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Analyzing the Effectiveness of Quantum Annealing with Meta-Learning

Riccardo Pellini, Maurizio Ferrari Dacrema

TL;DR

This work addresses the problem of understanding when quantum annealing (QA) is effective for solving QUBO problems. It introduces a meta-learning approach built on a dataset of more than five thousand QUBO instances across ten problem classes, with over 100 features describing problem structure, coefficients, and solution spaces, and it publicly releases the dataset. By training multiple meta-models to predict QA effectiveness, the study identifies that the distribution and values of the bias and coupling terms, as well as embedding-related features, strongly influence QA performance, and shows high predictive accuracy across large and small instances. The findings offer a generalizable methodology to probe QA behavior, guide QUBO formulation and embedding choices, and can be extended to other solvers such as VQE or QAOA, strengthening practical insights for selecting and tuning solvers in real-world optimization tasks.

Abstract

The field of Quantum Computing has gathered significant popularity in recent years and a large number of papers have studied its effectiveness in tackling many tasks. We focus in particular on Quantum Annealing (QA), a meta-heuristic solver for Quadratic Unconstrained Binary Optimization (QUBO) problems. It is known that the effectiveness of QA is dependent on the task itself, as is the case for classical solvers, but there is not yet a clear understanding of which are the characteristics of a problem that makes it difficult to solve with QA. In this work, we propose a new methodology to study the effectiveness of QA based on meta-learning models. To do so, we first build a dataset composed of more than five thousand instances of ten different optimization problems. We define a set of more than a hundred features to describe their characteristics, and solve them with both QA and three classical solvers. We publish this dataset online for future research. Then, we train multiple meta-models to predict whether QA would solve that instance effectively and use them to probe which are the features with the strongest impact on the effectiveness of QA. Our results indicate that it is possible to accurately predict the effectiveness of QA, validating our methodology. Furthermore, we observe that the distribution of the problem coefficients representing the bias and coupling terms is very informative to identify the probability of finding good solutions, while the density of these coefficients alone is not enough. The methodology we propose allows to open new research directions to further our understanding of the effectiveness of QA, by probing specific dimensions or by developing new QUBO formulations that are better suited for the particular nature of QA. Furthermore, the proposed methodology is flexible and can be extended or used to study other quantum or classical solvers.

Analyzing the Effectiveness of Quantum Annealing with Meta-Learning

TL;DR

This work addresses the problem of understanding when quantum annealing (QA) is effective for solving QUBO problems. It introduces a meta-learning approach built on a dataset of more than five thousand QUBO instances across ten problem classes, with over 100 features describing problem structure, coefficients, and solution spaces, and it publicly releases the dataset. By training multiple meta-models to predict QA effectiveness, the study identifies that the distribution and values of the bias and coupling terms, as well as embedding-related features, strongly influence QA performance, and shows high predictive accuracy across large and small instances. The findings offer a generalizable methodology to probe QA behavior, guide QUBO formulation and embedding choices, and can be extended to other solvers such as VQE or QAOA, strengthening practical insights for selecting and tuning solvers in real-world optimization tasks.

Abstract

The field of Quantum Computing has gathered significant popularity in recent years and a large number of papers have studied its effectiveness in tackling many tasks. We focus in particular on Quantum Annealing (QA), a meta-heuristic solver for Quadratic Unconstrained Binary Optimization (QUBO) problems. It is known that the effectiveness of QA is dependent on the task itself, as is the case for classical solvers, but there is not yet a clear understanding of which are the characteristics of a problem that makes it difficult to solve with QA. In this work, we propose a new methodology to study the effectiveness of QA based on meta-learning models. To do so, we first build a dataset composed of more than five thousand instances of ten different optimization problems. We define a set of more than a hundred features to describe their characteristics, and solve them with both QA and three classical solvers. We publish this dataset online for future research. Then, we train multiple meta-models to predict whether QA would solve that instance effectively and use them to probe which are the features with the strongest impact on the effectiveness of QA. Our results indicate that it is possible to accurately predict the effectiveness of QA, validating our methodology. Furthermore, we observe that the distribution of the problem coefficients representing the bias and coupling terms is very informative to identify the probability of finding good solutions, while the density of these coefficients alone is not enough. The methodology we propose allows to open new research directions to further our understanding of the effectiveness of QA, by probing specific dimensions or by developing new QUBO formulations that are better suited for the particular nature of QA. Furthermore, the proposed methodology is flexible and can be extended or used to study other quantum or classical solvers.
Paper Structure (72 sections, 53 equations, 2 figures, 11 tables)

This paper contains 72 sections, 53 equations, 2 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Background
  3. QUBO and Ising Models
  4. Quantum Annealing and Quantum Annealers
  5. Studies on the Effectiveness of QA
  6. Meta-Learning Dataset Generation
  7. Selection of Problems and Instances
  8. Evaluating the Effectiveness of a Solver
  9. Meta-Learning Features
  10. Hyperparameter Optimization of the Solvers
  11. Optimal Hyperparameters of Quantum Annealing
  12. Optimal Hyperparameters of the Classical Solvers
  13. Meta-Model Training and Optimization
  14. Results and Analysis
  15. Effectiveness of QA for Large Instances
  16. ...and 57 more sections

Figures (2)

  • Figure 2: Bar plot showing the Balanced Accuracy of the meta-models which predict whether QA is at least as good of all the classical solvers combined (QA-over-all) on the large instances. The domains or component sets the model is trained on are listed on the x-axis. Domains and component sets are ordered according to the Balanced Accuracy of the best related meta-model, in descending order. The vertical black segments on the top of each bar represent the standard deviation of the meta-models.
  • Figure 3: Bar plot showing the Balanced Accuracy of the meta-models which predict whether QA will find the global optimum (Optimal) on small problem instances. The domains or components the model is trained on are listed on the x-axis. Domains and component sets are ordered according to the Balanced Accuracy of the best related meta-model, in descending ordered. The vertical black segments on the top of each bar represent the standard deviation of the meta-models.