Loading [MathJax]/extensions/Safe.js
SciPost logo

SciPost Submission Page

Adaptive sampling-based optimization of quantics tensor trains for noisy functions: applications to quantum simulations

by Kohtaroh Sakaue, Hiroshi Shinaoka, Rihito Sakurai

Submission summary

Authors (as registered SciPost users): Kohtaroh Sakaue
Submission information
Preprint Link: scipost_202405_00037v2  (pdf)
Date accepted: July 7, 2025
Date submitted: May 12, 2025, 2:33 p.m.
Submitted by: Sakaue, Kohtaroh
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Quantum Physics
Approach: Computational

Abstract

Tensor cross interpolation (TCI) is a powerful technique for learning a tensor train (TT) by adaptively sampling a target tensor based on an interpolation formula. However, when the tensor evaluations contain random noise, optimizing the TT is more advantageous than interpolating the noise. Here, we propose a new method that starts with an initial guess of TT and optimizes it using non-linear least-squares by fitting it to measured points obtained from TCI. We use quantics TCI (QTCI) in this method and demonstrate its effectiveness on sine and two-time correlation functions, with each evaluated with random noise. The resulting TT exhibits increased robustness against noise compared to the QTCI method. Furthermore, we employ this optimized TT of the correlation function in quantum simulation based on pseudo-imaginary-time evolution, resulting in ground-state energy with higher accuracy than the QTCI or Monte Carlo methods.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block

Author comments upon resubmission

Dear Editor and Referees,

We would like to sincerely thank the Editor and Referees for their time and effort in reviewing our manuscript and for providing thoughtful and constructive feedback. We are especially grateful for the positive assessments from both Referee 1 and Referee 2, as well as their helpful suggestions for improving the clarity and presentation of our work.

In the revised manuscript, we have addressed the comments by expanding the explanation of the intuition behind our method, providing a more detailed description of Step (c), and including a benchmark to illustrate the relevance of Step (b). We have also improved the figures for better readability. We believe these changes have strengthened the manuscript and made it more accessible to a broader audience.

We greatly appreciate the opportunity to revise our submission and thank the Editor for guiding the review process. We hope that the revised manuscript will now be found suitable for publication in SciPost Physics.

Sincerely,
Kohtaroh Sakaue, Hiroshi Shinaoka, Rihito Sakurai

List of changes

  • Expanded the discussion on the intuition behind the method, particularly clarifying the roles and motivations of Steps (a) and (b).
  • Added a more detailed explanation of Step (c), including a description of the cost function, the optimization procedure, and its computational complexity.
  • Conducted and included a benchmark comparison to demonstrate the relevance and effectiveness of Step (b) (bond dimension compression).
  • Improved the clarity and presentation of Figure 5 by reducing data density and adjusting visual transparency.
  • Revised the introductory text before the formalization of the algorithm to provide better context and improve readability.
  • Performed minor edits throughout the manuscript to enhance clarity, accuracy, and consistency of notation.
  • Updated captions and figure labels for clarity and to avoid redundancy.
Current status:
Accepted in target Journal

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)


Reports on this Submission

Report #2 by Anonymous (Referee 2) on 2025-6-17 (Invited Report)

Report

I thank the authors for addressing the points raised in the first report. I believe the manuscript has improved that it can be published in its current form.

Recommendation

Publish (meets expectations and criteria for this Journal)

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Report #1 by Anonymous (Referee 1) on 2025-6-13 (Invited Report)

Strengths

  1. The proposed algorithm works well in the cases shown and is explored in detail.
  2. The second version of the paper goes to greater lengths to explain the steps of the algorithm, provide references, and justify why the algorithm works.

Weaknesses

The algorithm may fail in more challenging cases not yet explored. Here I believe the authors' suggestion of making the last step of their algorithm include a regularization could help in such cases.

Report

The authors have addressed my requested changes and I think those of the other referee in a satisfactory way that has improved the paper. I already believed that the paper meets the acceptance criteria, conditional on the requested changes, so now the paper should be published.

Recommendation

Publish (meets expectations and criteria for this Journal)

  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Login to report or comment