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Noise-Resilient Optimization of Parameterized Quantum Circuits for Near-Term Quantum Devices

Deepika D, K Vanishree, Munishamaiah Krishna

Published Jan 28, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.21203/rs.3.rs-8510087/v1

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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.
Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy intermediate-scale quantum (NISQ) processors. Such systems leverage classical optimization to tune the parameters of a parameterized quantum circuit (PQC). The goal is minimizing a cost function that depends on measurement outputs obtained from the PQC. Optimization is typically implemented via stochastic gradient descent (SGD). On NISQ computers, gate noise due to imperfections and decoherence affects the stochastic gradient estimates by introducing a bias. Quantum error mitigation (QEM) techniques can reduce the estimation bias without requiring any increase in the number of qubits, but they in turn cause an increase in the variance of the gradient estimates. This work studies the impact of quantum gate noise on the convergence of SGD for the variational eigensolver (VQE), a fundamental instance of VQAs. The main goal is ascertaining conditions under which QEM can enhance the performance of SGD for VQEs. It is shown that quantum gate noise induces a nonzero error-floor on the convergence error of SGD (evaluated with respect to a reference noiseless PQC), which depends on the number of noisy gates, the strength of the noise, as well as the eigenspectrum of the observable being measured and minimized. In contrast, with QEM, any arbitrarily small error can be obtained. Furthermore, for error levels attainable with or without QEM, QEM can reduce the number of required iterations, but only as long as the quantum noise level is sufficiently large, and a sufficiently large number of measurements is allowed at each SGD iteration. Numerical examples for a max-cut problem corroborate the main theoretical findings.
Noisy Intermediate-Scale Quantum (NISQ) devices show great promise for quantum advantage via Parametrized Quantum Circuits (PQCs) and Variational Quantum Algorithms (VQAs). Due to hardware imperfections, however, especially barren plateaus and environmental Pauli noise, the cost landscape is highly distorted, resulting in inaccurate classical optimization during training. To overcome these challenges, a robust quantum gradient descent framework is presented with the integration of error mitigation directly within the optimization loop. A noise-resilient parameter-shift rule is defined and modeled analytically, as is a variant of stochastic gradient descent with real-time Pauli noise mitigation. The framework is based on a 6-qubit system, which is tested on the Max-Cut problem in the presence of different amounts of depolarizing noise. It is shown experimentally that the proposed algorithm is able to achieve the final cost error of 0.045 under significant noise, whereas the standard quantum gradient descent fails to achieve better than 0.320 under this noise. Moreover, the methodology is consistent, converging without a noise-induced flat landscape and without local minima. The method offers a scalable route towards future applications of quantum machine learning on non-fault-tolerant hardware that does not suffer from the large sampling overhead often associated with conventional error mitigation techniques.
The Quantum Approximate Optimization Algorithm (QAOA) is widely regarded as a promising near-term quantum algorithm for addressing hard combinatorial optimization problems on Noisy Intermediate-Scale Quantum (NISQ) devices; however, its real-world effectiveness is severely constrained by hardware noise, including gate infidelities, decoherence, and measurement errors. This work explores an error mitigation–driven approach to enhance the performance and robustness of QAOA without altering its algorithmic structure or requiring fault-tolerant quantum resources. Measurement error mitigation and zero-noise extrapolation are incorporated into the execution and post-processing stages of QAOA circuits and evaluated using the Minimum Vertex Cover problem as a representative benchmark. Performance is assessed through approximation ratios, solution stability, and noise sensitivity across multiple circuit depths. The results indicate that error mitigation not only improves approximation accuracy but also stabilizes output distributions and delays performance degradation at increased circuit depths. Additionally, the mitigated executions demonstrate better consistency across repeated runs, highlighting improved resilience to stochastic noise. These findings emphasize that lightweight and hardware-efficient error mitigation techniques can significantly extend the practical usability of QAOA on current NISQ hardware, providing a scalable and realistic pathway for executing quantum optimization algorithms more reliably in near-term quantum computing environments.
Parameterized quantum circuits (PQCs) are pivotal components of variational quantum algorithms (VQAs), which represent a promising pathway to quantum advantage in noisy intermediate-scale quantum (NISQ) devices. PQCs enable flexible encoding of quantum information through tunable quantum gates and have been successfully applied across domains such as quantum chemistry, combinatorial optimization, and quantum machine learning. Despite their potential, PQC performance on NISQ hardware is hindered by noise, decoherence, and the presence of barren plateaus, which can impede gradient-based optimization. To address these limitations, we propose novel methods for improving gradient-free optimizers Rotosolve, Fraxis, and FQS, incorporating information from previous parameter iterations. Our approach conserves computational resources by reallocating optimization efforts toward poorly optimized gates, leading to improved convergence. The experimental results demonstrate that our techniques consistently improve the performance of various optimizers, contributing to more robust and efficient PQC optimization.
The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for solving combinatorial optimization problems on near-term quantum hardware. However, its practical deployment remains severely limited by hardware-induced noise and decoherence. In the absence of full fault tolerance, Quantum Error Mitigation (QEM) techniques offer a viable approach to enhance QAOA performance on noisy intermediate-scale quantum (NISQ) devices. In this work, we present a unified classification of QEM strategies specifically tailored for QAOA, systematically categorized into preprocessing, during execution, and post-processing phases. We further classify QAOA deployment settings—such as hardware-constrained devices, stochastic noise-dominated environments, and dense graphs problem—and recommend appropriate QEM techniques for each. A comparative analysis highlights the trade-offs among mitigation accuracy, resource overhead, and robustness to different noise types. By synthesizing recent advances and identifying open challenges, our paper provides both a comprehensive survey and a practical framework for designing robust, noise-resilient QAOA pipelines on near-term quantum platforms.
Quantum Neural Networks (QNNs) based on parameterized quantum circuits (PQCs) are gaining significant research attention due to their potential to achieve quantum advantages on Near-Term Noisy Intermediate-Scale Quantum (NISQ) computers. However, executing QNNs on NISQ devices is challenging due to quantum noise. To address this, we propose a noise-resilient QNN (NR-QNN) that leverages the unique characteristics of PQCs to perform noise-aware optimizations during the inference stage of QNNs. Specifically, NR-QNN employs two optimization techniques to mitigate the impact of noise on QNNs: quantum pruning and sensitivity-aware qubit mapping. The first technique is quantum pruning which identifies gates with small angle of rotations and removes them to simplify circuit of QNNs. The second optimization technique is sensitivity-aware qubit mapping which maps more important logical qubits to more reliable physical qubits. This technique is based on the observation that there can be variation in the sensitivity of an output to input qubits in a QNN. NR-QNN exploits this variability and guides qubit allocation to use reliable physical qubits for sensitive logical qubits. Our evaluation on a real quantum computer demonstrates that NR-QNN enhances the robustness of QNNs, enabling them to operate effectively on NISQ devices.