Decoding techniques applied to the compilation of CNOT circuits for NISQ architectures
Timothée Goubault de Brugière, Marc Baboulin, Benoît Valiron, Simon Martiel, Cyril Allouche · Science of Computer Programming · 2021
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.