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Universal Error Bound for Constrained Quantum Dynamics.

Zongping Gong1, Nobuyuki Yoshioka1,2, Naoyuki Shibata1

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This summary is machine-generated.

A large energy gap in quantum systems can constrain dynamics within a subspace. This study provides a time-dependent, observable-based error bound for this approximation in gapped quantum systems and quantum many-body systems.

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Area of Science:

  • Quantum Mechanics
  • Condensed Matter Physics
  • Quantum Information

Background:

  • Constrained dynamics approximations are widely used in quantum mechanics.
  • A quantitative justification for these approximations in gapped systems is lacking.
  • Understanding the validity of these approximations is crucial for predicting quantum system behavior.

Purpose of the Study:

  • To establish a general and quantitative error bound for constrained-dynamics approximations in gapped quantum systems.
  • To investigate the behavior of this error bound in quantum many-body systems.
  • To provide a rigorous foundation for using constrained dynamics in quantum simulations and theoretical models.

Main Methods:

  • Derivation of an observable-based error bound.
  • Analysis of the bound's dependence on the energy gap and coupling strength.
  • Generalization to quantum many-body systems with local interactions.

Main Results:

  • A universal, time-linear error bound is established for generic gapped quantum systems.
  • The bound depends linearly on time, energy gap, and coupling strength.
  • For quantum many-body systems, the error grows no faster than a power law t^{d+1} in d dimensions.

Conclusions:

  • The study provides a rigorous, quantitative justification for constrained-dynamics approximations in gapped quantum systems.
  • The derived error bound offers a universal tool for assessing the accuracy of these approximations.
  • The findings have implications for quantum simulations and the theoretical understanding of complex quantum phenomena.