Unified approach to the resources of tensor network and stabilizer simulations

• URL: http://arxiv.org/abs/2505.09512v2
• Date: Thu, 09 Oct 2025 16:00:38 GMT
• Title: Unified approach to the resources of tensor network and stabilizer simulations
• Authors: Zhong-Xia Shang, Si-Yuan Chen, Wenjun Yu, Giulio Chiribella, Qi Zhao,
• Abstract summary: We introduce a general resource indicator, called the bra-ket entanglement, which can be used to bound the resource dependence of classical simulations.<n>For the tensor network framework, our bounds indicate that bra-ket entanglement governs the interplay between two physical resources, the coherence and the magic.<n>For the stabilizer formalism approach, we find that magic is always the dominant resource regardless of bra-ket entanglement.
• Score: 17.88771848927935
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a general resource indicator, called the bra-ket entanglement, which can be used to bound the resource dependence of classical simulations in the tensor network framework and in the stabilizer formalism. For the tensor network framework, our bounds indicate that bra-ket entanglement governs the interplay between two physical resources, the coherence and the magic. As bra-ket entanglement increases, the dominant resource that governs the complexity of the tensor network framework, quantified by entanglement, shifts from coherence to magic. For the stabilizer formalism approach, we find that magic is always the dominant resource regardless of bra-ket entanglement. This conclusion is obtained by developing an operator stabilizer formalism, which extends the standard stabilizer formalism for pure states and has additional advantages in simulating certain quantum circuits. Therefore, our results indicate that as bra-ket entanglement increases, the resource governing the complexity of the two approaches goes from different to the same.

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