class TestCliffordGroup:
"""
Test a sufficient set of conditions to prove that we have a full Clifford
group for a single qubit.
"""
clifford = list(gates.qubit_clifford_group())
pauli = [qutip.qeye(2), qutip.sigmax(), qutip.sigmay(), qutip.sigmaz()]
def test_single_qubit_group_dimension_is_24(self):
assert len(self.clifford) == 24
def test_all_elements_different(self):
clifford = [_remove_global_phase(gate) for gate in self.clifford]
for i, gate in enumerate(clifford):
for other in clifford[i + 1:]:
# Big tolerance because we actually want to test the inverse.
assert not np.allclose(gate.full(), other.full(), atol=1e-3)
@pytest.mark.parametrize("gate", gates.qubit_clifford_group())
def test_gate_normalises_pauli_group(self, gate):
"""
Test the fundamental definition of the Clifford group, i.e. that it
normalises the Pauli group.
"""
# Assert that each Clifford gate maps the set of Pauli gates back onto
# itself (though not necessarily in order). This condition is no
# stronger than simply considering each (gate, Pauli) pair separately.
pauli_gates = [_remove_global_phase(x) for x in self.pauli]
normalised = [
_remove_global_phase(gate * pauli * gate.dag())
for pauli in self.pauli
]
for gate in normalised:
for i, pauli in enumerate(pauli_gates):
if np.allclose(gate.full(), pauli.full(), atol=1e-10):
del pauli_gates[i]
break
assert len(pauli_gates) == 0
def test_are_cliffords(self):
for U in qubit_clifford_group():
assert_(self.case_is_clifford(U))
def test_clifford_group_len(self):
assert_(len(list(qubit_clifford_group())) == 24)