from numpy import * from scipy.linalg import sqrtm from tqdm import tqdm import itertools as it from abp import clifford from abp import qi 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(): """ Test that slightly suspicious function """ assert lc.find(id, lc.unitaries) == 0 assert lc.find(px, lc.unitaries) == 1 assert lc.find(exp(1j*pi/4.)*ha, lc.unitaries) == 4 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, phase = 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