Parallelizable Exact Synthesis of Quantum Circuits via Semi-Tensor Product

• URL: http://arxiv.org/abs/2607.24195v1
• Date: Mon, 27 Jul 2026 09:14:53 GMT
• Title: Parallelizable Exact Synthesis of Quantum Circuits via Semi-Tensor Product
• Abstract summary: This paper introduces an exact framework for CNOT and undirected phase circuits.<n>By enumerating partial-gate topologies and solving the missing gate directions separately, we are able to parallelize both stages.<n>Our algorithm outperforms the SAT-based approach on 89% of cases in QASM.
• Score: 5.247996019685446
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 $1.91\times$.

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