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This paper presents a novel algorithm for simulating open quantum systems by significantly reducing the computational dimensionality of the Caldeira-Leggett model. By combining low-rank spatial approximations with frozen Gaussian temporal methods, it halves simulation costs while maintaining accuracy in complex scenarios like double-slit experiments. These advances are critical for scaling up real-time dynamics simulations required to develop practical fault-tolerant quantum hardware and error correction protocols.
Reducing Spatial and Temporal Dimensionality in the Multidimensional Caldeira-Leggett Model
arXiv:2509.24525v3 Announce Type: replace Abstract: Focusing on the real-time dynamics of the reduced density matrix of the multidimensional Caldeira-Leggett model, several techniques are adopted in this paper to reduce the spatial and temporal dimensionality, combined into an efficient algorithm. From a spatial perspective, an equivalent formulation of the Dyson series is presented. With the aid of a low-rank approximation, the spatial dimensionality of open quantum system simulations is halved. From a temporal perspective, the frozen Gaussian approximation is used to approximate both the evolution operator and the interaction operator in the multidimensional Caldeira-Leggett model. This reduces the high-dimensional integrals to one- and two-dimensional integrals independent of the truncation level of the Dyson series. Through these techniques, we design an efficient algorithm whose validity is verified through several numerical experiments, including a two-dimensional double slit simulation.
Abstract:Focusing on the real-time dynamics of the reduced density matrix of the multidimensional Caldeira-Leggett model, several techniques are adopted in this paper to reduce the spatial and temporal dimensionality, combined into an efficient algorithm. From a spatial perspective, an equivalent formulation of the Dyson series is presented. With the aid of a low-rank approximation, the spatial dimensionality of open quantum system simulations is halved. From a temporal perspective, the frozen Gaussian approximation is used to approximate both the evolution operator and the interaction operator in the multidimensional Caldeira-Leggett model. This reduces the high-dimensional integrals to one- and two-dimensional integrals independent of the truncation level of the Dyson series. Through these techniques, we design an efficient algorithm whose validity is verified through several numerical experiments, including a two-dimensional double slit simulation.
arXiv:2509.24525 [quant-ph]
(or arXiv:2509.24525v3 [quant-ph] for this version)
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