from numpy import * from scipy.linalg import sqrtm from tqdm import tqdm import itertools as it from abp import clifford from abp import qi from nose.tools import raises def identify_pauli(m): """ Given a signed Pauli matrix, name it. """ for sign in (+1, -1): for pauli_label, pauli in zip("xyz", qi.paulis): if allclose(sign * pauli, m): return sign, pauli_label def test_find_clifford(): """ Test that slightly suspicious function """ assert clifford.find_clifford(qi.id, clifford.unitaries) == 0 assert clifford.find_clifford(qi.px, clifford.unitaries) == 1 @raises(IndexError) def test_find_non_clifford(): """ Test that looking for a non-Clifford gate fails """ clifford.find_clifford(qi.t, clifford.unitaries) def get_action(u): """ What does this unitary operator do to the Paulis? """ return [identify_pauli(u.dot(p.dot(qi.hermitian_conjugate(u)))) for p in qi.paulis] def format_action(action): return "".join("{}{}".format("+" if s >= 0 else "-", p) for s, p in action) def test_we_have_24_matrices(): """ Check that we have 24 unique actions on the Bloch sphere """ actions = set(tuple(get_action(u)) for u in clifford.unitaries) assert len(set(actions)) == 24 def test_we_have_all_useful_gates(): """ Check that all the interesting gates are included up to a global phase """ for name, u in qi.by_name.items(): clifford.find_clifford(u, clifford.unitaries) def test_group(): """ Test we are really in a group """ matches = set() for a, b in tqdm(it.combinations(clifford.unitaries, 2), "Testing this is a group"): i = clifford.find_clifford(a.dot(b), clifford.unitaries) matches.add(i) assert len(matches) == 24 def test_conjugation_table(): """ Check that the table of Hermitian conjugates is okay """ assert len(set(clifford.conjugation_table)) == 24 def test_times_table(): """ Check the times table """ assert clifford.times_table[0][4] == 4 def test_cz_table_is_symmetric(): """ Test the CZ table is symmetric """ for bond, (a, b) in it.product([0, 1], it.combinations(xrange(24), 2)): _, a1, a2 = clifford.cz_table[bond, a, b] _, b1, b2 = clifford.cz_table[bond, b, a] assert (a1, a2) == (b2, b1) def test_cz_table_makes_sense(): """ Test the CZ table is symmetric """ hadamard = clifford.by_name["hadamard"] assert all(clifford.cz_table[0, 0, 0] == [1, 0, 0]) assert all(clifford.cz_table[1, 0, 0] == [0, 0, 0]) assert all( clifford.cz_table[0, hadamard, hadamard] == [0, hadamard, hadamard]) def test_commuters(): """ Test that commutation is good """ print clifford.get_commuters(clifford.unitaries)