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Symmetry
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Quantum Optimization & Machine Learning
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Quantum Optimization & Machine Learning

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 6272

Special Issue Editor

Dr. Alexey A. Melnikov

E-Mail Website
Guest Editor
Terra Quantum AG, 9000 St. Gallen, Switzerland
Interests: quantum machine learning; applied quantum technologies; artificial intelligence in physics; quantum walk based algorithms; quantum optimization

Special Issue Information

Dear Colleagues,

Optimization and machine learning algorithms that use quantum effects to process information have caught a lot of attention in recent years. Quantum optimization and machine learning algorithms may allow for solving problems that are intractable for known classical algorithms.

Advances in variational quantum circuit theory offer techniques to design new quantum optimization and machine learning algorithms. Several of these algorithms, e.g., the quantum approximate optimization algorithm, and quantum neural networks, are among leading candidates for demonstrating quantum advantage in solving practical industry problems. Thus, there is an increasing need to understand in which problems and with which algorithms quantum advantage can be expected. In particular, understanding underlying problem symmetry, and parametrized quantum circuit’s symmetry, could allow for achieving helpful quantum interference effects leading to quantum advantage.

This Special Issue is intended to discuss quantum algorithms for optimization and machine learning, and how machine learning techniques can help in improving these algorithms.

Dr. Alexey A. Melnikov
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quantum optimization
  • Quantum machine learning
  • Machine learning in quantum physics
  • Quantum information science
  • Quantum approximate optimization algorithm
  • Variational quantum algorithms
  • Hybrid quantum-classical algorithms
  • Neural networks in quantum algorithms
  • Quantum neural networks
  • Parametrized quantum circuits

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Published Papers (2 papers)

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Research

13 pages, 595 KiB  
Article
Capturing Symmetries of Quantum Optimization Algorithms Using Graph Neural Networks
by Ajinkya Deshpande and Alexey Melnikov
Symmetry 2022, 14(12), 2593; https://doi.org/10.3390/sym14122593 - 7 Dec 2022
Cited by 4 | Viewed by 2323
Abstract
Quantum optimization algorithms are some of the most promising algorithms expected to show a quantum advantage. When solving quadratic unconstrained binary optimization problems, quantum optimization algorithms usually provide an approximate solution. The solution quality, however, is not guaranteed to be good enough to [...] Read more.
Quantum optimization algorithms are some of the most promising algorithms expected to show a quantum advantage. When solving quadratic unconstrained binary optimization problems, quantum optimization algorithms usually provide an approximate solution. The solution quality, however, is not guaranteed to be good enough to warrant selecting it over the classical optimizer solution, as it depends on the problem instance. Here, we present an algorithm based on a graph neural network that can choose between a quantum optimizer and classical optimizer using performance prediction. In addition, we present an approach that predicts the optimal parameters of a variational quantum optimizer. We tested our approach with a specific quantum optimizer, the quantum approximate optimization algorithm, applied to the Max-Cut problem, which is an example of a quadratic unconstrained binary optimization problem. We observed qualitatively and quantitatively that graph neural networks are suited for a performance prediction of up to nine-vertex Max-Cut instances with a quantum approximate optimization algorithm with a depth of up to three. For the performance prediction task, the average difference between the actual quantum algorithm performance and the predicted performance is below 19.7% and, for the parameter prediction task, the solution using the predicted parameters is within 2.7% of the optimal parameter solution. Our method therefore has the capacity to find problems that are best suited for quantum solvers. The proposed method and the corresponding algorithm can be used for hybrid quantum algorithm selection. Full article
(This article belongs to the Special Issue Quantum Optimization & Machine Learning)
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10 pages, 1660 KiB  
Article
Direct Parameter Estimations from Machine Learning-Enhanced Quantum State Tomography
by Hsien-Yi Hsieh, Jingyu Ning, Yi-Ru Chen, Hsun-Chung Wu, Hua Li Chen, Chien-Ming Wu and Ray-Kuang Lee
Symmetry 2022, 14(5), 874; https://doi.org/10.3390/sym14050874 - 25 Apr 2022
Cited by 13 | Viewed by 2648
Abstract
With the power to find the best fit to arbitrarily complicated symmetry, machine-learning (ML)-enhanced quantum state tomography (QST) has demonstrated its advantages in extracting complete information about the quantum states. Instead of using the reconstruction model in training a truncated density matrix, we [...] Read more.
With the power to find the best fit to arbitrarily complicated symmetry, machine-learning (ML)-enhanced quantum state tomography (QST) has demonstrated its advantages in extracting complete information about the quantum states. Instead of using the reconstruction model in training a truncated density matrix, we develop a high-performance, lightweight, and easy-to-install supervised characteristic model by generating the target parameters directly. Such a characteristic model-based ML-QST can avoid the problem of dealing with a large Hilbert space, but cab keep feature extractions with high precision, capturing the underlying symmetry in data. With the experimentally measured data generated from the balanced homodyne detectors, we compare the degradation information about quantum noise squeezed states predicted by the reconstruction and characteristic models; both are in agreement with the empirically fitting curves obtained from the covariance method. Such a ML-QST with direct parameter estimations illustrates a crucial diagnostic toolbox for applications with squeezed states, from quantum information process, quantum metrology, advanced gravitational wave detectors, to macroscopic quantum state generation. Full article
(This article belongs to the Special Issue Quantum Optimization & Machine Learning)
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