Optimizing the architecture of variational quantum circuits (VQCs) is crucial for advancing quantum computing (QC) towards practical applications. Current methods range from static ansatz design and evolutionary methods to machine learned VQC optimization, but are either slow, sample inefficient or require infeasible circuit depth to realize advantages. Quality diversity (QD) search methods combine diversity-driven optimization with user-specified features that offer insight into the optimization quality of circuit solution candidates. However, the choice of quality measures and the representational modeling of the circuits to allow for optimization with the current state-of-the-art QD methods like covariance matrix adaptation (CMA), is currently still an open problem. In this work we introduce a directly matrix-based circuit engineering, that can be readily optimized with QD-CMA methods and evaluate heuristic circuit quality properties like expressivity and gate-diversity as quality measures. We empirically show superior circuit optimization of our QD optimization w.r.t. speed and solution score against a set of robust benchmark algorithms from the literature on a selection of NP-hard combinatorial optimization problems.
Optimizing the architecture of variational quantum circuits (VQCs) is crucial for advancing quantum computing (QC) towards practical applications. Current methods range from static ansatz design and evolutionary methods to machine learned VQC optimization, but are either slow, sample inefficient or require infeasible circuit depth to realize advantages. Quality diversity (QD) search methods combine diversity-driven optimization with user-specified features that offer insight into the optimization quality of circuit solution candidates. However, the choice of quality measures and the representational modeling of the circuits to allow for optimization with the current state-of-the-art QD methods like covariance matrix adaptation (CMA), is currently still an open problem. In this work we introduce a directly matrix-based circuit engineering, that can be readily optimized with QD-CMA methods and evaluate heuristic circuit quality properties like expressivity and gate-diversity as quality measures. We empirically show superior circuit optimization of our QD optimization w.r.t. speed and solution score against a set of robust benchmark algorithms from the literature on a selection of NP-hard combinatorial optimization problems.
Variational quantum circuits (VQCs) are highly sensitive to circuit architecture, yet most quantum machine learning pipelines select a single best design and discard the remaining candidates. This paper addresses whether the structural diversity across quantum circuit search spaces can be used to produce stronger predictions through model fusion. We apply Combinatorial Fusion Analysis (CFA), a model fusion framework that selects and combines multiple scoring systems using rank-score function (RSF) and cognitive diversity (CD), to a pool of 29 architecturally diverse classical models and quantum circuits. Using a diversity-aware model selection method, we identify subsets of maximally diverse models and combine them with both score and rank combination. Experiments on four binary classification benchmarks covering different domains demonstrate that CFA-based hybrid classical-quantum fusion consistently outperform the best individual model on every dataset considered with improvements up to 6.03% in accuracy. When comparing with relevant literatures, the CFA framework further achieves superior performance across all four datasets.
In recent years, Variational Quantum Algorithms (VQAs) have emerged as a promising approach for solving optimization problems on quantum computers in the NISQ era. However, one limitation of VQAs is their reliance on fixed-structure circuits, which may not be taylored for specific problems or hardware configurations. A leading strategy to address this issue are Adaptative VQAs, which dynamically modify the circuit structure by adding and removing gates, and optimize their parameters during the training. Several Adaptative VQAs, based on heuristics such as circuit shallowness, entanglement capability and hardware compatibility, have already been proposed in the literature, but there is still lack of a systematic comparison between the different methods. In this paper, we aim to fill this gap by analyzing three Adaptative VQAs: Evolutionary Variational Quantum Eigensolver (EVQE), Variable Ansatz (VAns), already proposed in the literature, and Random Adapt-VQE (RA-VQE), a random approach we introduce as a baseline. In order to compare these algorithms to traditional VQAs, we also include the Quantum Approximate Optimization Algorithm (QAOA) in our analysis. We apply these algorithms to QUBO problems and study their performance by examining the quality of the solutions found and the computational times required. Additionally, we investigate how the choice of the hyperparameters can impact the overall performance of the algorithms, highlighting the importance of selecting an appropriate methodology for hyperparameter tuning. Our analysis sets benchmarks for Adaptative VQAs designed for near-term quantum devices and provides valuable insights to guide future research in this area.
