def test_stiefel_tangent(self):
C = uni.choi(2, 1)
TX1 = C.stiefel_tangent()
TX2 = C.stiefel_tangent(full=True)
self.assertEqual(TX1.shape, (8, 2))
self.assertEqual(TX2.shape, (8, 8))
self.assertEqual(la.norm(TX1 - TX2[:, :2]), 0)
C2 = ch.QuantumChannel(la.expm(TX2)[:, :2], 'stiefel')
self.assertAlmostEqual(la.norm(C.choi() - C2.choi()), 0)
self.assertEqual(C2.rank(), 1)
self.assertTrue(C2.is_valid())
C = uni.choi(3, 9)
TX1 = C.stiefel_tangent()
TX2 = C.stiefel_tangent(full=True)
self.assertEqual(TX1.shape, (27, 3))
self.assertEqual(TX2.shape, (27, 27))
self.assertEqual(la.norm(TX1 - TX2[:, :3]), 0)
C2 = ch.QuantumChannel(la.expm(TX2)[:, :3], 'stiefel')
self.assertAlmostEqual(la.norm(C.choi() - C2.choi()), 0)
self.assertEqual(C2.rank(), 9)
self.assertTrue(C2.is_valid())
def test_is_extremal(self):
U1 = uni.choi(2, 1)
self.assertTrue(U1.is_extremal())
U2 = uni.choi(2, 1)
self.assertTrue(U2.is_extremal())
mix = np.random.rand()
unital_map = ch.QuantumChannel(mix * U1.choi() + (1 - mix) * U2.choi(),
'choi')
self.assertFalse(unital_map.is_extremal())
gamma = np.random.rand()
amp_damp = ch.QuantumChannel(
[[[1, 0], [0, np.sqrt(1 - gamma)]], [[0, np.sqrt(gamma)], [0, 0]]],
'kraus')
self.assertTrue(amp_damp.is_extremal())
C3 = uni.choi(2, 3)
self.assertFalse(C3.is_extremal())
C4 = uni.choi(2, 4)
self.assertFalse(C4.is_extremal())
def test_choi_seed(self):
rgen1 = np.random.RandomState(1)
choi1 = uniform.choi(2, 4, False, rgen1)
rgen2 = np.random.RandomState(1)
choi2 = uniform.choi(2, 4, False, rgen2)
self.assertEqual(la.norm(choi1 - choi2), 0)
def test_partial_trace(self):
ch1 = uni.choi(2)
ch2 = uni.choi(2)
cht1 = ch1 ^ ch2
self.assertAlmostEqual(np.linalg.norm(ch1.TrA() - ch1.TrA().conj().T),
0)
self.assertAlmostEqual(np.linalg.norm(ch1.TrB() - np.eye(2)), 0)
self.assertAlmostEqual(np.linalg.norm(cht1.TrB() - np.eye(4)), 0)
def test_kron_n(self):
X = uni.choi(2)
X3_a = X.kron(3)
X3_b = X ^ X ^ X
self.assertEqual(la.norm(X3_a.choi() - X3_b.choi()), 0)
def test_choi_as_matrix(self):
choi = uniform.choi(3, as_channel=False)
self.assertTrue(choi.shape == (9, 9))
self.assertEqual(type(choi), np.ndarray)
self.assertEqual(choi.dtype, np.complex128)
self.assertTrue(ch.QuantumChannel(choi, 'choi').is_valid())
def test_missing_ptm_paths(self):
ptm1 = uni.choi(2).ptm()
ptm2 = uni.choi(2).ptm()
ch1 = ch.QuantumChannel(ptm1, 'ptm')
ch2 = ch.QuantumChannel(ptm2, 'ptm')
out = ch1 * ch2
self.assertEqual(np.linalg.norm(ptm1 @ ptm2 - out.ptm()), 0)
bv = ptm1 @ (np.eye(4)[:, 1])
bv[0] = 1.0
rho = ch.QuantumState(bv[1:], 'bv')
rho_out = ch2 * rho
self.assertAlmostEqual(
np.linalg.norm((ptm2 @ bv)[1:, np.newaxis] -
rho_out.bloch_vector()), 0)
