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This research introduces novel algorithms for synthesizing CNOT and Clifford circuits, specifically targeting the minimization of entangling gate counts and circuit depth to enhance quantum error correction efficiency. By offering distinct approaches ranging from optimal synthesis for small systems to greedy methods for large-scale applications, this work provides a practical toolkit that outperforms existing literature in reducing two-qubit operations. The accompanying open-source implementation on GitHub further supports the community's ability to optimize classical-quantum hybrid workflows and quantum algorithm execution.
Heuristic and Optimal Synthesis of CNOT and Clifford Circuits
arXiv:2503.14660v2 Announce Type: replace Abstract: Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In this work we present methods for CNOT and general Clifford circuit synthesis which can be used to minimise either the entangling two-qubit gate count or the circuit depth. We present three families of algorithms - optimal synthesis which works on small circuits, A* synthesis for intermediate-size circuits and greedy synthesis for large circuits. We benchmark against existing methods in the literature and show that our approach results in circuits with lower two-qubit gate count than previous methods. The algorithms have been implemented in a GitHub repository for use by the classical and quantum computing community.
Abstract:Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In this work we present methods for CNOT and general Clifford circuit synthesis which can be used to minimise either the entangling two-qubit gate count or the circuit depth. We present three families of algorithms - optimal synthesis which works on small circuits, A* synthesis for intermediate-size circuits and greedy synthesis for large circuits. We benchmark against existing methods in the literature and show that our approach results in circuits with lower two-qubit gate count than previous methods. The algorithms have been implemented in a GitHub repository for use by the classical and quantum computing community.
arXiv:2503.14660 [quant-ph]
(or arXiv:2503.14660v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2503.14660 Focus to learn more arXiv-issued DOI via DataCite
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