SciPost Submission Page
A general learning scheme for classical and quantum Ising machines
by Ludwig Schmid, Enrico Zardini, Davide Pastorello
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Ludwig Schmid |
| Submission information | |
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| Preprint Link: | scipost_202311_00042v2 (pdf) |
| Code repository: | https://github.com/lsschmid/ising-learning-model |
| Data repository: | https://doi.org/10.5281/zenodo.10031307 |
| Date accepted: | 2024-03-07 |
| Date submitted: | 2024-02-09 09:10 |
| Submitted by: | Schmid, Ludwig |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
An Ising machine is any hardware specifically designed for finding the ground state of the Ising model. Relevant examples are coherent Ising machines and quantum annealers. In this paper, we propose a new machine learning model that is based on the Ising structure and can be efficiently trained using gradient descent. We provide a mathematical characterization of the training process, which is based upon optimizing a loss function whose partial derivatives are not explicitly calculated but estimated by the Ising machine itself. Moreover, we present some experimental results on the training and execution of the proposed learning model. These results point out new possibilities offered by Ising machines for different learning tasks. In particular, in the quantum realm, the quantum resources are used for both the execution and the training of the model, providing a promising perspective in quantum machine learning.
Author comments upon resubmission
Dear Editors and Reviewers,
Many thanks for the thorough consideration of our manuscript, the positive feedback, and the provided suggestions.
In the following comments on the feedback of Report 1 indicated by ">>>><<<<" and “**** Response:” respectively. When referring to changes in the manuscript, the corresponding line numbers are mentioned, and the changes are highlighted in the provided pdf in blue and sans-serif.
Strengths 1- The paper introduces an innovative machine learning model centered around Ising machines, showcasing a new perspective in the field. 2-The report is well-written and structured, effectively conveying complex concepts in a clear and comprehensible manner. 3-The proposed model demonstrates versatility by addressing tasks such as function approximation and binary classification. <<<<
**** Response: Thank you for the nice summary of our work and the positive review.
Weaknesses 1- The report acknowledges the lack of a comprehensive performance evaluation, including statistical repetitions and comparisons to alternative models. A more thorough evaluation would strengthen the robustness of the findings.
2- While the paper provides a proof of concept, the deferral of statistical analysis to future work leaves some uncertainty about the model's performance and generalizability. <<<<
**** Response 1 + 2: As correctly indicated, the current evaluation lacks the necessary number and broadness of example runs to offer the statistical weight necessary to comment on the model performance. This is due mainly because of the limited access to computational time on the quantum hardware, and we plan to address this point in future work.
3- The paper touches on the model's capabilities in tasks such as function approximation and binary classification but does not extensively explore its variability or limitations in handling more complex scenarios. <<<<
**** Response 3: Due to the very general definition of the proposed model, it can be applied to almost arbitrary machine-learning tasks. Similar to the early days of neural networks, it is currently unclear in which cases the model performs well/poorly. Exploring these possible applications basically opens a new research direction, which will be addressed in future work.
4- The report could benefit from a discussion on the computational cost associated with the proposed model, especially when using quantum annealers, providing a more comprehensive perspective for readers. <<<<
**** Response 4: We thank the referee very much for pointing this out. We fully agree and added an additional section, 3.4, “Computational cost” (l.324-347), addressing this issue. Both for general Ising machines, but also in regard of quantum annealers and their classical counterparts.
Overall, thank you for your careful consideration and best regards,
The authors.
List of changes
- added section 3.4, “Computational cost” (l.324-347): We added a subsection discussing the computational cost to initialize, train, and evaluate the proposed model. Predicting the runtime of the Ising machine (in particular, the quantum annealer) is a highly non-trivial task as the Ising model to be solved changes throughout training, depending on the parameter updates. Nevertheless, we discussed different cases and added references that discuss in detail the runtime of quantum annealers in comparison to their classical alternatives, providing the reader with a more comprehensive overview.
- minor grammatical and spelling errors.
Published as SciPost Phys. Core 7, 013 (2024)