def test_missing_stiefel2(self):
ch1 = uni.choi(2)
ch2 = ch.QuantumChannel(ch1.stiefel2(), 'stiefel2')
self.assertAlmostEqual(
np.linalg.norm(ch1.liouvillian() - ch2.liouvillian()), 0)
ch2 = ch.QuantumChannel(ch1.stiefel2(), 'stiefel2')
for i, k in enumerate(ch1.kraus()):
self.assertAlmostEqual(np.linalg.norm(k - ch2.kraus()[i]), 0)
def test_1_qutrit_random_op(self):
state = uniform.density_matrix(3)
op = uniform.choi(3)
out = op*state
op2 = ch.QuantumChannel(op.ptm(),'ptm')
self.assertAlmostEqual(la.norm(op.choi()-op2.choi()),0,14)
bvout = op.ptm()[1:,1:]@state.bloch_vector()+op.ptm()[1:,0,np.newaxis]*1./np.sqrt(2)
bvout2 = ch.QuantumState(bvout,'bv')
self.assertAlmostEqual(la.norm(out.bloch_vector()-bvout),0,14)
self.assertAlmostEqual(la.norm(out.density_matrix()-bvout2.density_matrix()),0,14)
def test_2_qutrit_random_op(self):
state = uniform.density_matrix(9)
op = uniform.choi(9)
out = op*state
op2 = ch.QuantumChannel(op.ptm(),'ptm')
self.assertAlmostEqual(la.norm(op.choi()-op2.choi()),0,14)
#This illustrates the ugliness of wanting a unit sphere
bvout = op.ptm()[1:,1:]@state.bloch_vector()+op.ptm()[1:,0,np.newaxis]*1./np.sqrt(8)
bvout2 = ch.QuantumState(bvout,'bv')
self.assertAlmostEqual(la.norm(out.bloch_vector()-bvout),0,15)
self.assertAlmostEqual(la.norm(out.density_matrix()-bvout2.density_matrix()),0,14)
def test_dual(self):
D = uni.choi(N=3)
DD = D.dual()
DDD = DD.dual()
self.assertEqual(la.norm(D.choi() - DDD.choi()), 0)
P = ch.QuantumChannel(D.ptm(), 'ptm')
PP = P.dual()
PPP = PP.dual()
self.assertEqual(la.norm(P.ptm() - PPP.ptm()), 0)
K = ch.QuantumChannel(D.kraus(), 'kraus')
KK = K.dual()
KKK = KK.dual()
self.assertEqual(la.norm(K.stiefel() - KKK.stiefel()), 0)
self.assertAlmostEqual(la.norm(DD.choi() - KK.choi()), 0)
self.assertAlmostEqual(la.norm(DD.choi() - PP.choi()), 0)
def test_is_valid_gaps(self):
ch1 = uni.choi(2)
self.assertTrue(ch1.is_valid())
vals, vecs = la.eigh(ch1.choi())
C = vecs @ np.diag(vals * np.array([1, 1, 1, -1])) @ vecs.conj().T
C = ch.QuantumChannel(C, 'choi')
self.assertFalse(C.is_valid())
C = ch.QuantumChannel(1.1 * ch1.choi(), 'choi')
self.assertFalse(C.is_valid())
C = ch.QuantumChannel(ch1.kraus(), 'kraus')
self.assertTrue(C.is_valid())
ks = C.kraus()
ks[0] += np.random.randn(2, 2) * .02
C = ch.QuantumChannel(ks, 'kraus')
self.assertFalse(C.is_valid())
def test_choi_as_channel(self):
choi = uniform.choi(2)
self.assertTrue(choi.is_valid())
def test_rank_choi(self):
for i in range(1, 10):
choi = uniform.choi(3, i)
self.assertTrue(choi.rank() == i)
def test_2_qutrit_ptm_O(self):
U = uniform.choi(N=9,rank=1)
self.assertAlmostEqual(np.abs(la.det(U.ptm()[1:,1:])),1.0,10)