Efficient Classical Simulation of Low-Rank-Width Quantum Circuits Using ZX-Calculus
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| Format: | Preprint |
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2026
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| _version_ | 1866912949194457088 |
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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 |
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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 |