Unifying Graph Measures and Stabilizer Decompositions for the Classical Simulation of Quantum Circuits

• URL: http://arxiv.org/abs/2603.06377v1
• Date: Fri, 06 Mar 2026 15:27:23 GMT
• Title: Unifying Graph Measures and Stabilizer Decompositions for the Classical Simulation of Quantum Circuits
• Abstract summary: We present two new algorithms to simulate an $n$-qubit circuit $C$.<n>The proposed algorithms are simple, only require a linear amount of memory, are trivially parallel, and interact nicely with ZX-diagram simplification routines.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Various algorithms have been developed to simulate quantum circuits on classical hardware. Among the most prominent are approaches based on \emph{stabilizer decompositions} and \emph{tensor network contraction}. In this work, we present a unified framework that bridges these two approaches, placing them under a common formalism. Using this, we present two new algorithms to simulate an $n$-qubit circuit $C$: one that runs in $\tilde{O}(T^{\mathsf{tw}(C)})$ time and the other in $\tilde{O}(T^{γ\cdot \mathsf{tw}(C)})$ time, where $\mathsf{tw}(C)$ and $\mathsf{rw}(C)$ refer to the the tree-width and rank-width, respectively, of a tensor network associated to $C$, $T$ is the number of non-Clifford gates in $C$, and $γ\approx 3.42$. The proposed algorithms are simple, only require a linear amount of memory, are trivially parallelizable, and interact nicely with ZX-diagram simplification routines. Furthermore, we introduce the refined complexity measures \emph{focused tree-width} and \emph{focused rank-width}, which are always at least as efficient as their standard equivalent; these can be directly applied within our simulation algorithms, allowing for a more precise upper bound on the run time.

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