def test_gate_swap_and_split(self):
n = 10
p = MPS_computational_state('0' * n)
assert p.bond_sizes() == [1] * (n - 1)
G = qu.rand_uni(4)
p.gate_(G, (1, n - 2), contract='swap+split')
assert p.bond_sizes() == [1] + [2] * (n - 3) + [1]
def mat_herm_dense():
np.random.seed(1)
u = qu.rand_uni(4)
a = u @ qu.ldmul(np.array([-1, 2, 4, -3]), u.H)
# |--|--|--|--|--|--|--|
# -3 -1 2 4
return u, a
def test_rand_uni(self, dtype):
u = qu.rand_uni(3, dtype=dtype)
assert u.shape == (3, 3)
assert type(u) == qu.qarray
assert u.dtype == dtype
# low tolerances for float32 etc
assert_allclose(qu.eye(3), u @ u.H, atol=1e-7, rtol=1e-5)
assert_allclose(qu.eye(3), u.H @ u, atol=1e-7, rtol=1e-5)
def test_gate_no_contract(self, bsz, propagate_tags, contract):
p = MPS_rand_state(5, 7)
q = p.copy()
G = qu.rand_uni(2**bsz)
p = p.gate(G,
where=[i for i in range(2, 2 + bsz)],
tags='G',
contract=contract)
TG = p['G']
if propagate_tags or contract:
assert p.site_tag(2) in TG.tags
assert p.H @ p == pytest.approx(1.0)
assert abs(q.H @ p) < 1.0
assert len(p.tensors) == 6 - int(contract) * bsz
assert set(p.outer_inds()) == {'k{}'.format(i) for i in range(5)}
def test_auto_split_detection(self):
psi0 = MPS_computational_state('00')
CNOT = qu.controlled('not')
ISWAP = qu.iswap()
G = qu.rand_uni(4)
opts = {'contract': 'auto-split-gate', 'where': (0, 1)}
psi_cnot = psi0.gate(CNOT, **opts)
psi_iswap = psi0.gate(ISWAP, **opts)
psi_G = psi0.gate(G, **opts)
assert (psi_cnot.max_bond() == psi_iswap.max_bond() ==
psi_G.max_bond() == 2)
assert len(psi_cnot.tensors) == len(psi_iswap.tensors) == 4
assert len(psi_G.tensors) == 3
def test_gate_no_contract(self, bsz, propagate_tags, contract):
p = MPS_rand_state(5, 7, tags={'PSI0'})
q = p.copy()
G = qu.rand_uni(2**bsz)
p = p.gate_(G,
where=[i for i in range(2, 2 + bsz)],
tags='G',
contract=contract,
propagate_tags=propagate_tags)
TG = p['G']
if propagate_tags or contract:
assert p.site_tag(2) in TG.tags
assert ('PSI0' in TG.tags) == (propagate_tags is True) or contract
assert (p.H & p) ^ all == pytest.approx(1.0)
assert abs((q.H & p) ^ all) < 1.0
assert len(p.tensors) == 6 - int(contract) * bsz
assert set(p.outer_inds()) == {f'k{i}' for i in range(5)}
def ham_rcr_psi():
# Define a random hamiltonian with a known recurrence time
d = 3
np.random.seed(1)
ems = np.random.randint(1, 6, d)
ens = np.random.randint(1, 6, d) # eigenvalues as rational numbers
# numerator lowest common divisor
LCD = reduce(gcd, ems)
# denominator lowest common multiple
LCM = reduce(lambda a, b: a * b // gcd(a, b), ens)
trc = 2 * pi * LCM / LCD
evals = np.array(ems) / np.array(ens)
v = rand_uni(d)
ham = v @ np.diag(evals) @ v.H
p0 = rand_ket(d)
tm = 0.573 * trc
pm = v @ np.diag(np.exp(-1.0j * tm * evals)) @ v.H @ p0
return ham, trc, p0, tm, pm
def test_gate2split(self):
psi = MPS_rand_state(10, 3)
psi2 = psi.copy()
G = qu.eye(2) & qu.eye(2)
psi.gate2split(G, (2, 3), cutoff=0)
assert psi.bond_size(2, 3) == 6
assert psi.H @ psi2 == pytest.approx(1.0)
# check a unitary application
G = qu.rand_uni(2**2)
psi.gate2split(G, (7, 8))
psi.compress()
assert psi.bond_size(2, 3) == 3
assert psi.bond_size(7, 8) > 3
assert psi.H @ psi == pytest.approx(1.0)
assert abs(psi2.H @ psi) < 1.0
# check matches dense application of gate
psid = psi2.to_dense()
Gd = qu.ikron(G, [2] * 10, (7, 8))
assert psi.to_dense().H @ (Gd @ psid) == pytest.approx(1.0)
def mat_nherm_sparse():
np.random.seed(1)
u, v = rand_uni(5), rand_uni(5)
a = u @ ldmul(np.array([1, 2, 4, 3, 0.1]), v.H)
a = qu(a, sparse=True)
return u, v, a
def ham2():
u = qu.rand_uni(7)
el = np.array([-3.72, 0, 1, 1.1, 2.1, 2.2, 6.28])
return u @ qu.ldmul(el, u.H)
def ham1():
evecs = rand_uni(5)
evals = np.array([-5, -3, 0.1, 2, 4])
return dot(evecs, ldmul(evals, evecs.H))
def mat_nherm_sparse():
np.random.seed(1)
u, v = qu.rand_uni(5), qu.rand_uni(5)
a = u @ qu.ldmul(np.array([1, 2, 4, 3, 0.1]), v.H)
a = qu.sparse(a)
return u, v, a
def ham1():
u = qu.rand_uni(7)
el = np.array([-3, 0, 1, 2, 3, 4, 7])
return u @ qu.ldmul(el, u.H)
def mat_herm_sparse():
np.random.seed(1)
u = qu.rand_uni(4)
a = u @ qu.ldmul(np.array([-1, 2, 4, -3]), u.H)
a = qu.sparse(a)
return u, a
def test_rand_uni(self):
u = rand_uni(3)
assert u.shape == (3, 3)
assert type(u) == np.matrix
assert_allclose(eye(3), chop(u @ u.H, inplace=False))
assert_allclose(eye(3), chop(u.H @ u, inplace=False))
def prematsparse():
u = rand_uni(4)
a = u @ ldmul(np.array([-1, 2, 4, -3]), u.H)
a = qu(a, sparse=True)
return u, a
def mat_herm_sparse():
np.random.seed(1)
u = rand_uni(4)
a = u @ ldmul(np.array([-1, 2, 4, -3]), u.H)
a = qu(a, sparse=True)
return u, a
def mat_nherm_dense():
np.random.seed(1)
u, v = rand_uni(5), rand_uni(5)
a = u @ ldmul(np.array([1, 2, 4, 3, 0.1]), v.H)
return u, v, a
