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Thermalization in nature and on a quantum computer.

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This study reveals how thermal states emerge dynamically in quantum systems. A new perturbation theorem and quantum algorithm offer certified preparation of these states, advancing quantum computing capabilities.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Quantum information science

Background:

  • Understanding thermalization in isolated quantum systems is a fundamental challenge.
  • Dynamical typicality provides a framework for explaining the emergence of equilibrium states.

Purpose of the Study:

  • To demonstrate the dynamic emergence of Gibbs (thermal) states in closed quantum many-body systems.
  • To develop a general quantum algorithm for preparing Gibbs states with proven performance guarantees.

Main Methods:

  • Development of a novel perturbation theorem for weak system-bath couplings, valid in the thermodynamic limit.
  • Identification of conditions and underlying physics governing thermalization.
  • Construction of a quantum algorithm for Gibbs state preparation.

Main Results:

  • Established conditions for thermalization in closed quantum systems.
  • Introduced a perturbation theorem applicable to physically relevant weak couplings.
  • Presented a general quantum algorithm for Gibbs state preparation with certified runtime and error bounds.

Conclusions:

  • Dynamical typicality provides a mechanism for thermalization in closed quantum systems.
  • The novel quantum algorithm offers a reliable method for preparing Gibbs states, surpassing limitations of existing approaches like quantum Metropolis algorithms.