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 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 getTridiagonal(HL, HR, H, k, psi, psiCompare=None):
accuracy = 1e-10 # 1e-12
v = bops.multiContraction(psi[k], psi[k + 1], '2', '0')
# Small innaccuracies ruin everything!
v.set_tensor(v.get_tensor() / bops.getNodeNorm(v))
psiCopy = bops.copyState(psi)
base = []
base.append(v)
Hv = applyHToM(HL, HR, H, v, k)
alpha = bops.multiContraction(v, Hv, '0123', '0123*').get_tensor()
if psiCompare is not None:
copyV = bops.copyState([v])[0]
psiCopy = bops.assignNewSiteTensors(psiCopy, k, copyV, '>>')[0]
E = stateEnergy(psi, H)
w = bops.addNodes(Hv, bops.multNode(v, -alpha))
beta = bops.getNodeNorm(w)
# Start with T as an array and turn into tridiagonal matrix at the end.
Tarr = [[0, 0, 0]]
Tarr[0][1] = alpha
counter = 0
formBeta = 2 * beta # This is just some value to init formBeta > beta.
while (beta > accuracy) and (counter <= 50) and (beta < formBeta):
Tarr[counter][2] = beta
Tarr.append([0, 0, 0])
Tarr[counter + 1][0] = beta
counter += 1
v = bops.multNode(w, 1 / beta)
base.append(v)
if psiCompare is not None:
copyV = bops.copyState([v])[0]
psiCopy = bops.assignNewSiteTensors(psiCopy, k, copyV, '>>')[0]
Hv = applyHToM(HL, HR, H, v, k)
alpha = bops.multiContraction(v, Hv, '0123', '0123*').get_tensor()
Tarr[counter][1] = alpha
w = bops.addNodes(bops.addNodes(Hv, bops.multNode(v, -alpha)), \
bops.multNode(base[counter-1], -beta))
formBeta = beta
beta = bops.getNodeNorm(w)
T = np.zeros((len(Tarr), len(Tarr)), dtype=complex)
T[0][0] = Tarr[0][1]
if len(Tarr) > 1:
T[0][1] = Tarr[0][2]
for i in range(1, len(Tarr)-1):
T[i][i-1] = Tarr[i][0]
T[i][i] = Tarr[i][1]
T[i][i+1] = Tarr[i][2]
T[len(Tarr)-1][len(Tarr)-2] = Tarr[len(Tarr)-1][0]
T[len(Tarr) - 1][len(Tarr) - 1] = Tarr[len(Tarr) - 1][1]
return [T, base]
def getEMatrix(psi, startInd, endInd):
psiDagger = bops.copyState(psi, conj=True)
E = bops.multiContraction(psi[startInd], psiDagger[startInd], [1], [1])
for i in range(startInd + 1, endInd + 1):
E = bops.multiContraction(
E, bops.multiContraction(psi[i], psiDagger[i], [1], [1]), [1, 3],
[0, 2])
bops.removeState(psiDagger)
return E
def applyVecsToSite(site: tn.Node, vecUp: np.array, vecDown: np.array):
up = bops.multiContraction(site, tn.Node(vecUp), '4', '0', cleanOr2=True)
down = bops.multiContraction(site,
tn.Node(vecDown),
'4*',
'0*',
cleanOr2=True)
dm = tn.Node(np.kron(up.tensor, down.tensor))
return dm
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 getRowDM(GammaL, LambdaL, GammaR, LambdaR, sites, d):
c = bops.multiContraction(bops.multiContraction(LambdaR,
GammaL,
'1',
'0',
isDiag1=True),
LambdaL,
'2',
'0',
isDiag2=True)
row = bops.multiContraction(bops.multiContraction(c, GammaR, '2', '0'),
LambdaR,
'3',
'0',
isDiag2=True)
for i in range(sites):
row = bops.multiContraction(row, GammaL, [len(row.edges) - 1], [0])
row = bops.multiContraction(row,
LambdaL, [len(row.edges) - 1], [0],
isDiag2=True)
row = bops.multiContraction(row, GammaR, [len(row.edges) - 1], [0])
row = bops.multiContraction(row,
LambdaR, [len(row.edges) - 1], [0],
isDiag2=True)
dm = bops.multiContraction(row, row, [0, len(row.edges) - 1],
[0, len(row.edges) - 1, '*'])
rho = np.reshape(dm.tensor, [d**((2 + 2 * sites)), d**((2 + 2 * sites))])
return rho / np.trace(rho)
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 getIdentity(psi, k, dir):
psil = bops.copyState([psi[k]])[0]
psilCopy = bops.copyState([psi[k]], conj=True)[0]
if dir == '>>':
result = bops.multiContraction(psil, psilCopy, '01', '01').tensor
else:
result = bops.multiContraction(psil, psilCopy, '12', '12').tensor
for i in range(len(result)):
for j in range(len(result[0])):
result[i][j] = round(result[i][j], 2)
return result
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 getDensityMatrix(psi, A1Start, A1End, A2Start, A2End):
psiCopy = bops.copyState(psi)
