Tensor networks for p-spin models
ORAL
Abstract
We introduce a tensor network algorithm for the solution of p-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system exactly and is thus lossless, yet leads to qualitative changes in runtime scaling in different regimes of the model. First, we find that bond compression emulates the so-called leaf-removal algorithm, solving the problem efficiently in the "easy" phase. Past a dynamical phase transition, we observe superpolynomial runtimes, reflecting the appearance of a core component. We then develop a graphical method to study the scaling of contraction for a minimal ensemble of core-only instances. We find subexponential scaling, improving on the exponential scaling that occurs without compression. Our results suggest that our tensor network algorithm subsumes the classical leaf removal algorithm and simplifies redundancies in the p-spin model through lossless compression, all without explicit knowledge of the problem's structure.
*This work was supported by the Ministère de l'Économie, de l'Innovation et de l'Énergie du Québec through its Research Chair in Quantum Computing, an NSERC Discovery grant, and the Canada First Research Excellence Fund. This work made use of the compute infrastructure of Calcul Québec and the Digital Research Alliance of Canada.
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Publication: B. Lanthier, J. Côté, and S. Kourtis, "Tensor networks for p-spin models," Frontiers in Physics, vol. 12,
2024.
Lanthier, Benjamin, et al. Tensor Networks for p-Spin Models. arXiv:2405.08106, arXiv, 13 May 2024. arXiv.org, https://doi.org/10.48550/arXiv.2405.08106.
Presenters
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Benjamin Lanthier
- Université de Sherbrooke