Automated quantum circuit optimization with randomized replacements

TL;DR

This paper introduces a novel automated quantum circuit optimization method that employs randomized replacements and mixed channels to reduce resource requirements, especially in structured circuits like the quantum Fourier transform.

Contribution

It presents a new approximate circuit rewriting protocol based on ZX-calculus with stochastic mixtures, enabling resource reduction beyond traditional unitary transformations.

Findings

Modest two-qubit gate count reduction in random circuits

Substantial reduction in structured circuits like quantum Fourier transform

Outperforms other approximation methods by converting noise into engineered randomness

Abstract

Quantum circuit optimization - the process of transforming a quantum circuit into an equivalent one with reduced time and space requirements - is crucial for maximizing the utility of current and near-future quantum devices. While most automated optimization techniques focus on transforming circuits into equivalent ones that implement the same unitary, we show that substantial new opportunities for resource reduction can be achieved by (1) allowing approximate local transformations and (2) employing mixed quantum channels to approximate pure circuits. Our novel automated protocol for approximate circuit rewriting is a refined evolution of automated optimization techniques based on the ZX-calculus, where we add a greedy strategy that selectively replaces ZX-diagrams with small phase angles with stochastic mixtures of the identity and carefully chosen over-rotations, which are designed to reduce the overall gate count in expectation while staying within a strict error budget. This approach yields modest two-qubit gate count reduction in random quantum circuits, and achieves a substantial reduction in structured circuits such as the quantum Fourier transform. Fundamentally, our protocol converts experimental noise due to gate applications into deliberately engineered random noise, outperforming many other approximation methods on average. These results highlight the potential of mixed-channel approximations to enhance future quantum circuit performance, suggesting new directions for resource-aware automated quantum compilation beyond pure unitary channels.