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Extreme Quantum Advantage when Simulating Classical Systems with Long-Range Interaction.

Cina Aghamohammadi1, John R Mahoney2, James P Crutchfield3

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Summary
This summary is machine-generated.

Quantum simulators offer a memory advantage over classical methods for simulating complex spin systems. This quantum advantage grows with interaction range and temperature, even outperforming the most efficient classical algorithms.

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Area of Science:

  • Quantum Computing
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Classical stochastic processes are typically simulated using classical computers.
  • Quantum simulators are emerging as an alternative for simulating these processes.
  • A key advantage of quantum simulators is their potential for reduced memory requirements.

Purpose of the Study:

  • To investigate the memory advantage of quantum simulators for strongly coupled spin systems.
  • To analyze the scaling of this quantum advantage with system parameters.

Main Methods:

  • Examination of the Dyson one-dimensional Ising spin chain.
  • Analysis of systems with variable interaction length and temperature.
  • Comparison of memory requirements between quantum and classical simulation methods.

Main Results:

  • Quantum simulators demonstrate a significant memory advantage for simulating strongly coupled spin systems.
  • This advantage increases unboundedly with the interaction range.
  • The memory requirement for simulating Dyson's spin chain is infinite for the best classical algorithms, but finite for quantum simulators.

Conclusions:

  • Quantum systems provide a highly memory-efficient method for simulating strongly coupled one-dimensional classical spin systems.
  • The findings highlight a practical application of quantum simulation in statistical mechanics and condensed matter physics.