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ControlledUnitaryDecomposition

QuICT.qcda.synthesis.unitary_decomposition.ControlledUnitaryDecomposition 

ControlledUnitaryDecomposition(include_phase_gate: bool = True, recursive_basis: int = 2, method: str = 'uniformly_rotation', ancilla: int = 0, opt: bool = False)

Bases: object

Parameters:

  • include_phase_gate (bool, default: True ) –

    Whether to include a phase gate to keep synthesized gate matrix the same as input. If set False, the output gates might have a matrix which has a factor shift to input: np.allclose( * factor, ).

  • recursive_basis (int, default: 2 ) –

    Terminate recursion at which level. It could be set as 1 or 2, which would stop recursion when matrix is 2 or 4, respectively. When set as 2, the final step is done by KAK decomposition. Correctness of this algorithm is never influenced by recursive_basis.

  • method (str, default: 'uniformly_rotation' ) –

    chosen method in ['uniformly_rotation', 'diagonal_gate']

  • ancilla (int, default: 0 ) –

    the number of ancillary qubits when the method is 'diagonal_gate'

  • opt (bool, default: False ) –

    the switch of cnot optimizer when the method is 'diagonal_gate'

Source code in QuICT/qcda/synthesis/unitary_decomposition/controlled_unitary.py 
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def __init__(self,
             include_phase_gate: bool = True,
             recursive_basis: int = 2,
             method: str = 'uniformly_rotation',
             ancilla: int = 0,
             opt: bool = False):
    """
    Args:
        include_phase_gate (bool): Whether to include a phase gate to keep synthesized gate matrix the same
            as input. If set False, the output gates might have a matrix which has a factor shift to input:
            np.allclose(<matrix_of_return_gates> * factor, <input_matrix>).
        recursive_basis (int): Terminate recursion at which level. It could be set as 1 or 2, which would stop
            recursion when matrix is 2 or 4, respectively. When set as 2, the final step is done by KAK
            decomposition.
            Correctness of this algorithm is never influenced by recursive_basis.
        method (str, optional): chosen method in ['uniformly_rotation', 'diagonal_gate']
        If you choose the method of 'diagonal_gate', please pay attention to the ancilla and opt.
        ancilla (int):the number of ancillary qubits when the method is 'diagonal_gate'
        opt (bool): the switch of cnot optimizer when the method is 'diagonal_gate'
    """

    self.include_phase_gate = include_phase_gate
    self.recursive_basis = recursive_basis
    self.method = method
    self.ancilla = ancilla
    self.opt = opt
    if self.method not in ['uniformly_rotation', 'diagonal_gate']:
        self._logger.warn(
            "Only 'uniformly_rotation' and 'diagonal_gate' "
            "methods can decompose controlled unitary matrix. "
            "Please choose the correct method."
        )

execute 

execute(u1: ndarray, u2: ndarray) -> Union[Tuple[CompositeGate, None], Tuple[CompositeGate, complex]]

Transform a controlled-unitary matrix into CX gates and single qubit gates. A controlled-unitary is a block-diagonal unitary. Parameter u1 and u2 are the block diagonals.

Parameters:

  • u1 (ndarray) –

    Upper-left block diagonal.

  • u2 (ndarray) –

    bottom-right block diagonal.

Returns:

  • Union[Tuple[CompositeGate, None], Tuple[CompositeGate, complex]] –

    Union[Tuple[CompositeGate, None], Tuple[CompositeGate, complex]]: If self.inlclude_phase_gate==False, this function returns synthesized gates and a shift factor. Otherwise a tuple like (, None) is returned.

Source code in QuICT/qcda/synthesis/unitary_decomposition/controlled_unitary.py 
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def execute(
        self,
        u1: np.ndarray,
        u2: np.ndarray
) -> Union[Tuple[CompositeGate, None], Tuple[CompositeGate, complex]]:
    """
    Transform a controlled-unitary matrix into CX gates and single qubit gates.
    A controlled-unitary is a block-diagonal unitary. Parameter u1 and u2 are
    the block diagonals.

