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- import clifford as lc
- from numpy import *
- from scipy.linalg import sqrtm
-
- sqy = sqrtm(1j * lc.py)
- msqy = sqrtm(-1j * lc.py)
- sqz = sqrtm(1j * lc.pz)
- msqz = sqrtm(-1j * lc.pz)
- sqx = sqrtm(1j * lc.px)
- msqx = sqrtm(-1j * lc.px)
- paulis = (lc.px, lc.py, lc.pz)
-
-
- def identify_pauli(m):
- """ Given a signed Pauli matrix, name it. """
- for sign in (+1, -1):
- for pauli_label, pauli in zip("xyz", paulis):
- if allclose(sign * pauli, m):
- return sign, pauli_label
-
-
- def test_find_up_to_phase():
- """ Test that slightly suspicious function """
- assert lc.find_up_to_phase(lc.id) == (0, 0)
- assert lc.find_up_to_phase(lc.px) == (1, 0)
- assert lc.find_up_to_phase(exp(1j*pi/4.)*lc.ha) == (4, 7)
-
- def get_action(u):
- """ What does this unitary operator do to the Paulis? """
- return [identify_pauli(u * p * u.H) for p in 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 lc.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 """
- common_us = lc.id, lc.px, lc.py, lc.pz, lc.ha, lc.ph, sqz, msqz, sqy, msqy, sqx, msqx
- for u in common_us:
- lc.find_up_to_phase(u)
-
-
- def test_group():
- """ Test we are really in a group """
- matches = set()
- for a in lc.unitaries:
- for b in lc.unitaries:
- i, phase = lc.find_up_to_phase(a*b)
- matches.add(i)
- assert len(matches)==24
-
-
- def test_conjugation_table():
- """ Check that the table of Hermitian conjugates is okay """
- assert len(set(lc.conjugation_table))==24
-
- def test_times_table():
- """ Check the times table """
- assert lc.times_table[0][4]==4
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