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 test_GateSingle_to_matrix():
assert np.allclose(
GateSingle(Gate2('X'), 0, 2).to_matrix(),
[[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
assert np.allclose(
GateSingle(Gate2('X'), 1, 2).to_matrix(),
[[0, 0, 1, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 1, 0, 0]])
def test_GateFC_to_matrix():
assert np.allclose(
GateFC(Gate2('X'), 0).to_matrix(2),
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
assert np.allclose(
GateFC(Gate2('X'), 1).to_matrix(2),
[[1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]])
def unitary2x2_to_gates(A):
"""Decomposes 2x2 unitary to gates Ry, Rz, R1.
R1(x) = diag(1, exp(i*x)).
"""
assert is_unitary(A)
phi = np.angle(np.linalg.det(A))
if np.abs(phi) < 1e-9:
return su_to_gates(A)
elif np.allclose(A, PAULI_X):
return [Gate2('X')]
else:
A = np.diag([1.0, np.exp(-1j * phi)]) @ A
return su_to_gates(A) + [Gate2('R1', phi)]
def su_to_gates(A):
"""Decomposes 2x2 special unitary to gates Ry, Rz.
R_k(x) = exp(0.5*i*x*sigma_k).
"""
assert is_special_unitary(A)
u00 = A[0, 0]
u01 = A[0, 1]
theta = np.arccos(np.abs(u00))
lmbda = np.angle(u00)
mu = np.angle(u01)
result = []
result.append(Gate2('Rz', lmbda - mu))
result.append(Gate2('Ry', 2 * theta))
result.append(Gate2('Rz', lmbda + mu))
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 dump_flips():
global flip_mask
for qubit_id in range(qubit_count):
if (flip_mask & (2**qubit_id)) != 0:
result.append(GateSingle(Gate2('X'), qubit_id, qubit_count))
flip_mask = 0
def merge_gates(g1, g2):
assert can_merge(g1, g2)
new_gate2 = Gate2(g1.gate2.name, arg=g1.gate2.arg + g2.gate2.arg)
return GateSingle(new_gate2, g1.qubit_id, g1.qubit_count)