def test_rps(self):
a, b, c = (qu.rand_rho(2, sparse=True, density=0.5),
qu.rand_rho(3, sparse=True, density=0.5),
qu.rand_rho(2, sparse=True, density=0.5))
abc = a & b & c
pc = qu.core._trace_keep(abc, [2, 3, 2], 2)
assert_allclose(pc, c.A)
pb = qu.core._trace_keep(abc, [2, 3, 2], 1)
assert_allclose(pb, b.A)
pa = qu.core._trace_keep(abc, [2, 3, 2], 0)
assert_allclose(pa, a.A)
def test_rps(self):
a, b, c = (qu.rand_rho(2, sparse=True, density=0.5),
qu.rand_rho(3, sparse=True, density=0.5),
qu.rand_rho(2, sparse=True, density=0.5))
abc = a & b & c
pab = qu.core._trace_lose(abc, [2, 3, 2], 2)
assert_allclose(pab, (a & b).A)
pac = qu.core._trace_lose(abc, [2, 3, 2], 1)
assert_allclose(pac, (a & c).A)
pbc = qu.core._trace_lose(abc, [2, 3, 2], 0)
assert_allclose(pbc, (b & c).A)
def test_dop_reverse_sparse(self):
a = rand_rho(4, sparse=True, density=0.5)
b = perm_eyepad(a, np.array([2, 2, 2]), [2, 0])
c = (a & eye(2)).A.reshape([2, 2, 2, 2, 2, 2]) \
.transpose([1, 2, 0, 4, 5, 3]) \
.reshape([8, 8])
assert_allclose(b.A, c)
def test_dop_spread(self):
a = qu.rand_rho(4)
b = qu.pkron(a, [2, 2, 2], [0, 2])
c = ((a & qu.eye(2)).A.reshape([2, 2, 2, 2, 2,
2]).transpose([0, 2, 1, 3, 5,
4]).reshape([8, 8]))
assert_allclose(b, c)
def test_dop_spread(self):
a = rand_rho(4)
b = perm_eyepad(a, [2, 2, 2], [0, 2])
c = (a & eye(2)).A.reshape([2, 2, 2, 2, 2, 2]) \
.transpose([0, 2, 1, 3, 5, 4]) \
.reshape([8, 8])
assert_allclose(b, c)
def test_basic(self, rand_rank):
rho = qu.rand_rho(9)
ln = qu.logneg(rho, [3, 3])
for p in (0.2, 0.5, 0.8, 1.0):
rho_d = qu.dephase(rho, p, rand_rank=rand_rank)
assert qu.logneg(rho_d, [3, 3]) <= ln
assert rho_d.tr() == pytest.approx(1.0)
def test_dop_reverse(self):
a = rand_rho(4)
b = perm_eyepad(a, np.array([2, 2, 2]), [2, 0])
c = (a & eye(2)).A.reshape([2, 2, 2, 2, 2, 2]) \
.transpose([1, 2, 0, 4, 5, 3]) \
.reshape([8, 8])
assert_allclose(b, c)
def test_partial_trace_dop_product_state(self):
dims = [3, 2, 4, 2, 3]
ps = [qu.rand_rho(dim) for dim in dims]
pt = qu.kron(*ps)
for i, dim in enumerate(dims):
p = qu.partial_trace(pt, dims, i)
assert_allclose(p, ps[i])
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)
def test_dop_reverse(self):
a = qu.rand_rho(4)
b = qu.pkron(a, np.array([2, 2, 2]), [2, 0])
c = ((a & qu.eye(2)).A.reshape([2, 2, 2, 2, 2,
2]).transpose([1, 2, 0, 4, 5,
3]).reshape([8, 8]))
assert_allclose(b, c)
def test_dop_reverse_sparse(self):
a = qu.rand_rho(4, sparse=True, density=0.5)
b = qu.pkron(a, np.array([2, 2, 2]), [2, 0])
