def test_converting_hubbard_ham(self, Lx, Ly):
'''Evaluate energy of spinless Hubbard model
on a random state, using 'qubit numbers' and
qubit coordinates to specify target sites.
Check energies are equal.
'''
psi_trial = qnets.QubitEncodeVector.rand(Lx, Ly, bond_dim=2)
psi_trial.setup_bmps_contraction_()
norm, bra, ket = psi_trial.make_norm(return_all=True)
norm ^= all
# encoded Fermi-Hubbard with default parameters
HubbardHam = hams.SpinlessSimHam(Lx, Ly)
# terms specify qubit coos rather than qubit nums
CooHam = HubbardHam.convert_to_coordinate_ham(
qubit_to_coo_map=psi_trial.qubit_to_coo_map)
# energy computed with HubbardHam
E1 = 0
for where, gate in HubbardHam.gen_ham_terms():
E1 += (bra | ket.apply_gate(
gate, where, keys='qnumbers', contract=True)) ^ all
# energy computed with CooHam
E2 = 0
for coos, gate in CooHam.gen_ham_terms():
E2 += (bra | ket.apply_gate(
gate, where=coos, keys='coos', contract=True)) ^ all
E1 = E1 / norm
E2 = E2 / norm
assert np.allclose(E1, E2)
def test_compute_local_expectation_vs_dense(self, Lx, Ly, normalized):
# (2Lx-1) * (2Ly-1) lattice ePEPSvector
epeps = qnets.QubitEncodeVector.rand(Lx, Ly)\
.convert_to_ePEPS_vector()
# qubits + dummies
n_sites = (2 * Lx - 1) * (2 * Ly - 1)
# vertices + occupied faces in 'original' Lx*Ly lattice
n_qubits = (Lx * Ly) + int((Lx - 1) * (Ly - 1) / 2)
# 'qubit' Fermi-Hubbard with random parameters
t, V, mu = np.random.rand(3)
H = hams.SpinlessSimHam(Lx, Ly, t, V, mu)
# separate indices of qubits from 'aux' tensors
qubit_inds = tuple(
starmap(epeps.site_ind,
(epeps.qubit_to_coo_map[q] for q in range(n_qubits))))
non_qubit_inds = set(epeps.site_inds) - set(qubit_inds)
# 'densify' into vector with qubit dimensions first
psi_dense = epeps.to_dense((*qubit_inds, *non_qubit_inds))
if normalized:
qu.normalize(psi_dense)
dense_terms = [
qu.pkron(term, dims=[2] * n_sites, inds=where)
for where, term in H.gen_ham_terms()
]
exact = sum((qu.expec(h, psi_dense) for h in dense_terms))
# now compute energy with `ePEPSvector.compute_local_expectation`
q2coo = lambda q: epeps.qubit_to_coo_map[q]
CooHam = H.convert_to_coordinate_ham(q2coo)
terms = CooHam._coo_ham_terms
envs, plaqmap = epeps.calc_plaquette_envs_and_map(terms)
opts = dict(cutoff=2e-3, max_bond=9, contract_optimize='random-greedy')
e = epeps.compute_local_expectation(terms,
normalized=normalized,
autogroup=False,
plaquette_envs=envs,
plaquette_map=plaqmap,
**opts)
assert e == pytest.approx(exact, rel=1e-2)
def test_epeps_absorb_3body_tensor(self, Lx, Ly, method):
'''Currently only tests 3-body ops!
contract_methods = {0: False, 1: 'triangle_absorb'}
'''
# opts for splitting 'blob' in `triangle_absorb` method
compress_opts = {'method': method}
epeps = qnets.QubitEncodeVector.rand(Lx,
Ly).convert_to_ePEPS(dummy_size=1)
bra = epeps.H
# compile (vertex, vertex, face) 'target' qubits
LatticeCooHam = hams.SpinlessSimHam(Lx, Ly).\
convert_to_coordinate_ham(lambda q: epeps.qubit_to_coo_map[q])
for coos, _ in LatticeCooHam.gen_ham_terms():
# SKIP 2-body interactions
if len(coos) == 2:
continue
rand_gate = qu.rand_matrix(8) #use a random 3-body gate
G_ket_0 = epeps.gate(G=rand_gate, coos=coos, contract=False)
G_ket_1 = epeps.gate(G=rand_gate,
coos=coos,
contract='triangle_absorb',
**compress_opts)
expec_0 = (bra & G_ket_0) ^ all # `contract=False` reference
expec_1 = (bra & G_ket_1) ^ all # `triangle_absorb` reference
assert expec_1 == pytest.approx(expec_0, rel=1e-2)
coos = (coos[1], coos[0], coos[2]
) # now try w/ vertex qubits swapped
G_ket_0 = epeps.gate(G=rand_gate, coos=coos, contract=False)
G_ket_2 = epeps.gate(G=rand_gate,
coos=coos,
contract='triangle_absorb',
**compress_opts)
expec_0 = (bra & G_ket_0) ^ all
expec_2 = (bra & G_ket_2) ^ all
assert expec_2 == pytest.approx(expec_0, rel=1e-2)
def test_qev_triangle_absorb_method(self, Lx, Ly, method):
'''Test 'triangle_absorb' method, which works for
`QubitEncodeVector`-type geometry without rotating the
face tensors (i.e. non-rectangular lattice geometry).
