Non-stabilizerness Entanglement Entropy: a measure of hardness in the classical simulation of quantum many-body systems

• URL: http://arxiv.org/abs/2409.16895v1
• Date: Wed, 25 Sep 2024 13:06:04 GMT
• Title: Non-stabilizerness Entanglement Entropy: a measure of hardness in the classical simulation of quantum many-body systems
• Authors: Jiale Huang, Xiangjian Qian, Mingpu Qin,
• Abstract summary: We introduce the concept of non-stabilizerness entanglement entropy which is basically the minimum residual entanglement entropy for a quantum state. It can serve as a new practical and better measure of difficulty in the classical simulation of quantum many-body systems.
• Score: 0.49157446832511503
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classical and quantum states can be distinguished by entanglement entropy, which can be viewed as a measure of quantum resources. Entanglement entropy also plays a pivotal role in understanding computational complexity in simulating quantum systems. However, stabilizer states formed solely by Clifford gates can be efficiently simulated with the tableau algorithm according to the Gottesman-Knill theorem, although they can host large entanglement entropy. In this work, we introduce the concept of non-stabilizerness entanglement entropy which is basically the minimum residual entanglement entropy for a quantum state by excluding the contribution from Clifford circuits. It can serve as a new practical and better measure of difficulty in the classical simulation of quantum many-body systems. We discuss why it is a better criterion than previously proposed metrics such as Stabilizer R\'enyi Entropy. We also show numerical results of non-stabilizerness entanglement entropy with concrete quantum many-body models. The concept of non-stabilizerness entanglement entropy expands our understanding of the ``hardness`` in the classical simulation of quantum many-body systems.

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