    Args:
        u1 (np.ndarray): Upper-left block diagonal.
        u2 (np.ndarray): bottom-right block diagonal.

    Returns:
        Union[Tuple[CompositeGate, None], Tuple[CompositeGate, complex]]: If self.inlclude_phase_gate==False,
            this function returns synthesized gates and a shift factor. Otherwise a tuple like (<gates>, None)
            is returned.
    """
    gates, shift = self.inner_cutrans_build_gate(u1, u2, self.recursive_basis, method=self.method)
    if self.include_phase_gate:
        gates = add_factor_shift_into_phase(gates, shift)
        return gates, None
    else:
        return gates, shift

inner_cutrans_build_gate 

inner_cutrans_build_gate(u1: ndarray, u2: ndarray, recursive_basis: int = 2, keep_left_diagonal: bool = False, method: str = 'uniformly_rotation') -> Tuple[CompositeGate, complex]

Build gates from parameterized model without mapping

Returns:

  • Tuple[CompositeGate, complex] –

    Tuple[CompositeGate, complex]: Synthesized gates and factor shift.

Source code in QuICT/qcda/synthesis/unitary_decomposition/controlled_unitary.py 
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def inner_cutrans_build_gate(
    self,
    u1: np.ndarray,
    u2: np.ndarray,
    recursive_basis: int = 2,
    keep_left_diagonal: bool = False,
    method: str = 'uniformly_rotation',
) -> Tuple[CompositeGate, complex]:
    """
    Build gates from parameterized model without mapping

    Returns:
        Tuple[CompositeGate, complex]: Synthesized gates and factor shift.
    """
    qubit_num = 1 + int(round(np.log2(u1.shape[0])))
    v, d, w = quantum_shannon_decompose(u1, u2)
    shift: complex = 1.0

    # diag(u1, u2) == diag(v, v) @ diag(d, d_dagger) @ diag(w, w)
    # diag(v, v)
    v_gates, _shift = self._i_tensor_unitary(v, recursive_basis, keep_left_diagonal=True)
    shift *= _shift

    # diag(d, d_dagger)
    angle_list = []
    for i in range(d.shape[0]):
        s = d[i, i]
        theta = -2 * np.log(s) / 1j
        angle_list.append(theta)

    angle_list = np.array(angle_list)
    if method == 'uniformly_rotation':
        URz = UniformlyRotation(GateType.rz)
        reversed_rz = URz.execute(angle_list)
        reversed_rz & [(i + 1) % qubit_num for i in range(qubit_num)]

    if method == 'diagonal_gate':
        reversed_rz, dg_list = diagonal_urz_gate(angle_list,
                                                 self.ancilla,
                                                 self.opt,
                                                 self.include_phase_gate)

        real_qunum = int(np.floor(np.log2(len(angle_list)))) + 1
        ancilla_num = len(dg_list) - real_qunum

        if ancilla_num == 0:
            reversed_rz & [(i + 1) % qubit_num for i in range(qubit_num)]
        else:
            reversed_rz & (
                [(i + 1) % real_qunum for i in range(real_qunum)]
                + [qubit_num + i for i in range(ancilla_num)]
            )

    # diag(w, w)
    if recursive_basis == 2:
        v_gates.flatten()
        forwarded_d_gate: BasicGate = v_gates.pop(0)
        forwarded_mat = forwarded_d_gate.matrix
        for i in range(0, w.shape[0], 4):
            for k in range(4):
                w[i + k, :] *= forwarded_mat[k, k]

    w_gates, _shift = self._i_tensor_unitary(w, recursive_basis, keep_left_diagonal=keep_left_diagonal)
    shift *= _shift

    gates = CompositeGate()
    w_gates | gates
    reversed_rz | gates
    v_gates | gates

    return gates, shift