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A Simple Solution to Trivial Crossings: A Stochastic State Tracking Approach
Story Temen1, Alexey V Akimov1
1Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States.
The Journal of Physical Chemistry Letters
|January 11, 2021
Summary
A novel stochastic state tracking algorithm improves quantum system simulations by reducing population fluctuations and promoting thermalization. This method offers computational advantages and simplifies the handling of state identity changes.
Area of Science:
- Quantum mechanics
- Computational physics
Background:
- Accurate state tracking is crucial for simulating quantum systems.
- Existing methods like deterministic min-cost algorithms have limitations in managing population dynamics.
Purpose of the Study:
- To introduce a new stochastic state tracking algorithm for quantum systems.
- To assess its performance against established methods and analyze its impact on state population dynamics.
Main Methods:
- Developed a stochastic state reassignment algorithm based on quantum mechanical time-overlaps.
- Tested the algorithm using various model Hamiltonians.
- Compared results with a deterministic min-cost algorithm.
Main Results:
- The stochastic algorithm shows results consistent with the deterministic min-cost algorithm.
- It effectively reduces state population fluctuations near equilibrium.
- Facilitates thermalization and suppresses population revivals/oscillations in many-state systems.
Conclusions:
- The new stochastic algorithm offers a computationally efficient and transparent approach to state tracking.
- It enhances the simulation of quantum systems by improving population dynamics and handling state identity changes robustly.
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