def test_rank(self, bond_dim, cyclic):
psi = qu.rand_matrix_product_state(
10, bond_dim, cyclic=cyclic)
rhoa = qu.ptr(psi, [2] * 10, [0, 1, 2, 3])
el = qu.eigvalsh(rhoa)
# bond_dim squared as cyclic mps is generated
assert sum(el > 1e-12) == bond_dim ** (2 if cyclic else 1)
def test_half_filling_groundstate(self):
H = qu.ham_hubbard_hardcore(8, t=0.5, V=1.0, mu=1.0)
gs = qu.groundstate(H)
dims = [2] * 8
cn = qu.num(2)
ens = [qu.expec(cn, qu.ptr(gs, dims, i)) for i in range(8)]
for en in ens:
assert en == pytest.approx(0.5, rel=1e-6)
def test_bell_states(self):
for s, dic in zip(("psi-", "psi+", "phi+", "phi-"), ({
"qtype": 'dop'
}, {}, {
"sparse": True
}, {})):
p = bell_state(s, **dic)
assert_allclose(expec(p, p), 1.0)
pa = ptr(p, [2, 2], 0)
assert_allclose(expec(pa, pa), 0.5)
def one_qubit_dm(self, qstate, i):
'''
Returns subsystem density
matrix for qubit i by tracing out
all other qubits in `qstate`.
`qstate` needs to be in *full* qubit space!
'''
assert qstate.size == qu.prod(self._sim_dims)
return qu.ptr(qstate, dims=self._sim_dims, keep=i)
def test_mutinf_subsys(self):
p = qu.rand_ket(2**9)
dims = (2**3, 2**2, 2**4)
# exact
rho_ab = qu.ptr(p, dims, [0, 2])
mi0 = qu.mutual_information(rho_ab, [8, 16])
mi1 = qu.mutinf_subsys(p, dims, sysa=0, sysb=2, approx_thresh=1e30)
assert_allclose(mi1, mi0)
# approx
mi2 = qu.mutinf_subsys(p, dims, sysa=0, sysb=2, approx_thresh=1)
assert_allclose(mi1, mi2, rtol=0.1)
def test_entanglement(self):
rho = qu.rand_seperable([2, 3, 2], 10)
assert_allclose(qu.tr(rho), 1.0)
assert qu.isherm(rho)
assert qu.logneg(rho, [2, 6]) < 1e-12
assert qu.logneg(rho, [6, 2]) < 1e-12
rho_a = qu.ptr(rho, [2, 3, 2], 1)
el = qu.eigvalsh(rho_a)
assert np.all(el < 1 - 1e-12)
assert np.all(el > 1e-12)
def test_entanglement(self):
rho = rand_seperable([2, 3, 2], 10)
assert_almost_equal(tr(rho), 1.0)
assert isherm(rho)
assert logneg(rho, [2, 6]) < 1e-12
assert logneg(rho, [6, 2]) < 1e-12
rho_a = ptr(rho, [2, 3, 2], 1)
el = eigvals(rho_a)
assert np.all(el < 1 - 1e-12)
assert np.all(el > 1e-12)
def test_logneg_subsys(self):
p = qu.rand_ket(2**(2 + 3 + 1 + 2))
dims = (2**2, 2**3, 2**1, 2**2)
sysa = [0, 3]
sysb = 1
# exact 1
ln0 = qu.logneg(qu.ptr(p, dims, [0, 1, 3]), [4, 8, 4], [0, 2])
# exact 2
ln1 = qu.logneg_subsys(p, dims, sysa, sysb, approx_thresh=1e30)
assert_allclose(ln0, ln1)
# approx
ln2 = qu.logneg_subsys(p, dims, sysa, sysb, approx_thresh=1)
assert ln1 != ln2
assert_allclose(ln1, ln2, rtol=5e-2)
def test_mixed_sub(self, inds):
a = qu.rand_rho(2**3)
rho_ab = qu.ptr(a, [2, 2, 2], inds)
ixy = qu.mutual_information(rho_ab, (2, 2))
assert (0 <= ixy <= 2.0)
def test_rank(self, m):
k = qu.rand_ket(2**4)
pab = qu.ptr(k, [2, 2, 2, 2], range(m))
ef = qu.entropy(pab)
er = qu.entropy(pab, rank=2**m)
assert_allclose(ef, er)
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)
