We propose using variational quantum algorithms (VQAs) to simulate established quantum algorithms under realistic noise conditions, aiming to surpass the fidelity of theoretical circuits in noisy environments. Focusing on the Quantum Fourier Transform (QFT), we perform numerical simulations for two qubits under both coherent and incoherent noise. To enhance generalization, we further introduce the use of Mutually Unbiased Bases (MUBs) during the optimization. Our results show that the variational circuit can reproduce the QFT with higher fidelity in scenarios dominated by coherent noise. This demonstrates the potential of the approach as an effective error-mitigation strategy for small- to medium-scale quantum systems, particularly in settings where coherent noise strongly impacts performance. Beyond mitigating noise and improving fidelity, the method can be adapted to the noise profile of a specific device, providing a versatile and practical route to enhance the reliability of quantum algorithms in near-term quantum hardware.
We propose using variational quantum algorithms (VQAs) to simulate established quantum algorithms under realistic noise conditions, aiming to surpass the fidelity of theoretical circuits in noisy environments. Focusing on the Quantum Fourier Transform (QFT), we perform numerical simulations for two qubits under both coherent and incoherent noise. To enhance generalization, we further introduce the use of Mutually Unbiased Bases (MUBs) during the optimization. Our results show that the variational circuit can reproduce the QFT with higher fidelity in scenarios dominated by coherent noise. This demonstrates the potential of the approach as an effective error-mitigation strategy for small- to medium-scale quantum systems, particularly in settings where coherent noise strongly impacts performance. Beyond mitigating noise and improving fidelity, the method can be adapted to the noise profile of a specific device, providing a versatile and practical route to enhance the reliability of quantum algorithms in near-term quantum hardware.
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.
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 (VQA) are one of the most promising candidates for near-term quantum advantage. Traditionally, these algorithms are parameterized by rotational gate angles whose values are tuned over iterative execution on quantum machines. The iterative tuning of these gate angle parameters make VQAs more robust to a quantum machine's noise profile. However, the effect of noise is still a significant detriment to VQA's target estimations on real quantum machines - they are far from ideal. Thus, it is imperative to employ effective error mitigation strategies to improve the fidelity of these quantum algorithms on near-term machines.While existing error mitigation techniques built from theory do provide substantial gains, the disconnect between theory and real machine execution characteristics limit the scope of these improvements. Thus, it is critical to optimize mitigation techniques to explicitly suit the target application as well as the noise characteristics of the target machine.We propose VAQEM, which dynamically tailors existing error mitigation techniques to the actual, dynamic noisy execution characteristics of VQAs on a target quantum machine. We do so by tuning specific features of these mitigation techniques similar to the traditional rotation angle parameters -by targeting improvements towards a specific objective function which represents the VQA problem at hand. In this paper, we target two types of error mitigation techniques which are suited to idle times in quantum circuits: single qubit gate scheduling and the insertion of dynamical decoupling sequences. We gain substantial improvements to VQA objective measurements - a mean of over 3x across a variety of VQA applications, run on IBM Quantum machines.More importantly, while we study two specific error mitigation techniques, the proposed variational approach is general and can be extended to many other error mitigation techniques whose specific configurations are hard to select a priori. Integrating more mitigation techniques into the VAQEM framework in the future can lead to further formidable gains, potentially realizing practically useful VQA benefits on today's noisy quantum machines.
In the field of robotics, optimization problems with high computational costs, such as motion planning, multi-robot cooperation, and manipulation, are constrained by the exponential growth of the complexity of classical algorithms. This paper discusses practical methods for robot optimization, specifically using noise-aware variational quantum algorithms (VQAs) on current noisy intermediate-scale quantum hardware. To address the inherent errors of quantum devices, a specific framework has been proposed. The framework clearly defines noise modeling, adjusts error mitigation methods, and creates quantum-classical workflows. Using actual quantum computers and high-fidelity simulations, this paper will systematically evaluate four benchmark robotic domains. The statistical data from numerous experiments (up to 100 trials per scenario) indicate that, in the presence of significant hardware noise, noise-aware VQAs can improve the target value by up to 14% compared to standard quantum methods and reduce the number of convergence iterations by 45%. Cross-platform tests indicate that all six robotic tasks run stably, with an accuracy rate exceeding 90% for all devices. In real-world environments, this trajectory generation method performs excellently under noisy conditions when using physical robots. In order to ensure the accuracy of quantum accelerated optimization in robotics, it is necessary to reduce noise. According to the aforementioned research, reducing noise can be practically applied outside of laboratory conditions.
Variational Quantum Algorithms (VQA) are one of the most promising candidates for near-term quantum advantage. Traditionally, these algorithms are parameterized by rotational gate angles whose values are tuned over iterative execution on quantum machines. The iterative tuning of these gate angle parameters make VQAs more robust to a quantum machine’s noise profile. However, the effect of noise is still a significant detriment to VQA’s target estimations on real quantum machines — they are far from ideal. Thus, it is imperative to employ effective error mitigation strategies to improve the fidelity of these quantum algorithms on near-term machines.While existing error mitigation techniques built from theory do provide substantial gains, the disconnect between theory and real machine execution characteristics limit the scope of these improvements. Thus, it is critical to optimize mitigation techniques to explicitly suit the target application as well as the noise characteristics of the target machine.We propose VAQEM, which dynamically tailors existing error mitigation techniques to the actual, dynamic noisy execution characteristics of VQAs on a target quantum machine. We do so by tuning specific features of these mitigation techniques similar to the traditional rotation angle parameters -by targeting improvements towards a specific objective function which represents the VQA problem at hand. In this paper, we target two types of error mitigation techniques which are suited to idle times in quantum circuits: single qubit gate scheduling and the insertion of dynamical decoupling sequences. We gain substantial improvements to VQA objective measurements — a mean of over 3x across a variety of VQA applications, run on IBM Quantum machines.More importantly, while we study two specific error mitigation techniques, the proposed variational approach is general and can be extended to many other error mitigation techniques whose specific configurations are hard to select a priori. Integrating more mitigation techniques into the VAQEM framework in the future can lead to further formidable gains, potentially realizing practically useful VQA benefits on today’s noisy quantum machines.
This work provides a rigorous theoretical investigation of selective error correction strategies for variational quantum algorithms, with focus on understanding the interplay between error suppression, circuit trainability, and computational resource requirements. We develop a mathematical framework that characterizes how different error correction codes affect the optimization landscape of parameterized quantum circuits, deriving exact bounds on error-suppression capabilities as functions of code distance, syndrome extraction frequency, and variational parameter space dimensionality. Our analysis reveals that selective correction-applying error mitigation only to critical circuit components-can preserve trainability while significantly reducing quantum resource overhead compared to full error correction. We establish theoretical conditions under which selective strategies maintain solution quality guarantees and prove convergence theorems for variational algorithms operating under this paradigm. The framework incorporates noise models spanning coherent and incoherent errors, providing performance predictions across different hardware platforms. We further analyze the trade-off between error correction resource investment and algorithm performance, identifying optimal correction strategies for various problem classes. This theoretical foundation advances understanding of practical quantum algorithm design under realistic noise conditions and offers principled approaches to resource-efficient quantum error management in near-term devices.