c = ((a & qu.eye(2)).A.reshape([2, 2, 2, 2, 2,
2]).transpose([1, 2, 0, 4, 5,
3]).reshape([8, 8]))
assert_allclose(b.A, c)
def test_ptr_compare_to_manual(self):
a = qu.rand_rho(2**2)
b = qu.partial_trace(a, [2, 2], 0)
c = a.A.reshape([2, 2, 2, 2]).trace(axis1=1, axis2=3)
assert_allclose(b, c)
b = qu.partial_trace(a, [2, 2], 1)
c = a.A.reshape([2, 2, 2, 2]).trace(axis1=0, axis2=2)
assert_allclose(b, c)
def test_shapes_and_blocks(self, sz_blc, sz_p, calc_self_ent):
if sz_p // sz_blc > 0:
p = qu.rand_rho(2**sz_p)
n = sz_p // sz_blc
ecm = qu.ent_cross_matrix(p, sz_blc, calc_self_ent=calc_self_ent)
assert ecm.shape[0] == n
if not calc_self_ent:
assert_allclose(np.diag(ecm), [np.nan] * n, equal_nan=True)
def test_vs_ptr(self):
a = rand_rho(6, sparse=True, density=0.5)
b = _trace_lose(a, [2, 3], 1)
c = partial_trace(a.A, [2, 3], 0)
assert_allclose(b, c)
b = _trace_lose(a, [2, 3], 0)
c = partial_trace(a.A, [2, 3], 1)
assert_allclose(b, c)
def test_vs_ptr(self):
a = qu.rand_rho(6, sparse=True, density=0.5)
b = qu.core._trace_keep(a, [2, 3], 0)
c = qu.partial_trace(a.A, [2, 3], 0)
assert_allclose(b, c)
b = qu.core._trace_keep(a, [2, 3], 1)
c = qu.partial_trace(a.A, [2, 3], 1)
assert_allclose(b, c)
def test_partial_trace_simple_single(self):
a = qu.rand_rho(12, sparse=True, density=0.5)
dims = [2, 3, 2]
b = qu.partial_trace(a, dims, 1)
c = a.A.reshape([*dims, *dims]) \
.trace(axis1=2, axis2=5) \
.trace(axis1=0, axis2=2)
assert_allclose(c, b)
def test_partial_trace_simple_double(self):
a = qu.rand_rho(12, sparse=True, density=0.5)
dims = [2, 3, 2]
b = qu.partial_trace(a, dims, [0, 2])
c = qu.partial_trace(a.A, dims, [0, 2])
assert_allclose(b, c)
b = qu.partial_trace(a, dims, [1, 2])
c = qu.partial_trace(a.A, dims, [1, 2])
assert_allclose(b, c)
def srho_dot_ls():
rho = rand_rho(3)
ham = rand_herm(3, sparse=True, density=0.5)
gamma = 0.7
ls = [rand_matrix(3, sparse=True, density=0.5) for _ in range(3)]
rhodl = -1.0j * (ham @ rho - rho @ ham)
for l in ls:
rhodl += gamma * (l @ rho @ l.H)
rhodl -= gamma * 0.5 * (rho @ l.H @ l)
rhodl -= gamma * 0.5 * (l.H @ l @ rho)
return rho, ham, gamma, ls, rhodl
def rho_dot_ls():
np.random.seed(1)
rho = rand_rho(3)
ham = rand_herm(3)
gamma = 0.7
ls = [rand_matrix(3) for _ in range(3)]
rhodl = -1.0j * (ham @ rho - rho @ ham)
for l in ls:
rhodl += gamma * (l @ rho @ l.H)
rhodl -= gamma * 0.5 * (rho @ l.H @ l)
rhodl -= gamma * 0.5 * (l.H @ l @ rho)
return rho, ham, gamma, ls, rhodl
def test_types(self, dims, op_sps, p_sps, pre_c):
p = qu.rand_rho(4, sparse=p_sps)