'''
# opts for splitting 'blob' in `triangle_absorb` method
compress_opts = {'method': method}
# without rotating face tensors!
psi = qnets.QubitEncodeVector.rand(Lx, Ly, bond_dim=2)
bra = psi.H
# norm = (bra & psi) ^ all
# compile all 3-tuples (vertex, vertex, face) qubits to act on
LatticeHam = hams.SpinlessSimHam(Lx, Ly)
for where, _ in LatticeHam.gen_ham_terms():
# skip 2-body terms
if len(where) == 2:
continue
rand_gate = qu.rand_matrix(8)
# apply gate both 0) without contracting, and 1) with 'triangle-absorb'
G_ket_0 = psi.apply_gate(G=rand_gate, where=where, contract=False)
G_ket_1 = psi.apply_gate(G=rand_gate,
where=where,
contract='triangle_absorb',
**compress_opts)
expec_0 = (bra & G_ket_0) ^ all
expec_1 = (bra & G_ket_1) ^ all
assert expec_1 == pytest.approx(expec_0, rel=1e-2)
## also try with vertex qubits switched!
where = (where[1], where[0], where[2])
G_ket_0 = psi.apply_gate(G=rand_gate, where=where, contract=False)
G_ket_2 = psi.apply_gate(G=rand_gate,
where=where,
contract='triangle_absorb',
**compress_opts)
expec_0 = (bra & G_ket_0) ^ all
expec_2 = (bra & G_ket_2) ^ all
assert expec_2 == pytest.approx(expec_0, rel=1e-2)
def test_epeps_absorb_3body_gate(self, Lx, Ly, method):
'''Test absorbing a 3-body dense, random gate into the tn.
'''
# opts for splitting 'blob' in `triangle_absorb` method
compress_opts = {'method': method}
epeps = qnets.QubitEncodeVector.rand(Lx,
Ly).convert_to_ePEPS(dummy_size=1)
bra = epeps.H
# norm = (bra & epeps) ^ all
# use Ham to get (vertex, vertex, face) 'target' qubits
LatticeCooHam = hams.SpinlessSimHam(Lx, Ly).\
convert_to_coordinate_ham(lambda q: epeps.qubit_to_coo_map[q])
for coos, _ in LatticeCooHam.gen_ham_terms():
# skip 2-body interactions
if len(coos) == 2:
continue
rand_gate = qu.rand_matrix(8) #use a random 3-body gate
G_ket_0 = epeps.gate(G=rand_gate, coos=coos, contract=False)
G_ket_1 = epeps.absorb_three_body_gate(G=rand_gate,
coos=coos,
**compress_opts)
expec_0 = (bra & G_ket_0) ^ all # `contract=False` reference
expec_1 = (bra & G_ket_1) ^ all # `triangle_absorb` reference
assert expec_1 == pytest.approx(expec_0, rel=1e-2)
# now try with the vertex qubits swapped
coos = (coos[1], coos[0], coos[2])
G_ket_0 = epeps.gate(G=rand_gate, coos=coos, contract=False)
G_ket_2 = epeps.absorb_three_body_gate(G=rand_gate,
coos=coos,
**compress_opts)
expec_0 = (bra & G_ket_0) ^ all
expec_2 = (bra & G_ket_2) ^ all
assert expec_2 == pytest.approx(expec_0, rel=1e-2)
def test_epeps_2body_reduce_split(self, Lx, Ly, contract):
epeps = qnets.QubitEncodeVector.rand(Lx,
Ly).convert_to_ePEPS(dummy_size=1)
bra = epeps.H
# compile (vertex, vertex) 'target' qubit pairs
LatticeCooHam = hams.SpinlessSimHam(Lx, Ly).\
convert_to_coordinate_ham(lambda q: epeps.qubit_to_coo_map[q])
for coos, _ in LatticeCooHam.gen_ham_terms():
# skip 3-body terms here
if len(coos) == 3:
continue
rand_gate = qu.rand_matrix(4)
G_ket_0 = epeps.gate(G=rand_gate, coos=coos, contract=False)
