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Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits.

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Random circuits are powerful tools for simulating quantum systems on noisy quantum computers. This study shows a new algorithm that uses them to study hydrodynamics, even with errors.

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Area of Science:

  • Quantum Computing
  • Condensed Matter Physics
  • Quantum Many-Body Systems

Background:

  • Google's Sycamore processor demonstrated "quantum supremacy" using random circuits.
  • Noisy Intermediate-Scale Quantum (NISQ) devices present challenges for quantum simulations.
  • Simulating quantum many-body systems is crucial for understanding complex physical phenomena.

Purpose of the Study:

  • To propose and demonstrate a novel algorithm for simulating quantum many-body systems on NISQ devices.
  • To utilize random circuits as building blocks for studying hydrodynamics and transport coefficients.
  • To investigate the impact of errors on simulation accuracy and robustness.

Main Methods:

  • Algorithm combining random circuits with Trotterized Hamiltonian time evolution.
  • Numerical simulations of spatiotemporal correlation functions in 1D and 2D quantum spin systems.
  • Analysis of error impact on hydrodynamic scaling and transport coefficient extraction.

Main Results:

  • Hydrodynamic scaling of correlations is robust to Trotter step size, enabling longer time scales.
  • Errors within the random circuit part of the algorithm are found to be irrelevant.
  • Meaningful simulation results are achievable with error rates compatible with near-term quantum hardware.

Conclusions:

  • Random circuits are practical tools for quantum many-body simulations on NISQ devices beyond sampling.
  • The proposed algorithm offers a viable path for studying hydrodynamics and transport phenomena.
  • The robustness to errors highlights the potential of NISQ devices for realistic quantum simulations.