Hybrid quantum classical algorithms offer a promising approach for exploiting Noisy Intermediate Scale Quantum devices; however, their practical deployment remains limited by excessive circuit depth, hardware noise, and inefficient utilization of quantum resources. This paper presents a Hybrid Variational Optimization (HVO) framework that reduces quantum algorithmic complexity by integrating adaptive circuit pruning with classical feedback-driven optimization and a unified Quantum Complexity Metric (QCM). Unlike prior adaptive variational approaches such as RE-ADAPT-VQA, the proposed framework explicitly optimizes the trade-off between gate count, fidelity, and qubit resources while remaining modular and hardware-agnostic. To ensure a fair and transparent evaluation, the proposed method is compared against a well-tuned shallow Variational Quantum Eigensolver (VQE), QAOA, and RE-ADAPT-VQA. Experimental validation on IBM Quantum simulators and real NISQ hardware demonstrates up to a 35% reduction in circuit complexity, a 30% reduction in execution time, and improved fidelity of 0.94. Furthermore, performance evaluation using accuracy, precision, recall, and F1-score confirms the robustness and reliability of the proposed framework. These results demonstrate that HVO provides a scalable and noise-resilient solution for near term quantum computing applications.
Hybrid quantum classical algorithms offer a promising approach for exploiting Noisy Intermediate Scale Quantum devices; however, their practical deployment remains limited by excessive circuit depth, hardware noise, and inefficient utilization of quantum resources. This paper presents a Hybrid Variational Optimization (HVO) framework that reduces quantum algorithmic complexity by integrating adaptive circuit pruning with classical feedback-driven optimization and a unified Quantum Complexity Metric (QCM). Unlike prior adaptive variational approaches such as RE-ADAPT-VQA, the proposed framework explicitly optimizes the trade-off between gate count, fidelity, and qubit resources while remaining modular and hardware-agnostic. To ensure a fair and transparent evaluation, the proposed method is compared against a well-tuned shallow Variational Quantum Eigensolver (VQE), QAOA, and RE-ADAPT-VQA. Experimental validation on IBM Quantum simulators and real NISQ hardware demonstrates up to a 35% reduction in circuit complexity, a 30% reduction in execution time, and improved fidelity of 0.94. Furthermore, performance evaluation using accuracy, precision, recall, and F1-score confirms the robustness and reliability of the proposed framework. These results demonstrate that HVO provides a scalable and noise-resilient solution for near term quantum computing applications.
Variational quantum algorithms (VQAs) hold significant promise for solving complex problems across diverse fields. However, their practical implementation on near-term quantum devices is severely hampered by the pervasive effects of quantum noise. Traditional quantum circuit compilation techniques are largely static, failing to account for the unique noise profiles inherent in individual quantum hardware. This paper introduces a novel adaptive quantum circuit compilation framework designed to mitigate these limitations. The core concept centers around dynamically adjusting the circuit layout and gate decomposition in real-time, leveraging measurements of the quantum hardware's noise characteristics to optimize both the accuracy and circuit depth of the compiled quantum circuit. This approach represents a critical step towards unlocking the full potential of VQAs by enabling them to effectively operate within the constraints of noisy quantum computers. The framework incorporates feedback loops for continuous refinement, adapting to evolving noise conditions. The methodology is described, focusing on the key components: noise profiling, adaptive gate decomposition, and circuit re-optimization. Simulation results demonstrate the effectiveness of the adaptive approach in reducing circuit depth and improving the fidelity of VQA computations compared to static compilation methods. This work lays the foundation for robust and efficient VQA execution on future quantum hardware.
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.
Abstract Noisy Intermediate-Scale Quantum (NISQ) devices are near-term quantum computing devices that inherently suffer from imperfect gate implementation, decoherence, and measurement noise. The main type of variational quantum algorithms(VQAs) is based on Parameterized Quantum Circuits (PQCs), which, however, face practical challenges due to optimization instability of optimization caused by noise and reduced performance. In this paper, we suggest a comprehensive noise-resilient optimization framework for PQCs, which explicitly incorporates noise-resilient circuit architecture design, incorporating noise-aware training strategies into the variational optimization loop. The framework uses circuit structures that are efficient in depth and are hardware compatible in addition to adaptive optimizer choice, stochastic optimization, and averaging as a part of repeated measurement to reduce the impacts of realistic noise. Large-scale experiments are performed with different amounts of qubits, depths of the circuit and noise strengths with realistic noise models. The findings indicate that the convergence rate is faster, the stability is increased, the variability of run-to-run variability is minimized, and other robustness is better than the noise-unaware optimization techniques. Moreover, systematic studies determine optimal operating regions that optimally trade-off expressibility and noise tolerance to offer useful design advice on trusted implementation of VQAs with near-term quantum hardware.
