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Area of Science:

  • Quantum physics
  • Computational many-body theory

Background:

  • Quantum Monte Carlo (QMC) methods are essential for studying quantum many-body systems.
  • The sign problem in QMC leads to exponentially increasing computational costs, limiting applicability.
  • Efficiently overcoming the sign problem is crucial for advancing quantum simulations.

Purpose of the Study:

  • To develop a systematic and practical methodology for easing the sign problem in QMC.
  • To introduce computable measures of non-stoquasticity as figures of merit for the sign problem's severity.
  • To rigorously assess the computational complexity of mitigating the sign problem.

Main Methods:

  • Developing a framework for basis changes to reduce the sign problem.
  • Introducing and analyzing measures of non-stoquasticity.
  • Proving the computational complexity using reduction to the MAXCUT problem.

Main Results:

  • A practical and generally applicable methodology for easing the sign problem is presented.
  • Measures of non-stoquasticity are shown to be effective figures of merit for the sign problem's severity.
  • The task of easing the sign problem is proven to be NP-complete for nearest-neighbor Hamiltonians.

Conclusions:

  • The developed framework offers a systematic way to assess and alleviate the sign problem in QMC.
  • Non-stoquasticity measures provide a computable metric for the sign problem's difficulty.
  • The inherent computational complexity highlights the challenges in solving the sign problem universally.