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Simulating Bosonic Baths with Error Bars
M P Woods1,2, M Cramer1, M B Plenio1,2
1Institut für Theoretische Physik, Universität Ulm, Ulm D-89069, Germany.
Physical Review Letters
|October 10, 2015
Summary
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.
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.
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