aiqbench analysis
This research introduces optimized high-order Trotter-Suzuki schemes that significantly reduce error accumulation in simulating long-time quantum dynamics, offering a practical advantage over traditional methods like Leapfrog. By directly optimizing decomposition parameters, the study provides new 4th and 6th order protocols that outperform established benchmarks even with large time steps on models such as the Heisenberg system. These advancements address critical bottlenecks in Trotter error management for both classical emulators and future quantum hardware simulating many-body systems.
Efficient Trotter-Suzuki Schemes for Long-time Quantum Dynamics
arXiv:2601.18756v2 Announce Type: replace Abstract: Accurately simulating long-time dynamics of many-body systems is a challenge in both classical and quantum computing due to the accumulation of Trotter errors. While low-order Trotter-Suzuki decompositions are straightforward to implement, their rapidly growing error limits access to long-time observables. We present a framework for constructing efficient high-order Trotter-Suzuki schemes by identifying their structure and directly optimizing their parameters over a high-dimensional space. This method enables the discovery of new schemes with significantly improved efficiency compared to traditional constructions, such as those by Suzuki and Yoshida. Based on the theoretical efficiency and practical performance, we recommend two novel highly efficient schemes at $4^{\textrm{th}}$ and $6^{\textrm{th}}$ order. We also demonstrate the effectiveness of these decompositions on the Heisenberg model and the quantum harmonic oscillator, and find that for a fixed final time they perform better across the computational cost. Even when using large time steps, they surpass established low-order schemes like the Leapfrog. Finally, we investigate the in-practice performance of different Trotter schemes and find the decompositions with more uniform coefficients tend to feature improved error accumulation over long times. We have included this observation into our choice of recommended schemes.
Abstract:Accurately simulating long-time dynamics of many-body systems is a challenge in both classical and quantum computing due to the accumulation of Trotter errors. While low-order Trotter-Suzuki decompositions are straightforward to implement, their rapidly growing error limits access to long-time observables. We present a framework for constructing efficient high-order Trotter-Suzuki schemes by identifying their structure and directly optimizing their parameters over a high-dimensional space. This method enables the discovery of new schemes with significantly improved efficiency compared to traditional constructions, such as those by Suzuki and Yoshida. Based on the theoretical efficiency and practical performance, we recommend two novel highly efficient schemes at $4^{\textrm{th}}$ and $6^{\textrm{th}}$ order. We also demonstrate the effectiveness of these decompositions on the Heisenberg model and the quantum harmonic oscillator, and find that for a fixed final time they perform better across the computational cost. Even when using large time steps, they surpass established low-order schemes like the Leapfrog. Finally, we investigate the in-practice performance of different Trotter schemes and find the decompositions with more uniform coefficients tend to feature improved error accumulation over long times. We have included this observation into our choice of recommended schemes.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Lattice (hep-lat); Computational Physics (physics.comp-ph)
arXiv:2601.18756 [quant-ph]
(or arXiv:2601.18756v2 [quant-ph] for this version)
https://doi.org/10.1088/1751-8121/ae919f DOI(s) linking to related resources
Full text under the publisher's open licence · 223 words
Related coverage
Reducing the Gate Count with Efficient Trotter-Suzuki Schemes
arXiv · Jul 31, 2026
Quantum Simulation of Nuclear Dynamics in First Quantization
Quantum Journal · Sep 2, 2026
Quantum Resource Comparison for Two Leading Surface Code Lattice Surgery Approaches
Quantum Journal · Aug 10, 2026
Quantum algorithm simulates complex environments with fewer qubits
Quantum Zeitgeist · Oct 13, 2026