Efficient Classical Simulation of Low-Rank-Width Quantum Circuits Using ZX-Calculus

• URL: http://arxiv.org/abs/2603.06764v1
• Date: Fri, 06 Mar 2026 15:00:04 GMT
• Title: Efficient Classical Simulation of Low-Rank-Width Quantum Circuits Using ZX-Calculus
• Abstract summary: We numerically evaluate ZX-diagrams whose complexity scales with their rank-width.<n>Given a rank-decomposition of width $R$, our method simulates a graph-like ZX-diagram in $(4R)$ time.<n>Since finding optimal rank-decompositions is NP-hard, we introduce contractions that produce good decompositions in practice.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we introduce a technique for contracting (i.e. numerically evaluating) ZX-diagrams whose complexity scales with their rank-width, a graph parameter that behaves nicely under ZX rewrite rules. Given a rank-decomposition of width $R$, our method simulates a graph-like ZX-diagram in $Õ(4^R)$ time. Applied to classical simulation of quantum circuits, it is no slower than either naive state vector simulation or stabiliser decompositions with $α= 0.5$, and in practice can be significantly faster for suitably chosen rank-decompositions. Since finding optimal rank-decompositions is NP-hard, we introduce heuristics that produce good decompositions in practice. We benchmark our simulation routine against Quimb, a popular tensor contraction library, and observe substantial reductions in floating-point operations (often by several orders of magnitude) for random and structured non-Clifford circuits as well as random ZX-diagrams.

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