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

Fuente: arXiv
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Main Authors: Kuyanov, Fedor, Kissinger, Aleks
Format: Preprint
Published: 2026
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author Kuyanov, Fedor
Kissinger, Aleks
author_facet Kuyanov, Fedor
Kissinger, Aleks
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_06764
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Efficient Classical Simulation of Low-Rank-Width Quantum Circuits Using ZX-Calculus
Kuyanov, Fedor
Kissinger, Aleks
Quantum Physics
81P68 (Primary) 68Q12 (Secondary)
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.
title Efficient Classical Simulation of Low-Rank-Width Quantum Circuits Using ZX-Calculus
topic Quantum Physics
81P68 (Primary) 68Q12 (Secondary)
url https://arxiv.org/abs/2603.06764