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three_qubit_gate_decomposer

ThreeQubitGateDecomposer

Bases: Decomposer

Source code in opensquirrel/passes/decomposer/three_qubit_gate_decomposer.py 
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class ThreeQubitGateDecomposer(Decomposer):
    def decompose(self, instruction: Gate) -> list[Gate]:
        """Predefined decomposition of the three-qubit gates into CZ gates and single-qubit gates.

        The Toffoli gate (CCX) is decomposed into 6 CZ gates and single-qubit rotations, which is
        the minimum possible according to
        [Shende and Markov (2008)](https://arxiv.org/abs/0803.2316). The Fredkin gate (CSWAP) is
        decomposed as a Toffoli gate conjugated by two CNOT gates, giving 8 CZ gates.

        Note:
            This decomposition preserves the global phase of the three-qubit gate.
            Gates other than CCX and CSWAP are returned unchanged.

        Args:
            instruction: three-qubit gate to decompose.

        Returns:
            A sequence of CZ gates and single-qubit gates that decompose the three-qubit gate.

        """
        if not isinstance(instruction, ThreeQubitGate) or instruction.name not in ("CCX", "CSWAP"):
            return [instruction]

        gate = instruction

        if gate.name == "CCX":
            control_qubit_0, control_qubit_1, target_qubit = gate.qubit_operands
            return self._get_toffoli_gates(control_qubit_0, control_qubit_1, target_qubit)

        control_qubit, qubit_0, qubit_1 = gate.qubit_operands
        return [
            *self._get_cnot_gates(qubit_1, qubit_0),
            *self._get_toffoli_gates(control_qubit, qubit_0, qubit_1),
            *self._get_cnot_gates(qubit_1, qubit_0),
        ]

    def _get_cnot_gates(self, control_qubit: Qubit, target_qubit: Qubit) -> list[Gate]:
        """CNOT gate expressed as a CZ gate conjugated by Ry rotations, as in the CNOT2CZDecomposer."""
        return [
            Ry(target_qubit, -pi / 2),
            CZ(control_qubit, target_qubit),
            Ry(target_qubit, pi / 2),
        ]

    def _get_toffoli_gates(self, control_qubit_0: Qubit, control_qubit_1: Qubit, target_qubit: Qubit) -> list[Gate]:
        """Toffoli gate as 6 CNOT gates and T rotations, with every CNOT gate rewritten in terms of CZ.

        The Hadamard gates that conjugate the target qubit in the textbook circuit are replaced by
        the same Ry rotations used above, which likewise map Z onto X under conjugation.
        """
        a, b, c = control_qubit_0, control_qubit_1, target_qubit
        return [
            Ry(c, -pi / 2),
            *self._get_cnot_gates(b, c),
            TDagger(c),
            *self._get_cnot_gates(a, c),
            T(c),
            *self._get_cnot_gates(b, c),
            TDagger(c),
            *self._get_cnot_gates(a, c),
            T(b),
            T(c),
            Ry(c, pi / 2),
            *self._get_cnot_gates(a, b),
            T(a),
            TDagger(b),
            *self._get_cnot_gates(a, b),
        ]

decompose 

decompose(instruction: Gate) -> list[Gate]

Predefined decomposition of the three-qubit gates into CZ gates and single-qubit gates.

The Toffoli gate (CCX) is decomposed into 6 CZ gates and single-qubit rotations, which is the minimum possible according to Shende and Markov (2008). The Fredkin gate (CSWAP) is decomposed as a Toffoli gate conjugated by two CNOT gates, giving 8 CZ gates.

Note

This decomposition preserves the global phase of the three-qubit gate. Gates other than CCX and CSWAP are returned unchanged.

Parameters:

Name Type Description Default
instruction Gate

three-qubit gate to decompose.

 required

Returns:

Type Description
list[Gate]

A sequence of CZ gates and single-qubit gates that decompose the three-qubit gate.
Source code in opensquirrel/passes/decomposer/three_qubit_gate_decomposer.py 
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def decompose(self, instruction: Gate) -> list[Gate]:
    """Predefined decomposition of the three-qubit gates into CZ gates and single-qubit gates.

    The Toffoli gate (CCX) is decomposed into 6 CZ gates and single-qubit rotations, which is
    the minimum possible according to
    [Shende and Markov (2008)](https://arxiv.org/abs/0803.2316). The Fredkin gate (CSWAP) is
    decomposed as a Toffoli gate conjugated by two CNOT gates, giving 8 CZ gates.

    Note:
        This decomposition preserves the global phase of the three-qubit gate.
        Gates other than CCX and CSWAP are returned unchanged.

    Args:
        instruction: three-qubit gate to decompose.

    Returns:
        A sequence of CZ gates and single-qubit gates that decompose the three-qubit gate.

    """
    if not isinstance(instruction, ThreeQubitGate) or instruction.name not in ("CCX", "CSWAP"):
        return [instruction]

    gate = instruction

    if gate.name == "CCX":
        control_qubit_0, control_qubit_1, target_qubit = gate.qubit_operands
        return self._get_toffoli_gates(control_qubit_0, control_qubit_1, target_qubit)

    control_qubit, qubit_0, qubit_1 = gate.qubit_operands
    return [
        *self._get_cnot_gates(qubit_1, qubit_0),
        *self._get_toffoli_gates(control_qubit, qubit_0, qubit_1),
        *self._get_cnot_gates(qubit_1, qubit_0),
    ]