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This study provides rigorous error bounds for simulating quantum systems interacting with bosonic baths. These findings enable certified numerical treatments of system-environment interactions in quantum simulations.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Quantum information science

Background:

  • Simulating quantum systems interacting with bosonic baths is crucial for understanding various physical phenomena.
  • Numerical simulations often require approximations, such as truncating the bath's modes and Hilbert space dimensions.
  • Rigorous error control is essential for the reliability of these simulations.

Purpose of the Study:

  • To derive rigorous truncation-error bounds for the spin-boson model and its generalizations.
  • To establish bounds for approximating infinite quantum systems with finite-dimensional ones.
  • To enable certified numerical simulations of system-environment interactions.

Main Methods:

  • Derivation of superexponential Lieb-Robinson-type bounds for bath mode truncation.
  • Development of methods for numerically monitoring errors from local Hilbert space truncation.
  • Application of derived bounds to quantum simulation algorithms.

Main Results:

  • Rigorous error bounds for truncating bosonic baths in quantum system simulations.
  • Efficient numerical monitoring of errors associated with local Hilbert space truncation.
  • Establishment of certified error bounds for finite-dimensional approximations of infinite systems.

Conclusions:

  • The derived error bounds provide a theoretical foundation for the reliable numerical simulation of quantum systems coupled to bosonic environments.
  • Numerical methods like the time-evolving density with orthogonal polynomials algorithm (TEDOPA) can now be applied with certified accuracy.
  • This work advances the field of quantum computation and simulation by ensuring the fidelity of system-environment interaction modeling.