Current proposals for quantum compilers involve the synthesis and optimization of linear reversible circuits and among them CNOT circuits. This class of circuits represents a significant part of the cost of running an entire quantum circuit and therefore we aim at reducing the size of CNOT circuits. 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. Benchmarks show that our algorithm outperforms existing algorithms in both cases of partial and full connectivity.
Quantum CNOT Circuits Synthesis for NISQ Architectures Using the Syndrome Decoding Problem