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  • Open Access

Tensor-network population annealing

Takumi Oshima1, Yuma Ichikawa2,3,*, and Koji Hukushima1,4,†

  • *Contact author: ichikawa.yuma@fujitsu.com
  • †Contact author: k-hukushima@g.ecc.u-tokyo.ac.jp
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Phys. Rev. E 114, 055301 – Published 2 November, 2026

DOI: https://doi.org/10.1103/tczz-49lg

Abstract

We propose a hybrid sampling method, tensor-network population annealing (TNPA), which combines tensor-network (TN) initialization with population annealing (PA). We apply this method to the two-dimensional ±J Edwards-Anderson Ising spin glass. The approach is motivated by the limitations of existing methods: TN-based samplers can become numerically unstable in frustrated spin systems at low temperatures, whereas conventional PA requires a long annealing schedule when started from the high-temperature limit. In TNPA, TN contractions are used only within a reliable temperature range to generate initial configurations that are close to the equilibrium distribution. The subsequent low-temperature equilibration is then carried out by PA. To stabilize the initialization process, we introduce a diagnostic based on the effective sample size that adaptively selects the initialization temperature. The proposed framework provides a practical and physically motivated route to low-temperature sampling by combining the complementary strengths of TN and PA.

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Phys. Rev. E 114, 055301– Published 2 November, 2026
  • Received 22 April 2026
  • Accepted 9 October 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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