A Pattern Matching-Based Framework for Quantum Circuit Rewriting

TL;DR

This paper introduces QRewriting, a pattern matching framework for quantum circuit rewriting that improves cross-platform compatibility and optimization by using a novel symbol sequence representation and dynamic programming algorithms.

Contribution

It presents a new symbol sequence-based representation for quantum circuits and a polynomial-time pattern matching algorithm, enabling efficient circuit rewriting and optimization.

Findings

Achieved 29% reduction in circuit depth.

Achieved 14% reduction in gate counts.

Successfully rewritten benchmarks from IBM to Sur gate set.

Abstract

The realization of quantum algorithms relies on specific quantum compilations according to the underlying quantum processors. However, there are various ways to physically implement qubits in different physical devices and manipulate those qubits. These differences lead to different communication methods and connection topologies, with each vendor implementing its own set of primitive gates. Therefore, quantum circuits have to be rewritten or transformed in order to be transplanted from one platform to another. We propose a pattern matching-based framework for rewriting quantum circuits, called QRewriting. It takes advantage of a new representation of quantum circuits using symbol sequences. Unlike the traditional way of using directed acyclic graphs, the new representation allows us to easily identify the patterns that appear non-consecutively but reducible. Then, we convert the problem of pattern matching into that of finding distinct subsequences and propose a polynomial-time dynamic programming-based pattern matching and replacement algorithm. We develop a rule library for basic optimizations and use it to rewrite the Arithmetic and Toffoli benchmarks from the $G_{IBM}$ gate set to the $G_{Sur}$ gate set. Compared with the existing tool PaF, QRewriting obtains an improvement of reducing depths (resp. gate counts) by 29\% (resp. 14\%).