c = qu.correlation(p,
qu.pauli('x', sparse=op_sps),
qu.pauli('z', sparse=op_sps),
0,
1,
dims=dims,
precomp_func=pre_c)
c = c(p) if pre_c else c
assert c >= -1.0
assert c <= 1.0
def test_depolarize(self, stack):
rho = qu.rand_rho(2)
I, X, Y, Z = (qu.pauli(s) for s in 'IXYZ')
es = [qu.expec(rho, A) for A in (X, Y, Z)]
p = 0.1
Ek = [(1 - p)**0.5 * I, (p / 3)**0.5 * X, (p / 3)**0.5 * Y,
(p / 3)**0.5 * Z]
if stack:
Ek = np.stack(Ek, axis=0)
sigma = qu.kraus_op(rho, Ek, check=True)
es2 = [qu.expec(sigma, A) for A in (X, Y, Z)]
assert qu.tr(sigma) == pytest.approx(1.0)
assert all(abs(e2) < abs(e) for e, e2 in zip(es, es2))
sig_exp = sum(E @ rho @ qu.dag(E) for E in Ek)
assert_allclose(sig_exp, sigma)
def test_subsystem(self):
rho = qu.rand_rho(6)
dims = [3, 2]
I, X, Y, Z = (qu.pauli(s) for s in 'IXYZ')
mi_i = qu.mutual_information(rho, dims)
p = 0.1
Ek = [(1 - p)**0.5 * I, (p / 3)**0.5 * X, (p / 3)**0.5 * Y,
(p / 3)**0.5 * Z]
with pytest.raises(ValueError):
qu.kraus_op(rho,
qu.randn((3, 2, 2)),
check=True,
dims=dims,
where=1)
sigma = qu.kraus_op(rho, Ek, check=True, dims=dims, where=1)
mi_f = qu.mutual_information(sigma, dims)
assert mi_f < mi_i
assert qu.tr(sigma) == pytest.approx(1.0)
sig_exp = sum(
(qu.eye(3) & E) @ rho @ qu.dag(qu.eye(3) & E) for E in Ek)
assert_allclose(sig_exp, sigma)
def test_subsystem(self):
p = qu.rand_rho(2**4)
e = qu.concurrence(p, [2, 2, 2, 2], 1, 2)
assert 0 <= e <= 1
def test_partial_trace_sparse_basic(self):
a = qu.rand_rho(4)
b = qu.partial_trace(a, [2, 2], 0)
assert type(b) == qu.qarray
assert qu.isherm(b)
assert_allclose(qu.tr(b), 1.0)
def test_auto_trace_out(self):
p = qu.rand_rho(2**3)
qd = qu.quantum_discord(p, [2, 2, 2], 0, 2)
assert (0 <= qd and qd <= 1)
def test_partial_trace_order_doesnt_matter(self):
a = qu.rand_rho(2**3)
dims = np.array([2, 2, 2])
b1 = qu.partial_trace(a, dims, [0, 2])
b2 = qu.partial_trace(a, dims, [2, 0])
assert_allclose(b1, b2)
def test_partial_trace_supply_ndarray(self):
a = qu.rand_rho(2**3)
dims = np.array([2, 2, 2])
keep = np.array(1)
b = qu.partial_trace(a, dims, keep)
assert (b.shape[0] == 2)
def p1():
return qu.rand_rho(3)
def test_partial_trace_basic(self):
a = qu.rand_rho(2**2)
b = qu.partial_trace(a, [2, 2], 0)
assert isinstance(b, qu.qarray)
assert qu.isherm(b)
assert_allclose(qu.tr(b), 1.0)
def test_permute_sparse_op(self):
dims = [3, 2, 5, 4]
a = qu.rand_rho(qu.prod(dims), sparse=True, density=0.5)
b = qu.permute(a, dims, [3, 1, 2, 0])
c = qu.permute(a.A, dims, [3, 1, 2, 0])
assert_allclose(b.A, c)
