def decompose_4x4_optimal(U):
"""Builds optimal decomposition of general 4x4 unitary matrix.
This decomposition consists of at most 3 CNOT gates, 15 Rx/Ry gates and one
R1 gate.
Returns list of `Gate`s.
"""
assert is_unitary(U)
magic_decomp = decompose_to_magic_diagonal(U)
result = []
result += apply_on_qubit(su_to_gates(magic_decomp['VA']), 1)
result += apply_on_qubit(su_to_gates(magic_decomp['VB']), 0)
result += decompose_magic_N(magic_decomp['alpha'])
result += apply_on_qubit(su_to_gates(magic_decomp['UA']), 1)
result += apply_on_qubit(su_to_gates(magic_decomp['UB']), 0)
# Adding global phase using Rz and R1.
gl_phase = magic_decomp['global_phase'] + 0.25 * np.pi
if np.abs(gl_phase) > 1e-9:
result.append(GateSingle(Gate2('Rz', 2 * gl_phase), 0))
result.append(GateSingle(Gate2('R1', 2 * gl_phase), 0))
result = skip_identities(result)
assert _allclose(U, gates_to_matrix(result, 2))
return result
def decompose_magic_N(a):
"""Decomposes "Magic N" matrix into 3 CNOTs, 4 Rz and 1 Ry gate.
Result is missing global phase pi/4.
Implements cirquit on fig. 7 from [1].
"""
t1 = 2 * a[2] - 0.5 * np.pi
t2 = 0.5 * np.pi - 2 * a[0]
t3 = 2 * a[1] - 0.5 * np.pi
result = []
result.append(GateSingle(Gate2('Rz', 0.5 * np.pi), 1))
result.append(GateFC(Gate2('X'), 0))
result.append(GateSingle(Gate2('Rz', t1), 0))
result.append(GateSingle(Gate2('Ry', t2), 1))
result.append(GateFC(Gate2('X'), 1))
result.append(GateSingle(Gate2('Ry', t3), 1))
result.append(GateFC(Gate2('X'), 0))
result.append(GateSingle(Gate2('Rz', -0.5 * np.pi), 0))
N = magic_N(a)
assert np.allclose(N, gates_to_matrix(result, 2) * np.exp(0.25j * np.pi))
return result
def check_decomp(matrix, gates, tol=1e-9):
"""Checks that `gates` is decomposition of `matrix`."""
qubits_count = int(np.log2(matrix.shape[0]))
assert_all_close(matrix, gates_to_matrix(gates, qubits_count), tol=tol)
def check_decomp(matrix, gates, tol=1e-9):
"""Checks that `gates` is decomposition of `matrix`."""
assert_all_close(matrix, gates_to_matrix(gates), tol=tol)
def test_matrix_to_gates_SWAP(self):
gates = qd.matrix_to_gates(SWAP)
assert np.allclose(SWAP, gates_to_matrix(gates))
def test_TwoLevelUnitary_to_fc_gates(self):
matrix = TwoLevelUnitary(unitary_group.rvs(2), 8, 1, 5)
gates = matrix.to_fc_gates()
assert np.allclose(gates_to_matrix(gates), matrix.get_full_matrix())