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 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 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 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
# print('<psi|hpsi> = ' + str(bops.getOverlap(psi, hpsi)))
R2 = bops.getRenyiEntropy(psi, 2, int(len(psi) / 2 - 1))
NU = 200
etas = [1, 2, 3, N, int(N * 1.5), N * 2, int(N * 2.5), N * 3]
results = [None] * len(etas)
dt = J * 1e-2
for e in range(len(etas)):
eta = etas[e]
sum = 0
for n in range(NU):
psiCopy = bops.copyState(psi)
for j in range(eta):
onsiteTermsA, neighborTermsA = getHAMatrices(N, C, Omega, delta)
HA = dmrg.getDMRGH(N, onsiteTermsA, neighborTermsA)
trotterGates = trotter.getTrotterGates(N, 2, onsiteTermsA, neighborTermsA, dt)
for i in range(int(T / dt)):
[psiCopy, truncErr] = trotter.trotterSweep(trotterGates, psiCopy, 0, int(len(psiCopy) / 2 - 1))
psiCopy2 = bops.copyState(psiCopy)
projectS(psiCopy, int(len(psiCopy)/2 - 1))
p = bops.getOverlap(psiCopy, psiCopy2)
sum += p * p
bops.removeState(psiCopy)
bops.removeState(psiCopy2)
avg = sum / NU
results[e] = avg * (2**int(len(psi)/2) * (2**int(len(psi)/2) + 1)) - 1
plt.plot(etas, [R2] * len(etas))
plt.plot(etas, results)
plt.show()
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]
print('line 196, k = ' + str(k) + ', overlap = ' +
str(bops.getOverlap(psiCopy, psiCompare)))
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]
print('line 219, k = ' + str(k) + ', counter = ' + str(counter) +
', overlap = ' + str(bops.getOverlap(psiCopy, psiCompare)))
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)))
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]
t = 0.5 onsiteTerm = np.zeros((2, 2)) onsiteTerm[1][1] = 0 onsiteTerm[0][0] = 0 neighborTerm = np.zeros((4, 4)) neighborTerm[1][2] = 1 neighborTerm[2][1] = 1 neighborTerm[0][0] = 0 neighborTerm[3][3] = 0 psi1 = bops.getStartupState(N) H = getDMRGH(N, onsiteTerm, neighborTerm) HLs, HRs = getHLRs(H, psi1) psi1, E0, truncErrs = getGroundState(H, HLs, HRs, psi1, None) print(stateEnergy(psi1, H)) print(len(truncErrs)) psi2 = bops.getOrthogonalState(psi1) print(bops.getOverlap(psi1, psi2)) HLs, HRs = getHLRs(H, psi2) psi2, E0, truncErrs = getGroundState(H, HLs, HRs, psi2, psi1) print(stateEnergy(psi2, H)) print(bops.getOverlap(psi1, psi2)) print(len(truncErrs)) # psi3 = bops.addStates(psi2, psi) # print(bops.getOverlap(psi, psi3)) # print(bops.getOverlap(psi2, psi3)) # psi3[0] = bops.multNode(psi3[0], 1 / math.sqrt(bops.getOverlap(psi3, psi3))) # H, HLs, HRs = getH(N, onsiteTerm, neighborTerm, psi3) # psi3, E0, truncErrs = getGroundState(H, HLs, HRs, N, psi3) # print(stateEnergy(psi3, H)) # print(bops.getOverlap(psi, psi3)) # print(bops.getOverlap(psi2, psi3))
