def test_pauli_decomp_singlet(self, qtype):
p = qu.singlet(qtype=qtype)
names_cffs = qu.pauli_decomp(p, mode='cp')
assert_allclose(names_cffs['II'], 0.25)
assert_allclose(names_cffs['ZZ'], -0.25)
assert_allclose(names_cffs['YY'], -0.25)
assert_allclose(names_cffs['ZZ'], -0.25)
for name in itertools.permutations('IXYZ', 2):
assert_allclose(names_cffs["".join(name)], 0.0)
class TestDecomp:
@pytest.mark.parametrize("qtype", ['ket', 'dop'])
def test_pauli_decomp_singlet(self, qtype):
p = qu.singlet(qtype=qtype)
names_cffs = qu.pauli_decomp(p, mode='cp')
assert_allclose(names_cffs['II'], 0.25)
assert_allclose(names_cffs['ZZ'], -0.25)
assert_allclose(names_cffs['YY'], -0.25)
assert_allclose(names_cffs['ZZ'], -0.25)
for name in itertools.permutations('IXYZ', 2):
assert_allclose(names_cffs["".join(name)], 0.0)
def test_pauli_reconstruct(self):
p1 = qu.rand_rho(4)
names_cffs = qu.pauli_decomp(p1, mode='c')
pr = sum(
qu.kron(*(qu.pauli(s) for s in name)) * names_cffs["".join(name)]
for name in itertools.product('IXYZ', repeat=2))
assert_allclose(pr, p1)
@pytest.mark.parametrize("state, out", [(qu.up() & qu.down(), {
0: 0.5,
1: 0.5,
2: 0,
3: 0
}), (qu.down() & qu.down(), {
0: 0,
1: 0,
2: 0.5,
3: 0.5
}), (qu.singlet() & qu.singlet(), {
'00': 1.0,
'23': 0.0
})])
def test_bell_decomp(self, state, out):
names_cffs = qu.bell_decomp(state, mode='c')
for key in out:
assert_allclose(names_cffs[str(key)], out[key])
def test_ham_heis_2(self):
h = qu.ham_heis(2, cyclic=False)
evals = qu.eigvalsh(h)
assert_allclose(evals, [-0.75, 0.25, 0.25, 0.25])
gs = qu.groundstate(h)
assert_allclose(qu.expec(gs, qu.singlet()), 1.)
def test_negative_expec(self, qtype, sparse, s):
a = qu.singlet(qtype=qtype)
b = qu.pauli(s, sparse=sparse) & qu.pauli(s, sparse=sparse)
assert_allclose(qu.expec(a, b), -1)
def test_interleaving(self):
p = qu.permute(qu.singlet() & qu.singlet(), [2, 2, 2, 2], [0, 2, 1, 3])
assert qu.logneg(p, [2] * 4, sysa=[0, 3]) > 2 - 1e-13
def test_mutinf_interleave_pure(self):
p = qu.singlet() & qu.singlet()
ixy = qu.mutual_information(p, [2] * 4, sysa=(0, 2))
assert_allclose(ixy, 4)
def test_bell_state_singlet(self):
p = singlet(qtype="dop", sparse=True)
assert_allclose(expec(p, p), 1.0)
pa = ptr(p, [2, 2], 0)
assert_allclose(expec(pa, pa), 0.5)
def test_interleaving(self):
p = permute(singlet() & singlet(), [2, 2, 2, 2], [0, 2, 1, 3])
assert logneg(p, [2] * 4, sysa=[0, 3]) > 2 - 1e-13
def test_mutinf_interleave(self):
p = dop(singlet() & singlet())
ixy = mutual_information(p, [2] * 4, sysa=(0, 2))
assert_allclose(ixy, 4)
def test_ham_heis_2(self):
h = ham_heis(2, cyclic=False)
evals = eigvals(h)
assert_allclose(evals, [-0.75, 0.25, 0.25, 0.25])
gs = groundstate(h)
assert_allclose(expec(gs, singlet()), 1.)