Although quantum computers will not necessarily transform ML in general, they hold immense potential for specific uses, such as dealing with high-dimensional data and complex correlations that cannot be effectively modeled using classical systems. It is, however, difficult to design efficient quantum circuits, especially with the existing Noisy Intermediate-Scale Quantum (NISQ) hardware that has constraints including decoherence, a limited number of qubits, and gate fidelity limitations. The authors propose an Adaptive Quantum Circuit Architecture Search (AQCAS) framework whose structure and parameters are optimized dynamically to improve the performance of the task-specific ML. The framework integrates quantum circuit encoding, a hybrid search strategy that is based on reinforcement learning and evolutionary algorithms, and a task-specific adaptivity mechanism. Benchmark datasets were used for experimental evaluations of both simulation using Qiskit Aer and classical optimization using the Python frameworks TensorFlow and PennyLane. Fixed and standard variational quantum circuits were compared with performance measurements like the classification accuracy, circuit depth, convergence speed, and computational efficiency. The results show that the accuracy of AQCAS can be raised to 94.1%, and the circuit depth is lowered at the same time. It converged rapidly and is computationally efficient. Ablation studies show that both hybrid search and adaptivity mechanisms help to enhance generalization and stability under NISQ constraints. The results demonstrate the potential of AQCAS as a practical approach to using adaptive quantum circuits in specialized ML applications, and lay the groundwork for future development of scaling to larger devices, implementing noise-aware optimization, and integrating with hybrid quantum-classical ML pipelines.
For quantum algorithms to achieve their full potential, we need methodologies to optimize them, such as reaching a given output accuracy with minimal resource costs. Here, we develop such a methodology for a class of Noisy Intermediate-Scale Quantum (NISQ) algorithms. We leverage simulations of a Variational Quantum Eigensolver (VQE) to propose a phenomenological model of such algorithms that captures the complex relationship between algorithmic accuracy, algorithmic resource costs, and the noise that exists in realistic quantum hardware. For this, we take the algorithmic resource cost to be the total number of quantum gate-operations in the algorithm; minimizing this cost typically makes the algorithm faster and more energy-efficient. We consider the subtle trade-off between quantum circuit size (small circuits are too imprecise, but large ones are too noisy), and the number of iterations of that quantum circuit for the full algorithm to sufficiently converge. Using a noise-metric-resource methodology, we identify the sweet spot (of circuit size versus iterations) that minimizes the algorithmic resource costs for a desired algorithm accuracy. It also gives the circuit size that maximizes algorithm accuracy for a fixed resource cost. Our methodology provides a practical guideline for near-term deployment of variational algorithms on realistic noisy hardware, including hardware that uses error mitigation.
This paper presents a novel approach to quantum circuit compilation that leverages the feedback capabilities of the Variational Quantum Eigensolver (VQE) to achieve adaptive optimization. Traditional quantum compilation methods are static, assuming a known and consistent noise profile for the target quantum hardware. However, real quantum devices exhibit significant noise variations, leading to suboptimal circuit execution. Our strategy addresses this challenge by dynamically adjusting compilation parameters based on the VQE's error estimations during runtime. The core idea is to implement a real-time optimization loop where the VQE provides error estimates for individual gate operations, and the compiler subsequently modifies the circuit topology and gate choices to minimize overall error. This adaptive compilation scheme allows the quantum circuit to 'learn' the noise characteristics of the hardware, leading to a reduction in gate count and improved fidelity. The presented framework offers a pathway towards more robust and efficient quantum computation, particularly relevant as quantum hardware matures and noise mitigation techniques become more sophisticated. We outline the key components of the system, including the VQE integration, the compilation algorithm, and a discussion of potential challenges and future research directions.