Quantum Simulation of Non-Markovian Open Quantum Systems via Low-Rank Kernel Compression and Coupling Dilution
Abstract
We present an error-controlled framework for the quantum simulation of non-Markovian open-system dynamics in Gaussian environments. For a system coupled linearly to a Gaussian environment with zero mean, the bath's influence on the reduced dynamics is completely determined by its two-time correlation kernel. This allows us to replace the microscopic environment with an equivalent bath that has the same kernel. On a finite simulation interval, a rank-N approximation of the kernel yields an effective bath of N bosonic modes with time-dependent couplings to the system. To encode these modes in qubits, we first truncate each mode to its lowest d occupation levels. When stronger couplings lead to large occupations, we introduce coupling dilution, which replaces each mode with several more weakly coupled copies while preserving the bath correlation kernel. This distributes excitations across more modes and trades additional modes for smaller local dimensions. We derive explicit reduced-state error bounds and establish polynomial circuit width and depth in simulation time and inverse accuracy under stated spectral-decay and coupling-regularity assumptions, provided elementary unitaries admit polynomial-cost implementations.
Related
- Quantum Simulation of Markovian and Non-Markovian Open Quantum Dynamics in Heavy-Ion Collisions
- Reusable selected-time channels for quantum simulation of non-Markovian dynamics
- Scalable simulation of non-Markovian quantum transport by stochastic-phase bath reduction
- Quantum Simulation of Dissipative Non-Markovian Coupled Classical Oscillators
- Dissipation dilution enhances SiV coupling to vdW diamond nanomechanics
BibTeX
@misc{chen2026quantum,
title = {{Quantum Simulation of Non-Markovian Open Quantum Systems via Low-Rank Kernel Compression and Coupling Dilution}},
author = {Hengzhun Chen and Zhenning Cai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29372},
eprint = {2610.29372},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29372},
}
RIS
TY - UNPB
TI - Quantum Simulation of Non-Markovian Open Quantum Systems via Low-Rank Kernel Compression and Coupling Dilution
AU - Hengzhun Chen
AU - Zhenning Cai
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29372
UR - https://arxiv.org/abs/2610.29372
AB - We present an error-controlled framework for the quantum simulation of non-Markovian open-system dynamics in Gaussian environments. For a system coupled linearly to a Gaussian environment with zero mean, the bath's influence on the reduced dynamics is completely determined by its two-time correlation kernel. This allows us to replace the microscopic environment with an equivalent bath that has the same kernel. On a finite simulation interval, a rank-N approximation of the kernel yields an effective bath of N bosonic modes with time-dependent couplings to the system. To encode these modes in qubits, we first truncate each mode to its lowest d occupation levels. When stronger couplings lead to large occupations, we introduce coupling dilution, which replaces each mode with several more weakly coupled copies while preserving the bath correlation kernel. This distributes excitations across more modes and trades additional modes for smaller local dimensions. We derive explicit reduced-state error bounds and establish polynomial circuit width and depth in simulation time and inverse accuracy under stated spectral-decay and coupling-regularity assumptions, provided elementary unitaries admit polynomial-cost implementations.
ER -