Optimization of path-integral tensor-multiplication schemes for open quantum systems

Hall, L. M. J., Gisdakis, A. and Muljarov, E. A. ORCID: https://orcid.org/0000-0002-2878-4148 2026. Optimization of path-integral tensor-multiplication schemes for open quantum systems. Physical Review B 114 , 125302. 10.1103/YCRC-VTBK

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Abstract

Path-integral techniques are a powerful tool for obtaining exact solutions for the non-Markovian dynamics of open quantum systems. However, the exponential scaling of the tensor size with the quantum memory length limits their applicability to systems with long memory times. Here we provide a general optimization of tensor multiplication schemes for systems with pair correlations and finite memory times. This optimization effectively reduces the tensor sizes by using a matrix representation of tensors combined with singular value decomposition to filter out negligible contributions. This approach dramatically reduces both computational time and memory usage of the traditional tensor-multiplication schemes. While more memory-efficient representations exist, this approach enables a consistent extrapolation scheme for the rapid estimation of the exact value. As a demonstration, we apply it to the Trotter decomposition with linked cluster expansion technique and use it to investigate a quantum dot-microcavity system at large coupling strengths. We also apply the optimization in a case where the memory time is very long—specifically in a system containing two spatially separated quantum dots in a common phonon bath.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Physics and Astronomy Schools > Physical, Chemical & Environmental Sciences
Publisher:	American Physical Society
ISSN:	2469-9950
Date of First Compliant Deposit:	28 September 2026
Date of Acceptance:	26 June 2026
Last Modified:	28 Sep 2026 11:01
URI:	https://orca.cardiff.ac.uk/id/eprint/189825

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