def test_spin_half(self):
Sx = qu.spin_operator('x', 1 / 2)
assert_allclose(Sx, [[0.0, 0.5], [0.5, 0.0]])
Sy = qu.spin_operator('y', 1 / 2)
assert_allclose(Sy, [[0.0, -0.5j], [0.5j, 0.0]])
Sz = qu.spin_operator('z', 1 / 2)
assert_allclose(Sz, [[0.5, 0.0], [0.0, -0.5]])
Sp = qu.spin_operator('+', 1 / 2)
assert_allclose(Sp, [[0.0, 1.0], [0.0, 0.0]])
Sm = qu.spin_operator('-', 1 / 2)
assert_allclose(Sm, [[0.0, 0.0], [1.0, 0.0]])
def test_insert_operator(self):
p = MPS_rand_state(3, 7, tags='KET')
q = p.H.retag({'KET': 'BRA'})
qp = q & p
sz = qu.spin_operator('z').real
qp.insert_operator(sz, ('KET', 'I1'), ('BRA', 'I1'),
tags='SZ', inplace=True)
assert 'SZ' in qp.tags
assert len(qp.tensors) == 7
x1 = qp ^ all
x2 = qu.expec(p.to_dense(), qu.ikron(sz, [2, 2, 2], inds=1))
assert x1 == pytest.approx(x2)
def test_1d_vector_methods(self):
X = qu.spin_operator('X', sparse=True)
mera = qt.MERA.rand(16)
meraX = mera.gate(X.A, 7, inplace=False)
assert mera is not meraX
x1 = mera.H @ meraX
md = mera.to_dense()
mdX = qu.ikron(X, [2] * 16, 7) @ md
x2 = md.H @ mdX
# check against dense
assert x1 == pytest.approx(x2)
# check 'outside lightcone' unaffected
assert mera.select(3).H @ meraX.select(3) == pytest.approx(1.0)
# check only need 'lightcone' to compute local
assert mera.select(7).H @ meraX.select(7) == pytest.approx(x2)
def test_spin_high(self, label, S):
D = int(2 * S + 1)
op = qu.spin_operator(label, S)
assert_allclose(qu.eigvalsh(op), np.linspace(-S, S, D), atol=1e-13)