Breaking the Treewidth Barrier in Quantum Circuit Simulation with Decision Diagrams

• URL: http://arxiv.org/abs/2510.06775v1
• Date: Wed, 08 Oct 2025 08:58:58 GMT
• Title: Breaking the Treewidth Barrier in Quantum Circuit Simulation with Decision Diagrams
• Abstract summary: This work rigorously analyzes FeynmanDD, a decision diagram-based simulation method proposed in CAV 2025 by a subset of the authors.<n>We show that the method remains efficient if we use the Solovay-Kitaev algorithm to expand arbitrary single-qubit gates to sequences of Hadamard and T gates.
• Score: 8.586836962892443
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Classical simulation of quantum circuits is a critical tool for validating quantum hardware and probing the boundary between classical and quantum computational power. Existing state-of-the-art methods, notably tensor network approaches, have computational costs governed by the treewidth of the underlying circuit graph, making circuits with large treewidth intractable. This work rigorously analyzes FeynmanDD, a decision diagram-based simulation method proposed in CAV 2025 by a subset of the authors, and shows that the size of the multi-terminal decision diagram used in FeynmanDD is exponential in the linear rank-width of the circuit graph. As linear rank-width can be substantially smaller than treewidth and is at most larger than the treewidth by a logarithmic factor, our analysis demonstrates that FeynmanDD outperforms all tensor network-based methods for certain circuit families. We also show that the method remains efficient if we use the Solovay-Kitaev algorithm to expand arbitrary single-qubit gates to sequences of Hadamard and T gates, essentially removing the gate-set restriction posed by the method.

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