def test_contract_scalar(self, backend):
qstate = peps.random(3, 4, 2, backend=backend)
norm = qstate.norm(contract_option=Snake())
for contract_option in contract_options:
if contract_option is not Snake:
for svd_option in (None, ReducedSVD(16), RandomizedSVD(16),
ImplicitRandomizedSVD(16),
ImplicitRandomizedSVD(
16, orth_method='local_gram')):
with self.subTest(contract_option=contract_option.__name__,
svd_option=svd_option):
self.assertTrue(
np.isclose(
norm,
qstate.norm(contract_option=contract_option(
svd_option))))
def test_einsumsvd_options(self, tb):
from tensorbackends.interface import ReducedSVD, RandomizedSVD, ImplicitRandomizedSVD
a = tb.astensor(
[[0, 2e-3j, 0, 0], [1e-3, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4j]],
dtype=complex)
p = tb.astensor(
[[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]],
dtype=complex)
s_true = tb.astensor([4, 3])
low_rank = tb.astensor(
[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4j]],
dtype=complex)
options = [
ReducedSVD(rank=2),
RandomizedSVD(rank=2, niter=2, oversamp=1),
ImplicitRandomizedSVD(rank=2, niter=2)
]
for option in options:
with self.subTest(option=option):
u, s, v = tb.einsumsvd('ij,jk->is,sk', p, a, option=option)
usv = tb.einsum('is,s,sk->ik', u, s, v)
self.assertEqual(u.shape, (4, 2))
self.assertEqual(s.shape, (2, ))
self.assertEqual(v.shape, (2, 4))
self.assertTrue(tb.allclose(s, s_true))
self.assertTrue(tb.allclose(usv, low_rank, atol=1e-9))
def test_amplitude_nonlocal(self, backend):
update_options = [
None,
peps.DirectUpdate(ImplicitRandomizedSVD(rank=2)),
peps.QRUpdate(rank=2),
peps.LocalGramQRUpdate(rank=2),
peps.LocalGramQRSVDUpdate(rank=2),
]
for option in update_options:
with self.subTest(update_option=option):
qstate = peps.computational_zeros(2, 3, backend=backend)
qstate.apply_circuit([
Gate('X', [], [0]),
Gate('H', [], [1]),
Gate('CX', [], [0, 5]),
Gate('CX', [], [1, 3]),
Gate('S', [], [1]),
],
update_option=option)
self.assertTrue(
np.isclose(qstate.amplitude([1, 0, 0, 0, 0, 1]),
1 / np.sqrt(2)))
self.assertTrue(
np.isclose(qstate.amplitude([1, 1, 0, 1, 0, 1]),
1j / np.sqrt(2)))
def test_inner_approx(self, backend):
psi = peps.computational_zeros(2, 3, backend=backend)
psi.apply_circuit([
Gate('H', [], [0]),
Gate('CX', [], [0,3]),
Gate('H', [], [3]),
], update_option=peps.DirectUpdate(ImplicitRandomizedSVD(rank=2)))
phi = peps.computational_zeros(2, 3, backend=backend)
contract_option = peps.BMPS(ReducedSVD(rank=2))
self.assertTrue(backend.isclose(psi.inner(phi, contract_option), 0.5))
def test_einsumsvd_absorb_s(self, tb):
from tensorbackends.interface import ReducedSVD, RandomizedSVD, ImplicitRandomizedSVD
a = tb.astensor([[0,2e-3j,0,0],[1e-3,0,0,0],[0,0,3,0],[0,0,0,4j]], dtype=complex)
p = tb.astensor([[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]], dtype=complex)
s_true = tb.astensor([4,3])
low_rank = tb.astensor([[0,0,0,0],[0,0,0,0],[0,0,3,0],[0,0,0,4j]], dtype=complex)
options = [
ReducedSVD(rank=2),
RandomizedSVD(rank=2, niter=2, oversamp=1),
ImplicitRandomizedSVD(rank=2, niter=2, orth_method='qr'),
ImplicitRandomizedSVD(rank=2, niter=2, orth_method='local_gram'),
]
for option in options:
for absorb_s in ['even', 'u', 'v']:
with self.subTest(option=option):
u, _, v = tb.einsumsvd('ij,jk->is,sk', p, a, option=option, absorb_s=absorb_s)
usv = tb.einsum('is,sk->ik', u, v)
self.assertEqual(u.shape, (4,2))
self.assertEqual(v.shape, (2,4))
self.assertTrue(tb.allclose(usv, low_rank, atol=1e-9))
def test_amplitude_approx(self, backend):
qstate = peps.computational_zeros(2, 3, backend=backend)
qstate.apply_circuit([
Gate('X', [], [0]),
Gate('H', [], [1]),
Gate('CX', [], [0,3]),
Gate('CX', [], [1,4]),
Gate('S', [], [1]),
], update_option=peps.DirectUpdate(ImplicitRandomizedSVD(rank=2)))
contract_option = peps.BMPS(ReducedSVD(rank=2))
self.assertTrue(backend.isclose(qstate.amplitude([1,0,0,1,0,0], contract_option), 1/np.sqrt(2)))
self.assertTrue(backend.isclose(qstate.amplitude([1,1,0,1,1,0], contract_option), 1j/np.sqrt(2)))
def test_contract_vector(self, backend):
qstate = peps.random(3, 3, 2, backend=backend)
statevector = qstate.statevector(contract_option=Snake())
for contract_option in [
BMPS(None),
BMPS(ReducedSVD(16)),
BMPS(RandomizedSVD(16)),
BMPS(ImplicitRandomizedSVD(16))
]:
with self.subTest(contract_option=contract_option):
contract_result = qstate.statevector(
contract_option=contract_option)
self.assertTrue(
backend.allclose(statevector.tensor,
contract_result.tensor))
def test_expectation_use_cache_approx(self, backend):
qstate = peps.computational_zeros(2, 3, backend=backend)
qstate.apply_circuit([
Gate('X', [], [0]),
Gate('CX', [], [0,3]),
Gate('H', [], [2]),
], update_option=peps.DirectUpdate(ImplicitRandomizedSVD(rank=2)))
observable = 1.5 * Observable.sum([
Observable.Z(0) * 2,
Observable.Z(1),
Observable.Z(2) * 2,
Observable.Z(3),
])
contract_option = peps.BMPS(ReducedSVD(rank=2))
self.assertTrue(backend.isclose(qstate.expectation(observable, use_cache=True, contract_option=contract_option), -3))
def test_expectation_single_layer(self, backend):
qstate = peps.computational_zeros(2, 3, backend=backend)
qstate.apply_circuit([
Gate('X', [], [0]),
Gate('CX', [], [0,3]),
Gate('H', [], [2]),
])
observable = 1.5 * Observable.sum([
Observable.Z(0) * 2,
Observable.Z(1),
Observable.Z(2) * 2,
Observable.Z(3),
])
contract_option = peps.SingleLayer(ImplicitRandomizedSVD(rank=2))
self.assertTrue(backend.isclose(qstate.expectation(observable, contract_option=contract_option), -3))