Reinforcement Learning to Harness Approximation Errors for Long-Time Quantum Simulation
Abstract
Accurate digital quantum simulation at long times is limited by the accumulation of errors inherent to approximate simulation. Here we introduce RL-Trotter, a reinforcement-learning framework that treats unavoidable approximation errors as resources for error correction rather than merely imperfections to suppress. We show that low-dimensional information from conservation laws, such as the energy and energy variance, provides a sufficient learning signal to guide the agent, which learns to adapt a single scalar---the next Trotter step size---without access to the target wave function. By optimizing the entire long-time evolution rather than individual steps, RL-Trotter discovers self-correcting sequences in which later errors compensate for those accumulated earlier, increasing the accuracy of the long-time dynamics. The learned policies are intrinsically robust to measurement noise, substantially reducing measurement overhead. They also generalize to previously unseen, physically similar initial states and transfer from small, classically simulable systems to systems an order of magnitude larger. This enables a practical protocol based on classical pretraining followed by direct deployment or limited fine-tuning on quantum hardware. Our results establish a broader perspective for quantum algorithms: errors in approximate evolution can be orchestrated into resources for accurate and resource-efficient quantum dynamics.
Related
- Reinforcement Learning Assisted Quantum Simulation of Many-Body Excited States and Real-Time Dynamics
- Integrating YOLOv8-based disaster detection with deep reinforcement learning for closed-loop UAV emergency response scheduling: A simulation study
- What Do CAE Simulation Agents Really Need Beyond a Generic Harness?
- Reinforcement learning for robust calibration of multiqudit quantum gates
- Reinforcement learning to disentangle multiqubit quantum states from partial observations
BibTeX
@misc{shi2026reinforcement,
title = {{Reinforcement Learning to Harness Approximation Errors for Long-Time Quantum Simulation}},
author = {Yu-Bo Shi and Markus Heyl and Roderich Moessner and Marin Bukov and Hongzheng Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.20139},
eprint = {2608.20139},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.20139},
}
RIS
TY - UNPB
TI - Reinforcement Learning to Harness Approximation Errors for Long-Time Quantum Simulation
AU - Yu-Bo Shi
AU - Markus Heyl
AU - Roderich Moessner
AU - Marin Bukov
AU - Hongzheng Zhao
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2608.20139
UR - https://arxiv.org/abs/2608.20139
AB - Accurate digital quantum simulation at long times is limited by the accumulation of errors inherent to approximate simulation. Here we introduce RL-Trotter, a reinforcement-learning framework that treats unavoidable approximation errors as resources for error correction rather than merely imperfections to suppress. We show that low-dimensional information from conservation laws, such as the energy and energy variance, provides a sufficient learning signal to guide the agent, which learns to adapt a single scalar---the next Trotter step size---without access to the target wave function. By optimizing the entire long-time evolution rather than individual steps, RL-Trotter discovers self-correcting sequences in which later errors compensate for those accumulated earlier, increasing the accuracy of the long-time dynamics. The learned policies are intrinsically robust to measurement noise, substantially reducing measurement overhead. They also generalize to previously unseen, physically similar initial states and transfer from small, classically simulable systems to systems an order of magnitude larger. This enables a practical protocol based on classical pretraining followed by direct deployment or limited fine-tuning on quantum hardware. Our results establish a broader perspective for quantum algorithms: errors in approximate evolution can be orchestrated into resources for accurate and resource-efficient quantum dynamics.
ER -