MonteQ: A Monte Carlo Tree Search Based Quantum Circuit Synthesis Framework

Quantum Physics [Submitted on 21 Apr 2026] MonteQ: A Monte Carlo Tree Search Based Quantum Circuit Synthesis Framework Mulundano Machiya, Matt Menickelly, Paul Hovland, Ji Liu Hamiltonian simulation is one of the most promising paths toward quantum advantage. Most prior approaches to Hamiltonian simulation circuit synthesis focus on local rewrite rules and low-level optimizations, and give limited attention to high-level scheduling of Pauli terms under varying constraints. In practice, different simulation algorithms require different orderings of the Pauli terms, yet many prior IR-based methods assume a fixed commutation structure, which limits their flexibility. We present MonteQ, a novel quantum circuit synthesis framework for Hamiltonian simulation. MonteQ leverages a two-level design that combines low-level synthesis heuristics with an upper-level tree structure to explore sequences of Pauli rotations. To avoid enumerating this factorially large tree, the Monte Carlo Tree Search algorithm serves as workhorse for judiciously exploring promising paths to leaf nodes. With this two-level design, MonteQ supports both logical-level and hardware-aware synthesis by selecting different low-level heuristics. It also supports different ordering constraints on the Pauli rotations by adjusting the high-level tree structure. For example, MonteQ can preserve the target unitary by using a directed acyclic graph that records the commutation relations among the Pauli rotations, or it can relax unitary preservation constraint to uncover additional optimization options. Our experimental results show that MonteQ can achieve an improvement, as measured in CNOT gate counts, of up to 53% (30% on average) against state-of-the-art compilers like Rustiq on a set of representative synthesis tasks. Comments: 12 pages, 5 figures, 8 tables Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.19029 [quant-ph]   (or arXiv:2604.19029v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.19029 Focus to learn more Submission history From: Ji Liu [view email] [v1] Tue, 21 Apr 2026 03:26:25 UTC (309 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)