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.

Related papers

• Chaos and magic in the dissipative quantum kicked top [0.0]
  We consider an infinite-range interacting quantum spin-1/2 model, undergoing periodic kicking and dissipatively coupled with an environment. At finite size, we describe the system dynamics using quantum trajectories.
  arXiv  Detail & Related papers  (2024-06-24T12:19:19Z)
• Computational supremacy in quantum simulation [22.596358764113624]
  We show that superconducting quantum annealing processors can generate samples in close agreement with solutions of the Schr"odinger equation. We conclude that no known approach can achieve the same accuracy as the quantum annealer within a reasonable timeframe.
  arXiv  Detail & Related papers  (2024-03-01T19:00:04Z)
• Quantum Thermal State Preparation [39.91303506884272]
  We introduce simple continuous-time quantum Gibbs samplers for simulating quantum master equations. We construct the first provably accurate and efficient algorithm for preparing certain purified Gibbs states. Our algorithms' costs have a provable dependence on temperature, accuracy, and the mixing time.
  arXiv  Detail & Related papers  (2023-03-31T17:29:56Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Quantum Instability [30.674987397533997]
  We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system. An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
  arXiv  Detail & Related papers  (2022-08-05T19:53:46Z)
• Demonstrating Quantum Microscopic Reversibility Using Coherent States of Light [58.8645797643406]
  We propose and experimentally test a quantum generalization of the microscopic reversibility when a quantum system interacts with a heat bath. We verify that the quantum modification for the principle of microscopic reversibility is critical in the low-temperature limit.
  arXiv  Detail & Related papers  (2022-05-26T00:25:29Z)
• Interscale entanglement production in a quantum system simulating classical chaos [0.0]
  We study standard classical chaos in a framework of quantum mechanics. By simulating a quantum lattice system corresponding to the Hamiltonian of the kicked rotor, we find that the long-time average of the interscale entanglement entropy becomes positive.
  arXiv  Detail & Related papers  (2022-01-23T09:57:56Z)
• Quantum Entropy [0.12183405753834559]
  We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair of observables forming the quantum phase space. We conjecture an entropy law whereby that entropy of a closed system never decreases, implying a time arrow for particles physics.
  arXiv  Detail & Related papers  (2021-06-29T13:04:55Z)
• Canonical density matrices from eigenstates of mixed systems [0.0]
  We study the emergence of thermal states in the regime of a quantum analog of a mixed phase space. Our system can be tuned by means of a single parameter from quantum integrability to quantum chaos.
  arXiv  Detail & Related papers  (2021-03-10T10:19:05Z)
• Catalytic Transformations of Pure Entangled States [62.997667081978825]
  Entanglement entropy is the von Neumann entropy of quantum entanglement of pure states. The relation between entanglement entropy and entanglement distillation has been known only for the setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving results an operational meaning also in entangled single-copy setup.
  arXiv  Detail & Related papers  (2021-02-22T16:05:01Z)
• A Topos Theoretic Notion of Entropy [1.827510863075184]
  We show how a notion of entropy can be defined within the topos formalism. We show how this construction unifies Shannon and von Neumann entropy as well as classical and quantum Renyi entropies.
  arXiv  Detail & Related papers  (2020-06-04T21:37:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.