = 1
GammaTensor = np.ones((nonPhysicalLegs, d**2, nonPhysicalLegs), dtype=complex)
GammaC = tn.Node(GammaTensor, name='GammaC', backend=None)
LambdaC = tn.Node(np.eye(nonPhysicalLegs) / np.sqrt(nonPhysicalLegs),
backend=None)
GammaD = tn.Node(GammaTensor, name='GammaD', backend=None)
LambdaD = tn.Node(np.eye(nonPhysicalLegs) / np.sqrt(nonPhysicalLegs),
backend=None)
steps = 50
envOpAB = bops.permute(bops.multiContraction(AEnv, BEnv, '1', '3'),
[0, 3, 2, 4, 1, 5])
envOpBA = bops.permute(bops.multiContraction(BEnv, AEnv, '1', '3'),
[0, 3, 2, 4, 1, 5])
#
# curr = bops.permute(bops.multiContraction(envOpBA, envOpAB, '45', '01'), [0, 2, 4, 6, 1, 3, 5, 7])
#
# for i in range(50):
# [C, D, te] = bops.svdTruncation(curr, [0, 1, 2, 3], [4, 5, 6, 7], '>>', normalize=True)
# curr = bops.permute(bops.multiContraction(D, C, '23', '12'), [1, 3, 0, 5, 2, 4])
# curr = bops.permute(bops.multiContraction(curr, envOpAB, '45', '01'), [0, 2, 4, 6, 1, 3, 5, 7])
#
# currAB = curr
# [C, D, te] = bops.svdTruncation(curr, [0, 1, 2, 3], [4, 5, 6, 7], '>>', normalize=True)
# currBA = bops.permute(bops.multiContraction(D, C, '23', '12'), [1, 3, 0, 5, 2, 4])
# currBA = bops.permute(bops.multiContraction(currBA, envOpAB, '45', '01'), [0, 2, 4, 6, 1, 3, 5, 7])
#
