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Quantum localization bounds Trotter errors in digital quantum simulation.

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Digital quantum simulation (DQS) errors from Trotterization are bounded by quantum localization, making simulations more robust. This allows for fewer gate operations while maintaining accuracy for local observables.

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Area of Science:

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

Background:

  • Digital quantum simulation (DQS) faces challenges controlling errors introduced by Trotterization.
  • Trotterization discretizes quantum system time evolution into gate sequences, leading to inherent errors.

Purpose of the Study:

  • To investigate the impact of quantum localization on Trotterization errors in DQS.
  • To demonstrate that quantum localization can bound errors for local observables.

Main Methods:

  • Utilizing quantum localization, achieved by constraining time evolution via quantum interference.
  • Analyzing error bounds for local observables in DQS.

Main Results:

  • Quantum localization strongly bounds Trotterization errors for local observables.
  • Errors become independent of system size and simulation time.
  • A sharp threshold in Trotter step size separates localized, controllable error regimes from quantum chaotic regimes.

Conclusions:

  • DQS exhibits greater robustness than previously understood, particularly for local observables.
  • Controlled errors are achievable even with larger Trotter steps.
  • Reduced gate operations are possible for faithful time evolution representation in DQS.