Parallelizable Exact Synthesis of Quantum Circuits via Semi-Tensor Product

arXiv:2607.24195v1 Announce Type: new Abstract: Exact synthesis is a useful tool in quantum compilation by providing optimal alternative implementations of small circuit shards and is widely used as a circuit re-synthesis optimization kernel. However, existing exact synthesis methods suffer from encoding overhead, poor parallel scalability, and memory bottlenecks. This paper introduces a parallel exact synthesis framework for CNOT and phase polynomial circuits, which is based on the semi-tensor product (STP) theory of matrices. By enumerating undirected partial-gate topologies and solving the missing gate directions separately, we are able to parallelize both stages and achieve a parallel speedup of up to $12.8\times$ with 32 workers on this NP-hard problem. More specifically, for each topology, the circuit semantics are converted into canonical STP formulas, and feasibility is decided by a right-to-left factorization procedure that removes infeasible direction assignments. On randomly generated synthesis targets, STP is typically $100\times-1000\times$ faster than the SAT-based baseline on small instances, and remains competitive for more difficult instances. When integrated in a real-world circuit optimization workflow, our algorithm outperforms the SAT-based approach on 89% of cases in QASMBench, and achieves a median speedup of $1.91\times$.

Abstract:Exact synthesis is a useful tool in quantum compilation by providing optimal alternative implementations of small circuit shards and is widely used as a circuit re-synthesis optimization kernel. However, existing exact synthesis methods suffer from encoding overhead, poor parallel scalability, and memory bottlenecks. This paper introduces a parallel exact synthesis framework for CNOT and phase polynomial circuits, which is based on the semi-tensor product (STP) theory of matrices. By enumerating undirected partial-gate topologies and solving the missing gate directions separately, we are able to parallelize both stages and achieve a parallel speedup of up to $12.8\times$ with 32 workers on this NP-hard problem. More specifically, for each topology, the circuit semantics are converted into canonical STP formulas, and feasibility is decided by a right-to-left factorization procedure that removes infeasible direction assignments. On randomly generated synthesis targets, STP is typically $100\times-1000\times$ faster than the SAT-based baseline on small instances, and remains competitive for more difficult instances. When integrated in a real-world circuit optimization workflow, our algorithm outperforms the SAT-based approach on 89% of cases in QASMBench, and achieves a median speedup of $1.91\times$.

Quantum Physics (quant-ph); Emerging Technologies (cs.ET)

arXiv:2607.24195 [quant-ph]

(or arXiv:2607.24195v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.24195 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Parallelizable Exact Synthesis of Quantum Circuits via Semi-Tensor Product

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