def test_simulation_phase():
"""
Test if the Phase gate is applied correctly to the tableau
S|0> = |0>
S|+> = |R>
"""
prog = Program().inst(S(0))
qvmstab = QVM_Stabilizer(num_qubits=1)
qvmstab._apply_phase(prog.instructions[0])
true_stab = np.array([[1, 1, 0], [0, 1, 0]])
assert np.allclose(true_stab, qvmstab.tableau)
prog = Program().inst([H(0), S(0)])
qvmstab = QVM_Stabilizer(num_qubits=1)
qvmstab._apply_hadamard(prog.instructions[0])
qvmstab._apply_phase(prog.instructions[1])
true_stab = np.array([[0, 1, 0], [1, 1, 0]])
assert np.allclose(true_stab, qvmstab.tableau)
def test_simulation_cnot():
"""
Test if the simulation of CNOT is accurate
:return:
"""
prog = Program().inst([H(0), CNOT(0, 1)])
qvmstab = QVM_Stabilizer(num_qubits=2)
qvmstab._apply_hadamard(prog.instructions[0])
qvmstab._apply_cnot(prog.instructions[1])
# assert that ZZ XX stabilizes a bell state
true_stabilizers = [sX(0) * sX(1), sZ(0) * sZ(1)]
test_paulis = binary_stabilizer_to_pauli_stabilizer(qvmstab.tableau[2:, :])
for idx, term in enumerate(test_paulis):
assert term == true_stabilizers[idx]
# test that CNOT does nothing to |00> state
prog = Program().inst([CNOT(0, 1)])
qvmstab = QVM_Stabilizer(num_qubits=2)
qvmstab._apply_cnot(prog.instructions[0])
true_tableau = np.array([
[1, 1, 0, 0, 0], # X1 -> X1 X2
[0, 1, 0, 0, 0], # X2 -> X2
[0, 0, 1, 0, 0], # Z1 -> Z1
[0, 0, 1, 1, 0]
]) # Z2 -> Z1 Z2
# note that Z1, Z1 Z2 still stabilizees |00>
assert np.allclose(true_tableau, qvmstab.tableau)
# test that CNOT produces 11 state after X
prog = Program().inst([H(0), S(0), S(0), H(0), CNOT(0, 1)])
qvmstab = QVM_Stabilizer(num_qubits=2)
qvmstab._apply_hadamard(prog.instructions[0])
qvmstab._apply_phase(prog.instructions[1])
qvmstab._apply_phase(prog.instructions[2])
qvmstab._apply_hadamard(prog.instructions[3])
qvmstab._apply_cnot(prog.instructions[4])
true_tableau = np.array([[1, 1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1],
[0, 0, 1, 1, 0]])
# note that -Z1, Z1 Z2 still stabilizees |11>
assert np.allclose(true_tableau, qvmstab.tableau)
test_paulis = binary_stabilizer_to_pauli_stabilizer(
qvmstab.stabilizer_tableau())
state = project_stabilized_state(test_paulis,
qvmstab.num_qubits,
classical_state=[1, 1])
state_2 = project_stabilized_state(test_paulis, qvmstab.num_qubits)
assert np.allclose(np.array(state.todense()), np.array(state_2.todense()))
def test_simulation_hadamard():
"""
Test if Hadamard is applied correctly to the tableau
The first example will be a 1 qubit example. where we perform H | 0 > = |0> + |1>.
Therefore we expect the tableau to represent the stablizer X
"""
prog = Program().inst(H(0))
qvmstab = QVM_Stabilizer(num_qubits=1)
qvmstab._apply_hadamard(prog.instructions[0])
x_stabilizer = np.array([[0, 1, 0], [1, 0, 0]])
assert np.allclose(x_stabilizer, qvmstab.tableau)
qvmstab = QVM_Stabilizer(num_qubits=2)
qvmstab._apply_hadamard(prog.instructions[0])
x_stabilizer = np.array([[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0],
[0, 0, 0, 1, 0]])
assert np.allclose(x_stabilizer, qvmstab.tableau)
prog = Program().inst(H(1))
qvmstab = QVM_Stabilizer(num_qubits=2)
qvmstab._apply_hadamard(prog.instructions[0])
x_stabilizer = np.array([[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0],
[0, 1, 0, 0, 0]])
assert np.allclose(x_stabilizer, qvmstab.tableau)
prog = Program().inst([H(0), H(1)])
qvmstab = QVM_Stabilizer(num_qubits=2)
qvmstab._apply_hadamard(prog.instructions[0])
qvmstab._apply_hadamard(prog.instructions[1])
x_stabilizer = np.array([[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0],
[0, 1, 0, 0, 0]])
assert np.allclose(x_stabilizer, qvmstab.tableau)
prog = Program().inst([H(0), H(1), H(0), H(1)])
qvmstab = QVM_Stabilizer(num_qubits=2)
qvmstab._apply_hadamard(prog.instructions[0])
qvmstab._apply_hadamard(prog.instructions[1])
qvmstab._apply_hadamard(prog.instructions[2])
qvmstab._apply_hadamard(prog.instructions[3])
x_stabilizer = np.array([[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0],
[0, 0, 0, 1, 0]])
assert np.allclose(x_stabilizer, qvmstab.tableau)