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Quantum computers can efficiently simulate thermalization in open quantum systems. This study proves that high-temperature quantum Gibbs samplers achieve rapid thermalization, improving partition function estimation.

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Area of Science:

  • Quantum Many-Body Physics
  • Quantum Information Science
  • Computational Physics

Background:

  • Understanding thermalization in open quantum many-body systems is crucial.
  • Quantum computers offer efficient simulation capabilities for these systems.
  • Dissipative evolution models inspired by open system thermalization are being explored.

Purpose of the Study:

  • To rigorously analyze the thermalization properties of a specific dissipative evolution on quantum computers.
  • To establish the efficiency of high-temperature quantum Gibbs samplers for rapid thermalization.
  • To apply these findings to enhance partition function estimation algorithms.

Main Methods:

  • Theoretical analysis of dissipative evolution for open quantum many-body systems.
  • Proof of convergence to the Gibbs state under specific conditions (high temperature, Lieb-Robinson bound).
  • Logarithmic time scaling with system size for thermalization.

Main Results:

  • Demonstrated that high-temperature dissipative evolution rapidly reaches the Gibbs state.
  • Established logarithmic time complexity for thermalization, dependent on system size.
  • These are the first rigorous results on rapid mixing for high-temperature quantum Gibbs samplers.
  • The findings apply to both local and long-range Hamiltonians satisfying the Lieb-Robinson bound.

Conclusions:

  • High-temperature quantum Gibbs samplers exhibit rapid mixing, offering the fastest possible thermalization speed.
  • The developed methods provide a significant improvement for estimating partition functions at high temperatures.
  • This work advances the understanding and application of quantum computation for simulating complex quantum systems.