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  • Open Access

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

L. M. J. Hall1,*, A. Gisdakis2, and E. A. Muljarov1,†

  • *Contact author: Luke.Hall415@gmail.com
  • †Contact author: Egor.Muljarov@astro.cf.ac.uk
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Phys. Rev. B 114, 125302 – Published 4 August, 2026

DOI: https://doi.org/10.1103/ycrc-vtbk

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.

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Phys. Rev. B 114, 125302– Published 4 August, 2026
  • Received 25 August 2025
  • Accepted 26 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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