Variational Quantum Algorithms (VQAs) are promising methods for solving combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) devices. However, benchmarking VQAs is difficult due to their stochastic behavior and the lack of standardized performance criteria. This work introduces a general framework for evaluating VQAs applied to Quadratic Unconstrained Binary Optimization (QUBO) problems. The framework uses three complementary metrics: feasibility, quality, and reproducibility. It also introduces a quality diagram that visualizes trade-offs between success probability and computational resources. Reproducibility is formalized using Shannon entropy, and a decision rule is defined for selecting algorithms under resource constraints. As a demonstration, the framework is applied to several VQAs using Conditional Value at Risk (CVaR) cost functions and different shot counts on a 16-qubit QUBO instance. The results show how the framework supports systematic benchmarking and provides a foundation for adaptive algorithm selection in hybrid quantum-classical workflows.
Variational Quantum Algorithms (VQAs) are promising methods for solving combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) devices. However, benchmarking VQAs is difficult due to their stochastic behavior and the lack of standardized performance criteria. This work introduces a general framework for evaluating VQAs applied to Quadratic Unconstrained Binary Optimization (QUBO) problems. The framework uses three complementary metrics: feasibility, quality, and reproducibility. It also introduces a quality diagram that visualizes trade-offs between success probability and computational resources. Reproducibility is formalized using Shannon entropy, and a decision rule is defined for selecting algorithms under resource constraints. As a demonstration, the framework is applied to several VQAs using Conditional Value at Risk (CVaR) cost functions and different shot counts on a 16-qubit QUBO instance. The results show how the framework supports systematic benchmarking and provides a foundation for adaptive algorithm selection in hybrid quantum-classical workflows.
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.
With rapid advances in quantum hardware, a central question is whether quantum devices with or without full error correction can outperform classical computers on practically relevant problems. Variational quantum algorithms (VQAs) have gained significant attention as promising candidates in this pursuit, particularly for combinatorial optimization problems. While reports of their challenges and limitations continue to accumulate, many studies remain optimistic based on small-scale, idealized testing setups, leaving doubt about the scalability of VQAs for large-scale problems. We systematically investigate this scaling behavior by analyzing how classical optimizers minimize variational quantum loss functions for random Quadratic Unconstrained Binary Optimization instances in the presence of uncertainty, modeled as effective Gaussian noise. We find that the critical noise threshold for successful optimization decreases rapidly as system size grows. This decline exceeds what can be explained solely by shrinking loss variance, confirming deeper, fundamental limitations in the loss landscapes of VQAs beyond barren plateaus. Translating these thresholds into required measurement shots reveals that achieving sufficient precision in the evaluated loss values quickly becomes impractical, even for moderatelysized problems. Our findings demonstrate serious scalability challenges for VQAs in optimization stemming from mere uncertainty, indicating potential barriers to achieving practical quantum advantage with current hybrid approaches.
Variational quantum algorithms (VQAs) have emerged as a promising approach to quantum cryptanalysis on noisy intermediate-scale quantum (NISQ) devices. Although numerous variational attack schemes have been proposed for symmetric cryptosystems, a systematic and modular benchmarking framework to evaluate their performance is still lacking. In this work, we present a comprehensive benchmark study of variational quantum attacks on the Simplified Data Encryption Standard (S-DES), focusing on the modular design choices that determine attack efficiency. We formulate variational quantum attacks within a unified framework consisting of four components: initial state preparation, parameterized circuit (Ansatz) design, cost function construction, and classical optimization. Through numerical simulations, we systematically compare representative design alternatives and evaluate their combinations in terms of convergence behavior, success probability, and effective time complexity. We further introduce standardized metrics for assessing variational quantum attack performance. Our results reveal clear performance hierarchies among different modular configurations and show that carefully optimized designs can significantly outperform naive quantum search. This work establishes a principled benchmark methodology for variational quantum cryptanalysis and positions S-DES as a practical testbed for evaluating quantum attacks on symmetric ciphers in the NISQ era.
Quantum processors promise a paradigm shift in high-performance computing which needs to be assessed by accurate benchmarking measures. In this article, we introduce a benchmark for the variational quantum algorithm (VQA), recently proposed as a heuristic algorithm for small-scale quantum processors. In VQA, a classical optimization algorithm guides the processor's quantum dynamics to yield the best solution for a given problem. A complete assessment of the scalability and competitiveness of VQA should take into account both the quality and the time of dynamics optimization. The method of optimal stopping, employed here, provides such an assessment by explicitly including time as a cost factor. Here, we showcase this measure for benchmarking VQA as a solver for some quadratic unconstrained binary optimization. Moreover, we show that a better choice for the cost function of the classical routine can significantly improve the performance of the VQA algorithm and even improve its scaling properties.
Combinatorial optimization and large-scale data analytics present NP-hard computational challenges, where quantum algorithms promise potential exponential speedups. However, the practical realization of such advantage on Noisy Intermediate-Scale Quantum (NISQ) hardware remains uncertain. This systematic review synthesizes relevant literature to critically evaluate the empirical feasibility and scaling limitations of leading quantum algorithms. The analysis reveals that Variational Quantum Algorithms (VQAs) face persistent reliability challenges such as inconsistent optimality gaps and systemic failures to produce feasible solutions for constrained problems. The principal barrier to VQA scalability is the Measurement Imprecision Wall, where stochastic noise accumulation drives the required measurement shots to scale exponentially with system size, creating a resource deadlock that undermines quantum advantage for large problem instances. For data-centric algorithms, the exponential speedup of Quantum Linear Systems Problem (QLSP) solvers, such as HHL, is largely theoretical for arbitrary classical data due to the Encoding Bottleneck, which requires O(N) runtime for input state preparation. In contrast, Quantum Kernel Methods (QKM) exhibit superior empirical performance and efficient resource scaling, representing the most promising near-term pathway. Achieving practical quantum advantage therefore depends on noise-aware algorithmic design and effective solutions to the classical data ingestion challenge.
Variational quantum algorithms (VQAs) are promising for near-term noisy intermediate-scale quantum (NISQ) devices, but their performance is often limited by device noise, finite-shot uncertainty, and nonstationary behavior that destabilize optimization. This paper proposes a cost-aware closed-loop hybrid framework (Adaptive V16) that augments a standard VQA loop with an online decision policy to adapt measurement effort and mitigation actions during execution. At each iteration, the controller uses runtime signals such as objective progress and uncertainty to select an action comprising the shot budget, mitigation mode, and step-scaling factor, explicitly trading solution improvement against resource overhead under a fixed budget. Experimental evaluation on a representative molecular Hamiltonian optimization task shows that Adaptive V16 achieves a lower final energy than a static VQE baseline and reduces the absolute error from 0.1391 to 0.0657. The controller’s decision module also demonstrates strong predictive performance with 0.9700 accuracy, 0.9595 F1-score, and 0.9951 ROC–AUC, indicating reliable adaptive behavior across thresholds. These results suggest that policy-driven adaptation can improve robustness and budget efficiency for hybrid quantum–classical optimization in realistic NISQ settings.