Exact Positive-P Simulation of Open Quantum Spin Systems with Generalized Density Matrix Formalism
Abstract
The positive-P representation for bosons allows scalable exact simulations of many-body open quantum systems, provided dissipation is strong enough to stabilise stochastic trajectories. Designing analogous methods for spin systems, relevant to quantum technologies, remains challenging, as previous spin positive-P formulations can exhibit systematic errors even when simulations are numerically stable. Here, we develop a phase-space representation that maps spin-1/2 degrees of freedom onto parameters of a local generalized density matrix (GDM), rather than SU(2) coherent states. In all stable regimes, we observe no deviations from exact solutions, restoring the positive-P property: stable solutions are exact up to stochastic sampling noise. The GDM representation combines seamlessly with bosonic positive-P, enabling highly scalable treatment of coupled spin-boson systems. We map simulation stability versus spin and boson dissipation in the Jaynes-Cummings model and apply the method to a Jaynes-Cummings-Hubbard quasi-Lieb lattice, showing how spin dissipation and driving can destroy or restore excitation incompressibility.
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BibTeX
@misc{ferrier2026exact,
title = {{Exact Positive-P Simulation of Open Quantum Spin Systems with Generalized Density Matrix Formalism}},
author = {Alex Ferrier and Yi Shi and Marzena H. Szymańska and Piotr Deuar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38059},
eprint = {2610.38059},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38059},
}
RIS
TY - UNPB
TI - Exact Positive-P Simulation of Open Quantum Spin Systems with Generalized Density Matrix Formalism
AU - Alex Ferrier
AU - Yi Shi
AU - Marzena H. Szymańska
AU - Piotr Deuar
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.38059
UR - https://arxiv.org/abs/2610.38059
AB - The positive-P representation for bosons allows scalable exact simulations of many-body open quantum systems, provided dissipation is strong enough to stabilise stochastic trajectories. Designing analogous methods for spin systems, relevant to quantum technologies, remains challenging, as previous spin positive-P formulations can exhibit systematic errors even when simulations are numerically stable. Here, we develop a phase-space representation that maps spin-1/2 degrees of freedom onto parameters of a local generalized density matrix (GDM), rather than SU(2) coherent states. In all stable regimes, we observe no deviations from exact solutions, restoring the positive-P property: stable solutions are exact up to stochastic sampling noise. The GDM representation combines seamlessly with bosonic positive-P, enabling highly scalable treatment of coupled spin-boson systems. We map simulation stability versus spin and boson dissipation in the Jaynes-Cummings model and apply the method to a Jaynes-Cummings-Hubbard quasi-Lieb lattice, showing how spin dissipation and driving can destroy or restore excitation incompressibility.
ER -