def test_two_qubit_decomposition_tf(self, U, wires): """Test that a two-qubit operation in Tensorflow is correctly decomposed.""" tf = pytest.importorskip("tensorflow") U = tf.Variable(U, dtype=tf.complex128) obtained_decomposition = two_qubit_decomposition(U, wires=wires) with qml.tape.QuantumTape() as tape: for op in obtained_decomposition: qml.apply(op) obtained_matrix = get_unitary_matrix(tape, wire_order=wires)() assert check_matrix_equivalence(U, obtained_matrix, atol=1e-7)
def test_two_qubit_decomposition_1_cnot(self, U, wires): """Test that a two-qubit matrix using one CNOT is correctly decomposed.""" U = _convert_to_su4(np.array(U)) assert _compute_num_cnots(U) == 1 obtained_decomposition = two_qubit_decomposition(U, wires=wires) assert len(obtained_decomposition) == 5 with qml.tape.QuantumTape() as tape: for op in obtained_decomposition: qml.apply(op) obtained_matrix = get_unitary_matrix(tape, wire_order=wires)() assert check_matrix_equivalence(U, obtained_matrix, atol=1e-7)
def test_two_qubit_decomposition_tensor_products(self, U_pair, wires): """Test that a two-qubit tensor product matrix is correctly decomposed.""" U = _convert_to_su4( qml.math.kron(np.array(U_pair[0]), np.array(U_pair[1]))) assert _compute_num_cnots(U) == 0 obtained_decomposition = two_qubit_decomposition(U, wires=wires) assert len(obtained_decomposition) == 2 with qml.tape.QuantumTape() as tape: for op in obtained_decomposition: qml.apply(op) obtained_matrix = get_unitary_matrix(tape, wire_order=wires)() assert check_matrix_equivalence(U, obtained_matrix, atol=1e-7)
def test_two_qubit_decomposition_tensor_products_torch( self, U_pair, wires): """Test that a two-qubit tensor product in Torch is correctly decomposed.""" torch = pytest.importorskip("torch") U1 = torch.tensor(U_pair[0], dtype=torch.complex128) U2 = torch.tensor(U_pair[1], dtype=torch.complex128) U = qml.math.kron(U1, U2) obtained_decomposition = two_qubit_decomposition(U, wires=wires) with qml.tape.QuantumTape() as tape: for op in obtained_decomposition: qml.apply(op) obtained_matrix = get_unitary_matrix(tape, wire_order=wires)() assert check_matrix_equivalence(U, obtained_matrix, atol=1e-7)
def test_two_qubit_decomposition_3_cnots(self, U, wires): """Test that a two-qubit matrix using 3 CNOTs is correctly decomposed.""" U = _convert_to_su4(np.array(U)) assert _compute_num_cnots(U) == 3 obtained_decomposition = two_qubit_decomposition(U, wires=wires) assert len(obtained_decomposition) == 10 with qml.tape.QuantumTape() as tape: for op in obtained_decomposition: qml.apply(op) obtained_matrix = get_unitary_matrix(tape, wire_order=wires)() # We check with a slightly great tolerance threshold here simply because the # test matrices were copied in here with reduced precision. assert check_matrix_equivalence(U, obtained_matrix, atol=1e-7)
def test_two_qubit_decomposition_jax(self, U, wires): """Test that a two-qubit operation in JAX is correctly decomposed.""" jax = pytest.importorskip("jax") from jax.config import config remember = config.read("jax_enable_x64") config.update("jax_enable_x64", True) U = jax.numpy.array(U, dtype=jax.numpy.complex128) obtained_decomposition = two_qubit_decomposition(U, wires=wires) with qml.tape.QuantumTape() as tape: for op in obtained_decomposition: qml.apply(op) obtained_matrix = get_unitary_matrix(tape, wire_order=wires)() assert check_matrix_equivalence(U, obtained_matrix, atol=1e-7)
