catalyst.passes.parity_synth

parity_synth(qnode)

Pass for synthesizing phase polynomials in a circuit.

ParitySynth has been proposed by Vandaele et al. in arXiv:2104.00934 as a technique to synthesize phase polynomials into elementary quantum gates, namely CNOT and RZ. For this, it synthesizes the parity table of the phase polynomial, and defers the remaining parity matrix synthesis to RowCol.

Note

This transform requires decorating the workflow with qjit(). Additionally, this pass requires the networkx package, which can be installed via pip install networkx.

Parameters:

fn (QNode) – QNode to apply the pass to

Returns:

QNode

This pass walks over the input circuit and aggregates all CNOT and RZ operators into a subcircuit that describes a phase polyonomial. Other gates form the boundaries of these subcircuits, and whenever one is encountered the phase polynomial of the aggregated subcircuit is resynthesized with the ParitySynth algorithm. This implies that while this pass works on circuits containing any operations, it is recommended to maximize the subcircuits that represent phase polynomials (i.e. consist of CNOT and RZ gates) to enhance the effectiveness of the pass. This might be possible through decomposition or re-ordering of commuting gates.

Note that higher-level program structures, such as nested functions and control flow, are synthesized independently. I.e., boundaries of such structures are always treated as boundaries of phase polynomial subcircuits as well. Similarly, dynamic wires create boundaries around the operations using them, potentially causing the separation of consecutive phase polynomial operations into multiple subcircuits.

Example

In the following, we apply the pass to a simple quantum circuit that has optimization potential in terms of commuting gates that can be interchanged to unlock a cancellation of a self-inverse gate (CNOT) with itself. Concretely, the circuit is:

import pennylane as qp

dev = qp.device("lightning.qubit", wires=2)

@qp.qjit(capture=True)
@qp.transforms.parity_synth
@qp.qnode(dev)
def circuit(x: float, y: float, z: float):
    qp.CNOT((0, 1))
    qp.RZ(x, 1)
    qp.CNOT((0, 1))
    qp.RX(y, 1)
    qp.CNOT((1, 0))
    qp.RZ(z, 1)
    qp.CNOT((1, 0))
    return qp.state()

We can draw the circuit and observe the last RZ gate to be wrapped in a pair of CNOT gates that commute with it. Before the pass is applied:

>>> fig, ax = catalyst.draw_graph(circuit, level=0)(0.52, 0.12, 0.2)
>>> fig.savefig('path-to-file.png', dpi=300, bbox_inches='tight')

After the pass is applied:

>>> fig, ax = catalyst.draw_graph(circuit, level=1)(0.52, 0.12, 0.2)
>>> fig.savefig('path-to-file.png', dpi=300, bbox_inches='tight')

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