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Resource-efficient quantum approximate optimization algorithm via Bayesian optimization and maximum-probability evaluation

Siran Zhang, Shuming Cheng

Abstract

The quantum approximate optimization algorithm (QAOA) is a leading variational approach to combinatorial optimization, but its practical performance depends strongly on objective design, parameter search, and shot allocation. We present a resource-efficient QAOA framework that uses the cut value of the most probable measured bitstring as the optimization objective, combines it with Bayesian optimization, and adaptively allocates shots using dual criteria based on mode confidence and normalized cut-value variance. Numerical experiments on 3-regular MaxCut show that, for both unweighted and weighted instances, the proposed scheme achieves discrete-solution quality comparable to that of the conventional expectation-based objective while typically requiring fewer total shots to reach the same final mode accuracy. These results indicate that reorganizing QAOA around the maximum-probability bitstring provides an effective route to improving practical performance under limited measurement budgets.

Resource-efficient quantum approximate optimization algorithm via Bayesian optimization and maximum-probability evaluation

Abstract

The quantum approximate optimization algorithm (QAOA) is a leading variational approach to combinatorial optimization, but its practical performance depends strongly on objective design, parameter search, and shot allocation. We present a resource-efficient QAOA framework that uses the cut value of the most probable measured bitstring as the optimization objective, combines it with Bayesian optimization, and adaptively allocates shots using dual criteria based on mode confidence and normalized cut-value variance. Numerical experiments on 3-regular MaxCut show that, for both unweighted and weighted instances, the proposed scheme achieves discrete-solution quality comparable to that of the conventional expectation-based objective while typically requiring fewer total shots to reach the same final mode accuracy. These results indicate that reorganizing QAOA around the maximum-probability bitstring provides an effective route to improving practical performance under limited measurement budgets.

Paper Structure

This paper contains 13 sections, 28 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Theoretical Foundations and Methodology
  3. Problem Formulation
  4. Methodology
  5. Workflow and Resource Estimation
  6. Numerical Experiments and Results Analysis
  7. Experimental Setup and Chapter Organization
  8. Objective Design: From Conventional Expectation to the Maximum-Probability Bitstring
  9. Shot Allocation: From Fixed Shots to Adaptive Shots
  10. Overall Results from the Joint Design of the Three Components
  11. Noise Analysis
  12. Discussion and Conclusion
  13. Acknowledgements

Figures (9)

  • Figure 1: Comparison between the conventional expectation and the mode-based objective on unweighted 3-regular MaxCut.
  • Figure 2: Comparison between the conventional expectation and the mode-based objective on weighted 3-regular MaxCut.
  • Figure 3: Comparison of the shots required to reach a final mode accuracy of $0.80$. This figure directly reflects the quantum sampling cost needed to achieve the same discrete-solution quality and is therefore taken as the main figure for the resource-efficiency analysis in this chapter.
  • Figure 4: Resource saving rate relative to conventional expectation with Bayesian optimization under the constraint that the final mode accuracy is no lower than $0.80$. Positive values indicate that the proposed method uses fewer shots to achieve the same accuracy.
  • Figure 5: Accuracy--resource Pareto comparison in the qubit-scaling experiment. The horizontal axis denotes the total number of shots, and the vertical axis denotes the final mode accuracy.
  • ...and 4 more figures