def unitary_to_rot(tape): r"""Quantum function transform to decomposes all instances of single-qubit and select instances of two-qubit :class:`~.QubitUnitary` operations to parametrized single-qubit operations. For single-qubit gates, diagonal operations will be converted to a single :class:`.RZ` gate, while non-diagonal operations will be converted to a :class:`.Rot` gate that implements the original operation up to a global phase. Two-qubit gates will be decomposed according to the :func:`pennylane.transforms.two_qubit_decomposition` function. .. warning:: This transform is not fully differentiable for 2-qubit ``QubitUnitary`` operations. See usage details below. Args: qfunc (function): a quantum function **Example** Suppose we would like to apply the following unitary operation: .. code-block:: python3 U = np.array([ [-0.17111489+0.58564875j, -0.69352236-0.38309524j], [ 0.25053735+0.75164238j, 0.60700543-0.06171855j] ]) The ``unitary_to_rot`` transform enables us to decompose such numerical operations while preserving differentiability. .. code-block:: python3 def qfunc(): qml.QubitUnitary(U, wires=0) return qml.expval(qml.PauliZ(0)) The original circuit is: >>> dev = qml.device('default.qubit', wires=1) >>> qnode = qml.QNode(qfunc, dev) >>> print(qml.draw(qnode)()) 0: ──U0──┤ ⟨Z⟩ U0 = [[-0.17111489+0.58564875j -0.69352236-0.38309524j] [ 0.25053735+0.75164238j 0.60700543-0.06171855j]] We can use the transform to decompose the gate: >>> transformed_qfunc = unitary_to_rot(qfunc) >>> transformed_qnode = qml.QNode(transformed_qfunc, dev) >>> print(qml.draw(transformed_qnode)()) 0: ──Rot(-1.35, 1.83, -0.606)──┤ ⟨Z⟩ .. UsageDetails:: This decomposition is not fully differentiable. We **can** differentiate with respect to input QNode parameters when they are not used to explicitly construct a :math:`4 \times 4` unitary matrix being decomposed. So for example, the following will work: .. code-block:: python3 U = scipy.stats.unitary_group.rvs(4) def circuit(angles): qml.QubitUnitary(U, wires=["a", "b"]) qml.RX(angles[0], wires="a") qml.RY(angles[1], wires="b") qml.CNOT(wires=["b", "a"]) return qml.expval(qml.PauliZ(wires="a")) dev = qml.device('default.qubit', wires=["a", "b"]) transformed_qfunc = qml.transforms.unitary_to_rot(circuit) transformed_qnode = qml.QNode(transformed_qfunc, dev) >>> g = qml.grad(transformed_qnode) >>> params = np.array([0.2, 0.3], requires_grad=True) >>> g(params) array([ 0.00296633, -0.29392145]) However, the following example will **not** be differentiable: .. code-block:: python3 def circuit(angles): z = angles[0] x = angles[1] Z_mat = np.array([[np.exp(-1j * z / 2), 0.0], [0.0, np.exp(1j * z / 2)]]) c = np.cos(x / 2) s = np.sin(x / 2) * 1j X_mat = np.array([[c, -s], [-s, c]]) U = np.kron(Z_mat, X_mat) qml.Hadamard(wires="a") # U depends on the input parameters qml.QubitUnitary(U, wires=["a", "b"]) qml.CNOT(wires=["b", "a"]) return qml.expval(qml.PauliX(wires="a")) """ for op in tape.operations + tape.measurements: if isinstance(op, qml.QubitUnitary): # Single-qubit unitary operations if qml.math.shape(op.parameters[0]) == (2, 2): zyz_decomposition(op.parameters[0], op.wires[0]) # Two-qubit unitary operations elif qml.math.shape(op.parameters[0]) == (4, 4): two_qubit_decomposition(op.parameters[0], op.wires) else: qml.apply(op) else: qml.apply(op)