Variational Quantum Circuits (VQCs) have emerged as a cornerstone of hybrid quantum–classical algorithms designed to harness the computational potential of near-term quantum devices. By combining parameterized quantum gates with classical optimization, VQCs provide a flexible framework for tackling machine learning, chemistry, and optimization problems intractable for classical methods. This review comprehensively overviews VQC design principles, ansatz structures, optimization strategies, and real-world applications. Furthermore, we discuss fundamental challenges such as barren plateaus, the expressibility–trainability trade-off, and current noisy intermediate-scale quantum (NISQ) hardware limitations. Finally, we highlight emerging directions that could enable scalable, noise-resilient, and physically interpretable variational quantum models for future quantum computing applications
Variational quantum circuits (VQCs) constitute a central building block of near-term quantum machine learning (QML), yet the principled design of expressive and trainable architectures remains a major open challenge. The VQC design space grows combinatorially with the number of qubits, layers, entanglement structures, and gate parameterizations, rendering manual circuit construction inefficient and often suboptimal. We introduce an autonomous agent-based framework for VQC architecture search that integrates high-level reasoning with a quantum simulation environment. The agent proposes candidate circuit architectures, evaluates them through fully automated training and validation pipelines, and iteratively improves its design strategy via performance-driven feedback. Empirically, we show that the agent autonomously evolves circuit architectures from simple initial ansätze toward increasingly expressive designs, progressively trying to improve task performance. This demonstrates that agentic AI can effectively navigate and refine the VQC design landscape with minimal human intervention, providing a scalable methodology for automated quantum model development in the Noisy Intermediate-Scale Quantum (NISQ) regime.
Variational quantum circuits (VQCs) are an essential tool in applying noisy intermediate-scale quantum computers to practical problems. VQCs are used as a central component in many algorithms, for example, in quantum machine learning, optimization, and quantum chemistry. Several methods have been developed to optimize VQCs. In this work, we enhance the performance of the well-known Rotosolve method, a gradient-free optimization algorithm specifically designed for VQCs. We develop two hybrid algorithms that combine an improved version of Rotosolve with the free quaternion selection (FQS) algorithm, which is the main focus of this study. Through numerical simulations, we observe that these hybrid algorithms achieve higher accuracy and better average performance across different ansatz circuit sizes and cost functions. For shallow variational circuits, we identify a trade-off between the expressivity of the variational ansatz and the speed of convergence to the optimum: a more expressive ansatz ultimately reaches a closer approximation to the true minimum, but at the cost of requiring more circuit evaluations for convergence. By combining the less expressive but fast-converging Rotosolve with the more expressive FQS, we construct hybrid algorithms that benefit from the rapid initial convergence of Rotosolve while leveraging the superior expressivity of FQS. As a result, these hybrid approaches outperform either method used independently.
In the era of Noisy Intermediate-Scale Quantum (NISQ) computing, traditional quantum algorithms face the challenges of limited number of qubits, noise and decoherence. In order to address these issues, we propose a Quantum Architecture Search (QAS) method driven by Bayesian Optimization (BO), which is applied to variational quantum algorithms. In this work, QAS is regarded as a fixed-scale sampling problem. We innovatively propose a quantum gate pool and use a parameterized probabilistic model to dynamically determine the optimal quantum gate for each position in the quantum circuit, thus optimizing the circuit structure. Through using a gradient-free BO method based on radial basis function, we adaptively design end-to-end quantum circuits, significantly reducing circuit depths and improving computational accuracy. We conducted experiments on ground state energy estimation in quantum chemistry and combinatorial optimization problem. The experimental results show that our method is significantly superior to traditional methods and other meta-heuristic search methods in accuracy and efficiency. Our method not only reduces the depth of quantum circuits by up to 85% under a certain accuracy, but also improves the accuracy rate to nearly 100% in combinatorial optimization problem. This provides a powerful and efficient tool for designing optimal quantum circuits and promotes the practical application of quantum algorithms in the NISQ era.