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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 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_all_useful_gates():
- """ Check that all the interesting gates are included up to a global phase """
- names = "i", "px", "py", "pz", "h", "p"
- unitaries = lc.i, lc.px, lc.py, lc.pz, lc.h, lc.p
- for name, unitary in zip(names, unitaries):
- foundit = False
- for i, clifford in enumerate(lc.unitaries):
- if allclose(clifford, unitary):
- foundit = True
- print "{}\t=\tlc.unitaries[{}]".format(name, i)
- assert foundit
-
- names = "sqrt(ix)", "sqrt(-ix)", "sqrt(iy)", "sqrt(-iy)", "sqrt(iz)", "sqrt(-iz)",
- unitaries = sqz, msqz, sqy, msqy, sqx, msqx
- for name, unitary in zip(names, unitaries):
- foundit = False
- for phase in range(8):
- for i, clifford in enumerate(lc.unitaries):
- if allclose(exp(1j*phase*pi/4.)*clifford, unitary):
- foundit = True
- print "{}\t=\texp({} . i . pi/4).lc.unitaries[{}]".format(name, phase, i)
- assert foundit
-
-
- 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
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