for k in [len(psiCopy) - 1 - i for i in range(len(psiCopy) - A2End - 1)]:
psiCopy = bops.shiftWorkingSite(psiCopy, k, '<<')
E1 = getEMatrix(psiCopy, A1Start, A1End)
bops.copyState([E1])
N1, N1bar = getNMatrices(E1, 1)
N1bar.edges[0].name += '*'
E2 = getEMatrix(psiCopy, A2Start, A2End)
N2, N2bar = getNMatrices(E2, 2)
N2bar.edges[0].name += '*'
res = bops.multiContraction(bops.multiContraction(N1, N1bar, [0], [1]),
bops.multiContraction(N2, N2bar, [1], [2]),
[0, 3], [0, 3])
bops.removeState(psiCopy)
return res
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 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 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 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 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 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 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 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])
curr = bops.multiContraction(curr, currP, [2, 0], [0, 2])
for i in range(startInd + 1, endInd + 1):
curr = bops.multiContraction(curr, psi[i], [0], [0])
curr = bops.multiContraction(curr, psiDagger[i], [0], [0])
curr = bops.multiContraction(curr, psiP[i], [0, 4], [0, 1])
curr = bops.multiContraction(curr, psiPDagger[i], [0, 1], [0, 1])
bops.removeState(psiPDagger)
bops.removeState(psiPDagger)
return curr
def applyO(psi, psiP, startInd, endInd):
psiDagger = bops.copyState(psi, conj=True)
psiPDagger = bops.copyState(psi, conj=True)
OTensor = np.zeros((9, 9), dtype=complex)
for i in range(3):
for j in range(3):
OTensor[i * 3 + i, j * 3 + j] = 1
OTensor = np.reshape(OTensor, [3, 3, 3, 3])
O = tn.Node(OTensor, name='O', backend=None)
curr = bops.multiContraction(psi[endInd], psiDagger[endInd], [2], [2])
currP = bops.multiContraction(psiP[endInd], psiPDagger[endInd], [2], [2])
curr = bops.multiContraction(curr, O, [1, 3], [1, 3])
curr = bops.multiContraction(curr, currP, [2, 3], [1, 3])
for i in [endInd - j for j in range(1, endInd - startInd + 1)]:
O = tn.Node(OTensor, name='O', backend=None)
curr = bops.multiContraction(curr, psi[i], [0], [2])
curr = bops.multiContraction(curr, psiDagger[i], [0], [2])
curr = bops.multiContraction(curr, O, [3, 5], [1, 3])
curr = bops.multiContraction(curr, psiP[i], [0, 4], [2, 1])
curr = bops.multiContraction(curr, psiPDagger[i], [0, 3], [2, 1])
bops.removeState(psiPDagger)
bops.removeState(psiPDagger)
return curr
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 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 randomMeasurement(psi, startInd, endInd):
d = psi[0].tensor.shape[1]
res = [-1] * (endInd - startInd)
psiCopy = bops.copyState(psi)
for k in [len(psiCopy) - 1 - i for i in range(len(psiCopy) - startInd - 1)]:
psiCopy = bops.shiftWorkingSite(psiCopy, k, '<<')
for i in range(startInd, endInd):
rho = bops.multiContraction(psiCopy[i], psiCopy[i], '02', '02*')
measurement = np.random.uniform(low=0, high=1)
covered = 0
for s in range(len(rho.tensor)):
if covered < measurement < covered + rho.tensor[s, s]:
res[i - startInd] = s
break
covered += rho.tensor[s, s]
projectorTensor = np.zeros((d, d), dtype=complex)
projectorTensor[res[i - startInd], res[i - startInd]] = 1
projector = tn.Node(projectorTensor, backend=None)
bops.applySingleSiteOp(psiCopy, projector, i)
psiCopy = bops.shiftWorkingSite(psiCopy, i, '>>')
psiCopy[i + 1].tensor /= np.sqrt(bops.getOverlap(psiCopy, psiCopy))
tn.remove_node(rho)
bops.removeState(psiCopy)
return res
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
d = 2
baseTensor = np.zeros((d, d, d), dtype=complex)
for i in range(d):
baseTensor[i, 0, i] = 1 #np.sqrt(np.cosh(beta))
for i in range(d):
baseTensor[i, 1, i] = 0.5 * (
1 - 2 * i) #np.sqrt(np.sinh(beta)) * (1 - 2 * i) # sigma_z
base = tn.Node(baseTensor)
A = bops.multiContraction(bops.multiContraction(bops.multiContraction(
base, base, '2', '0'),
base,
'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)