Decoding techniques applied to the compilation of CNOT circuits for NISQ architectures

TL;DR

This paper introduces a new algorithm for synthesizing CNOT circuits in quantum computing, improving efficiency for both ideal and near-term hardware with restricted connectivity.

Contribution

The paper presents a novel syndrome decoding-based algorithm for CNOT circuit synthesis, outperforming existing methods in various connectivity scenarios.

Findings

Outperforms existing algorithms in benchmarks

Effective for ideal all-to-all connectivity

Adaptable to restricted connectivity in near-term devices

Abstract

Current proposals for quantum compilers require the synthesis and optimization of linear reversible circuits and among them CNOT circuits. Since these circuits represent a significant part of the cost of running an entire quantum circuit, we aim at reducing their size. In this paper we present a new algorithm for the synthesis of CNOT circuits based on the solution of the syndrome decoding problem. Our method addresses the case of ideal hardware with an all-to-all qubit connectivity and the case of near-term quantum devices with restricted connectivity. For both cases, we present benchmarks showing that our algorithm outperforms existing algorithms.