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Sample-Efficient Tuning of Quantum Circuit Parameters via Bayesian Optimization

Alessandro Pannone, Federico Tosone, Daniel Faccini, Francesco Romito, Nicolò Mazzi

Published Jan 1, 2025• 0 citations
OpenAlex

Abstract

In this work, we present a Bayesian Optimization (BO) approach for tuning the parameters of the Quantum Approximate Optimization Algorithm (QAOA) applied to max-cut problems. Within our black-box optimization framework, BO achieves competitive solutions while requiring significantly fewer quantum circuit evaluations compared to standard non-Bayesian global optimizers. These results highlight the potential of BO to enhance both the efficiency and the overall performance of variational quantum algorithms.

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In this work, we present a Bayesian Optimization (BO) approach for tuning the parameters of the Quantum Approximate Optimization Algorithm (QAOA) applied to max-cut problems. Within our black-box optimization framework, BO achieves competitive solutions while requiring significantly fewer quantum circuit evaluations compared to standard non-Bayesian global optimizers. These results highlight the potential of BO to enhance both the efficiency and the overall performance of variational quantum algorithms.
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.
The Quantum Approximate Optimization Algorithm (QAOA) adopts a hybrid quantum-classical approach to find approximate solutions to variational optimization problems. In fact, it relies on a classical subroutine to optimize the parameters of a quantum circuit. In this work we present a Bayesian optimization procedure to fulfil this optimization task, and we investigate its performance in comparison with other global optimizers. We show that our approach allows for a significant reduction in the number of calls to the quantum circuit, which is typically the most expensive part of the QAOA. We demonstrate that our method works well also in the regime of slow circuit repetition rates, and that few measurements of the quantum ansatz would already suffice to achieve a good estimate of the energy. In addition, we study the performance of our method in the presence of noise at gate level, and we find that for low circuit depths it is robust against noise. Our results suggest that the method proposed here is a promising framework to leverage the hybrid nature of QAOA on the noisy intermediate-scale quantum devices.
Probabilistic tensor optimization of quantum circuits for the max-kkk-cut problem
We propose a technique for optimizing parameterized circuits in variational quantum algorithms based on the probabilistic tensor sampling optimization. This method allows one to relax random initialization issues or heuristics for generating initial guess of variational parameters, and can be used to avoid local minima. We illustrate our approach on the example of the quantum approximate optimization algorithm (QAOA) applied to the max-kkk-cut problem based on the binary encoding efficient in the number of qubits. We discuss the advantages of our technique for searching optimal variational parameters of QAOA circuits in comparison to classical optimization methods.
We propose a technique for optimizing parameterized circuits in variational quantum algorithms based on the probabilistic tensor sampling optimization. This method allows one to relax random initialization issues or heuristics for generating initial guess of variational parameters, and can be used to avoid local minima. We illustrate our approach on the example of the quantum approximate optimization algorithm (QAOA) applied to the $\text{max}\text{\ensuremath{-}}k\text{\ensuremath{-}}\text{cut}$ problem based on the binary encoding efficient in the number of qubits. We discuss the advantages of our technique for searching optimal variational parameters of QAOA circuits in comparison to classical optimization methods.
Quantum Approximate Optimisation Algorithm (QAOA) has emerged as a promising hybrid quantum-classical approach for tackling NP-hard combinatorial optimisation problems by combining quantum and classical computational paradigms. However, efficiently optimising QAOA parameters is notoriously challenging due to the complex, high-dimensional landscapes involved, characterised by numerous local minima and barren plateaus. Bayesian Optimisation (BO) has shown promise in addressing these challenges, yet its effectiveness diminishes significantly with increasing problem dimensionality. In this work, we adopt the Minimum Average Variance Estimation for Bayesian Optimisation (MAVE-BO) method to address this scalability bottleneck. By leveraging the low-dimensional structure inherent in QAOA parameter spaces, our approach improves optimisation efficiency and robustness. We applied our model to a practical power systems problem, optimising eigenvector centrality (EC) in an IEEE 14-bus network. The proposed method demonstrates superior performance in both efficiency and solution quality compared to classical optimisers such as standard Bayesian Optimisation (Vanilla BO), COBYLA, L-BFGS-B, and genetic algorithms. These results underscore the potential of dimensionality-aware BO frameworks for realworld quantum applications in noisy, resource-constrained environments.
Bayesian Optimization (BO) is a powerful technique for optimizing black-box functions, frequently employed in areas such as machine learning hyperparameter tuning and experimental design. However, its performance can degrade significantly in high-dimensional spaces, leading to slow convergence and increased computational cost. This paper introduces a novel approach to Bayesian Optimization inspired by quantum amplitude amplification, a technique rooted in quantum computing. Our method utilizes a probabilistic representation of candidate solutions within a Hilbert space, employing amplitude amplification to systematically bias the search towards promising regions of the solution space. This approach aims to accelerate the optimization process, particularly in scenarios where traditional BO methods struggle due to the curse of dimensionality. The core claim of this work is to demonstrate a speedup in convergence compared to standard BO algorithms, leveraging the principles of amplitude amplification for enhanced exploration and exploitation. The theoretical framework is presented, alongside a detailed explanation of the algorithm's components, and the results are discussed, highlighting the potential for improved efficiency in complex optimization problems. We focus on the core mechanics of using amplitude amplification to enhance the probability of finding optimal solutions.