G_ket_1 = epeps.gate(G=rand_gate, coos=coos, contract=contract)
assert (bra & G_ket_1) ^ all == pytest.approx(
(bra & G_ket_0) ^ all, rel=1e-2)
def test_compute_local_expectation(self, Lx, Ly, normalized):
# 'qubit' Fermi-Hubbard with default parameters
t, V, mu = np.random.rand(3)
H = hams.SpinlessSimHam(Lx, Ly, t, V, mu)
psi_qev = qnets.QubitEncodeVector.rand(Lx, Ly)\
.setup_bmps_contraction_()
norm, bra, ket = psi_qev.make_norm(return_all=True)
norm ^= all
Exact = sum(((bra | ket.apply_gate(gate, where)) ^ all
for where, gate in H.gen_ham_terms()))
if normalized:
Exact /= norm
# Now compute with `ePEPSvector.compute_local_expectation`
epeps = psi_qev.convert_to_ePEPS_vector()
q2coo = lambda q: epeps.qubit_to_coo_map[q]
CooHam = H.convert_to_coordinate_ham(q2coo)
terms = CooHam._coo_ham_terms
envs, plaqmap = epeps.calc_plaquette_envs_and_map(terms)
opts = dict(cutoff=2e-3, max_bond=9, contract_optimize='random-greedy')
e = epeps.compute_local_expectation(terms,
normalized=normalized,
autogroup=False,
plaquette_envs=envs,
plaquette_map=plaqmap,
**opts)
assert e == pytest.approx(Exact, rel=1e-2)
def test_epeps_vs_qev_absorb_gate(self, Lx, Ly, method, tn_format):
'''Test that we get same result (for 3-body interactions)
whether we evaluate with a ``QubitEncodeVector`` or the
2D-regular-lattice version ``ePEPS``.
Methods tested:
---------------
QubitEncodeVector.apply_gate(..., contract='triangle_absorb)
ePEPS.absorb_three_body_gate(...)
'''
# opts for splitting 'blob' in `triangle_absorb` method
compress_opts = {'method': method}
# without rotating face tensors!
psi = qnets.QubitEncodeVector.rand(Lx, Ly, bond_dim=2)
bra = psi.H
# make into 'regular' 2D-square-lattice TN
if tn_format == 'epeps':
psi_2d = psi.convert_to_ePEPS(dummy_size=1)
elif tn_format == 'epeps_vec':
psi_2d = psi.convert_to_ePEPS_vector(dummy_size=1)
bra_2d = psi_2d.H
Ham = hams.SpinlessSimHam(Lx, Ly)
# LatticeCooHam = Ham.convert_to_coordinate_ham().\
# convert_to_coordinate_ham(psi_2d.qubit_to_coo_map)
for where, _ in Ham.gen_ham_terms():
# skip 2-body interactions
if len(where) == 2:
continue
coos = [psi_2d.qubit_to_coo_map[q] for q in where]
rand_gate = qu.rand_matrix(8) #use a random 3-body gate
G_psi = psi.apply_gate(G=rand_gate,
where=where,
contract='triangle_absorb',
**compress_opts)
expec_QEV = (bra & G_psi) ^ all
G_psi_2d = psi_2d.absorb_three_body_gate(G=rand_gate,
coos=coos,
**compress_opts)
expec_ePEPS = (bra_2d & G_psi_2d) ^ all
assert expec_ePEPS == pytest.approx(expec_QEV, rel=1e-2)
# now try with vertex qubits swapped
where = (where[1], where[0], where[2])
coos = [psi_2d.qubit_to_coo_map[q] for q in where]
# do the same test
G_psi = psi.apply_gate(G=rand_gate,
where=where,
contract='triangle_absorb',
**compress_opts)
expec_QEV = (bra & G_psi) ^ all
G_psi_2d = psi_2d.absorb_three_body_gate(G=rand_gate,
coos=coos,
**compress_opts)
expec_ePEPS = (bra_2d & G_psi_2d) ^ all
assert expec_ePEPS == pytest.approx(expec_QEV, rel=1e-2)