qml.transforms.match_relative_phase_toffoli

match_relative_phase_toffoli(tape)

Replace 4-qubit relative phase Toffoli gates with their equivalent circuit.

The equivalence is given in Maslov, Dmitri. “On the Advantages of Using Relative Phase Toffolis with an Application to Multiple Control Toffoli Optimization”, arXiv:1508.03273, arXiv, 2016. doi:10.48550/arXiv.1508.03273.

Note

This transform will also replace any subcircuits from the full pattern (composed of the 4-qubit relative phase Toffoli and its decomposition) that can be replaced by the rest of the pattern.

Parameters:

tape (QNode or QuantumScript or Callable) – A quantum circuit.

Returns:

The transformed circuit as described in qml.transform.

Return type:

qnode (QNode) or quantum function (Callable) or tuple[List[.QuantumScript], function]

Example

import pennylane as qml

@qml.transforms.match_relative_phase_toffoli
@qml.qnode(qml.device("default.qubit"))
def circuit():
    qml.Hadamard(wires=0)
    qml.Hadamard(wires=1)
    qml.X(0)

    # begin relative phase 4-qubit Toffoli

    qml.CCZ(wires=[0, 1, 3])
    qml.ctrl(qml.S(wires=[1]), control=[0])
    qml.ctrl(qml.S(wires=[2]), control=[0, 1])
    qml.MultiControlledX(wires=[0, 1, 2, 3])

    # end relative phase 4-qubit Toffoli

    qml.Hadamard(wires=1)
    qml.X(0)
    return qml.expval(qml.Z(0))

The circuit (containing a 4-qubit relative phase Toffoli) before decomposition:

>>> print(qml.draw(circuit, level=0)())
0: ──H──X─╭●─╭●─╭●─╭●──X─┤  <Z>
1: ──H────├●─╰S─├●─├●──H─┤
2: ───────│─────╰S─├●────┤
3: ───────╰Z───────╰X────┤

The 4-qubit relative phase Toffoli pattern is replaced after the transform:

>>> print(qml.draw(circuit, level=1)())
0: ──H──X───────────╭●───────────╭●──X────────────────────────┤  <Z>
1: ──H──────────────│─────╭●─────│─────╭●──H──────────────────┤
2: ───────╭●────────│─────│──────│─────│────────────╭●────────┤
3: ──H──T─╰X──T†──H─╰X──T─╰X──T†─╰X──T─╰X──T†──H──T─╰X──T†──H─┤

code/api/pennylane.transforms.match_relative_phase_toffoli

 

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