Relaxed Peephole Optimization: A Novel Compiler Optimization for Quantum Circuits

TL;DR

This paper introduces relaxed peephole optimization (RPO), a new compiler technique for quantum circuits that reduces gate counts and improves success rates by leveraging static basis and pure state information.

Contribution

The paper presents a novel relaxed peephole optimization approach that does not require identical unitaries, extending quantum gate optimization in compilers like Qiskit.

Findings

Up to 18% fewer CNOT gates in optimized circuits

Average of 11.7% reduction in CNOT gates

Success rates of quantum algorithms improved by 2.3x on real hardware

Abstract

In this paper, we propose a novel quantum compiler optimization, named relaxed peephole optimization (RPO) for quantum computers. RPO leverages the single-qubit state information that can be determined statically by the compiler. We define that a qubit is in a basis state when, at a given point in time, its state is either in the X-, Y-, or Z-basis. When basis qubits are used as inputs to quantum gates, there exist opportunities for strength reduction, which replaces quantum operations with equivalent but less expensive ones. Compared to the existing peephole optimization for quantum programs, the difference is that our proposed optimization does not require an identical unitary matrix, thereby named `relaxed' peephole optimization. We also extend our approach to optimize the quantum gates when some input qubits are in known pure states. Both optimizations, namely the Quantum Basis-state Optimization (QBO) and the Quantum Pure-state Optimization (QPO), are implemented in the IBM's Qiskit transpiler. Our experimental results show that our proposed optimization pass is fast and effective. The circuits optimized with our compiler optimizations obtain up to 18.0% (11.7% on average) fewer CNOT gates and up to 8.2% (7.1% on average) lower transpilation time than that of the most aggressive optimization level in the Qiskit compiler. When running on real quantum computers, the success rates of 3-qubit quantum phase estimation algorithm improve by 2.30X due to the reduced gate counts.