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.
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.
The hardware noise and drift, combined with the fragility of stationary hybrid algorithms like the variational quantum eigensolver (VQE), limit the usefulness of noise quantum advantage accessed through Noisy intermediate-scale quantum (NISQ) processors, but allow near-term quantum advantage. In this paper, a Hybrid Quantum-Classical Adaptive Intelligence Framework is suggested, which bridges the gap between quantum hardware, a parameterized quantum circuit, explicit error-mitigation routines, and a controller trained through learning. The quantum subsystem prepares variational states and calculates the expectation values of the problem Hamiltonian, and an AI/ML model approximates an online noise probability signal and moves an optimizer based on reinforcement learning (RL). The RL policy chooses the parameter updates and enables mitigation measures depending on noise-sensitive state functions, such as energy, gradient norm, and estimated noise level. It was demonstrated experimentally using a simulated NISQ-style molecular Hamiltonian that the adaptive controller can reduce the error in the absolute ground state of the system by about 52.8 percent versus a standard static VQE baseline using the same ansatz. The integrated classifier that drives the process of mitigation is accurate with 97 percent accuracy, 100 percent precision, 92 percent recall, 95.9 F1-score, and 99.5 AUC, which shows reliable decision-making with minimal false alarms. All these findings indicate that the close-knit quantum-classical adaptivity can significantly contribute to the robustness and accuracy of VQE-like workloads on NISQ and serve as a scalable template to design noise-aware hybrid algorithms in the future.
Quantum Reinforcement Learning (QRL) integrates reinforcement learning with parameterized quantum circuits and is a promising approach to combinatorial optimization. On Noisy Intermediate-Scale Quantum (NISQ) devices, however, decoherence, gate imperfections, and measurement errors reduce policy quality and make learning less reliable. Existing error mitigation techniques are generally applied as fixed corrections that do not adapt to changing noise conditions or to the evolving state of training. This work presents Adaptive Policy-Guided Error Mitigation (APGEM) as a context-aware orchestration layer of the hybrid quantum-classical training loop that dynamically selects the most suitable mitigation strategy during QRL training. APGEM evaluates Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), Clifford Data Regression (CDR), and Readout Error Mitigation (REM) using policy-level indicators, including quantum-state fidelity, policy entropy, cumulative reward, and approximation ratio, and integrates the selected strategy directly into the reinforcement learning loop. The framework is evaluated on the Capacitated Vehicle Routing Problem (CVRP), a representative NP-hard problem in urban logistics, under a range of NISQ noise models and noise levels. APGEM consistently outperforms conventional static mitigation methods, reaches approximately 94% of the utility of an oracle strategy, maintains higher quantum-state fidelity as noise increases, and produces more stable learning behaviour throughout training. Ablation studies show that the framework learns context-aware mitigation policies that adapt to different noise environments and circuit execution conditions. These findings demonstrate that integrating adaptive error mitigation into the learning process substantially improves the robustness and reliability of QRL on NISQ hardware.
Quantum Reinforcement Learning (QRL) represents policies as variational quantum circuits (VQCs), making it attractive for combinatorial optimization such as the Capacitated Vehicle Routing Problem (CVRP). On noisy intermediate-scale quantum (NISQ) hardware, however, decoherence degrades fidelity and destabilizes learning, and conventional error mitigation is applied statically without regard to the learning context. We introduce Adaptive Policy-Guided Error Mitigation (APGEM), a controller that selects among Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), Clifford Data Regression (CDR), and Readout Error Mitigation (REM) online, driven by a fidelity, entropy, and cost aware utility function and an epsilon-greedy rule over temporal-difference Q-scores. We evaluate on a realistic urban-logistics testbed, a Delhi-based CVRP over real landmarks with geodesic inter-node costs, exercised across five noise families and four severity levels. On this instance, the QRL agent outperforms constructive heuristics and approaches metaheuristics, while mitigation restores approximation ratios from 0.84-0.87 to 0.92-0.94 under high noise. The controller shifts from a CDR-dominated regime under short training horizons to a balanced deployment across all four techniques under longer horizons, indicating genuine regime-dependent selection. These preliminary results position adaptive, learning-aware mitigation as a practical route to noise-resilient QRL.
The noise of quantum-enhanced learning there is a potential of quantum-enhanced learning with noisy intermediate-scale quantum (NISQ) devices, which is limited by hardware noise and finding useful circuit architectures. In this paper, a Noise-Aware Adaptive Variational Quantum Neural Network (NAVQNN) structure is proposed, which is capable of solving such issues simultaneously. The angle encoding of classical feature vectors (variance, skewness, kurtosis, entropy) of cheque images into quantum states is done on a shallow variational circuit. The noise-sensitive adaptive ansatz generator, in turn, develops the circuit layer-by-layer by picking the new parameterized gate blocks based on their validation loss with an explicit noise model and discouraging depth and two-qubit interactions in their cost functional. The ensuing variational quantum classifier is then trained by a hybrid quantum-classical optimization cycle based on the parameter-shift rule. The experiments on the UCI banknote authentication dataset indicate the usefulness of the proposed approach with the accuracy of 0.9913, precision of 0.9869, recall of 0.9934, F1-score of 0.9902, and ROC-AUC of 0.9998. Figures of prediction score densities, decision boundary, and live inference outputs are additional proof that NAVQNN can gain a strong and well-calibrated decision-making function in compliance with practical NISQ requirements. These findings suggest that noise-conscious adaptive variational circuits can be a useful foundation for quantum-enhanced financial fraud detection and various classification problems.
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.
Abstract The paper introduces a novel hybrid Feedback-Based Quantum Optimization (FBQO) framework that integrates reinforcement learning (RL) for adaptive parameter control and Kalman filters for noise mitigation to enhance quantum optimization on noisy intermediate-scale quantum (NISQ) devices. Unlike traditional quantum Approximate optimization algorithm (QAOA), the proposed method dynamically tunes parameters through learned policies and statistically filtered feedback, enabling faster convergence and greater noise resilience. Key contributions include the formulation of quantum optimization as a Markov Decision Process, integration of deep quantum networks (DQNs) for adaptive control, and the use of Kalman filtering for robust state estimation. Experimental results on the Max-Cut problem demonstrate superior performance in convergence rate, stability, and optimization accuracy over existing techniques. The main finding is that RL-FBQO achieves convergence in 10–20 iterations, compared to 20–30 for FBQO and 40–50 for QAOA, with superior stability.