In the NISQ-era of quantum computing, we should not expect to see quantum devices that provide an exponential improvement in runtime for practical problems, due to the lack of error correction and small number of qubits available. Nevertheless, these devices should be able to provide other performance improvements, particularly when combined with existing classical machines. In this article, we develop several hybrid quantum-classical clustering algorithms that can be employed as subroutines on small, NISQ-era devices. These new hybrid algorithms require a number of qubits that is at most logarithmic in the size of the data, provide performance improvement and/or runtime improvement over their classical counterparts, and do not require a black-box oracle. Consequently, we are able to provide a promising near-term application of NISQ-era devices.
In the NISQ-era of quantum computing, we should not expect to see quantum devices that provide an exponential improvement in runtime for practical problems, due to the lack of error correction and small number of qubits available. Nevertheless, these devices should be able to provide other performance improvements, particularly when combined with existing classical machines. In this article, we develop several hybrid quantum-classical clustering algorithms that can be employed as subroutines on small, NISQ-era devices. These new hybrid algorithms require a number of qubits that is at most logarithmic in the size of the data, provide performance improvement and/or runtime improvement over their classical counterparts, and do not require a black-box oracle. Consequently, we are able to provide a promising near-term application of NISQ-era devices.
Quantum computers can exploit a Hilbert space whose dimension increases exponentially with the number of qubits. In experiment, quantum supremacy has recently been achieved by the Google team by using a noisy intermediate-scale quantum (NISQ) device with over 50 qubits. However, the question of what can be implemented on NISQ devices is still not fully explored, and discovering useful tasks for such devices is a topic of considerable interest. Hybrid quantum-classical algorithms are regarded as well-suited for execution on NISQ devices by combining quantum computers with classical computers, and are expected to be the first useful applications for quantum computing. Meanwhile, mitigation of errors on quantum processors is also crucial to obtain reliable results. In this article, we review the basic results for hybrid quantum-classical algorithms and quantum error mitigation techniques. Since quantum computing with NISQ devices is an actively developing field, we expect this review to be a useful basis for future studies.
Quantum computing has the potential to solve complex problems that are outside the scope of classical systems, making it a standard shifter. Current devices, which are considered as Noisy Intermediate-Scale Quantum (NISQ) systems, are insufficient in their practical utility due to hardware limitations, error rates, and qubit counts. The dynamic growths wanted to exceed the NISQ era and grow scalable quantum algorithms and architectures that can achieve useful quantum benefit in real-world applications are reviewed in this research. This research gives a comprehensive examination of the complications in scaling quantum systems, adjacent resource efficacy, qubit connectivity, and error correction. In addition to connecting architectural innovations like modular quantum computing, error-resilient circuit design, and distributed quantum systems, the paper provides new hybrid quantum-classical algorithms planned to exploit performance in noisy environments. Results from benchmarking in arenas like machine learning, optimization, and quantum chemistry show how these methods can provide short-term quantum benefit. Lastly, this paper proposes a research roadmap for quantum computing that highlights the requirement of co-designing algorithms, software, and hardware. The goal of this effort is to straighten the progress of quantum systems that can resolve problems in the real world at scale by addressing the inadequacies of NISQ devices and emphasizing scalable solutions.
The current stage of quantum computing development is defined by Noisy Intermediate-Scale Quantum (NISQ) devices, which operate with a moderate number of qubits that are inherently susceptible to noise and decoherence. Despite the absence of full error correction, NISQ systems have demonstrated the ability to perform computational tasks that challenge classical simulation under certain conditions. This paper explores the concept of quantum advantage in the NISQ era by analysing prominent algorithmic approaches, benchmarking methodologies, and the practical constraints imposed by contemporary hardware. Hybrid quantum–classical algorithms, sampling-based experiments, and performance metrics are examined to assess the extent to which near-term quantum devices can outperform classical systems. The study finds that while progress toward quantum advantage is evident, significant technical and algorithmic limitations prevent its widespread realization. The paper concludes by identifying key research directions required to bridge the gap between experimental demonstrations and practical quantum computing applications.
Quantum ant colony optimization (QACO) has drew much attention since it combines the advantages of quantum computing and ant colony optimization (ACO) algorithm overcoming some limitations of the traditional ACO algorithm. However,due to the hardware resource limitations of currently available quantum computers, the practical application of the QACO is still not realized. In this paper, we developed a quantum-classical hybrid algorithm by combining the clustering algorithm with QACO algorithm.This extended QACO can handle large-scale optimization problems with currently available quantum computing resource. We have tested the effectiveness and performance of the extended QACO algorithm with the Travelling Salesman Problem (TSP) as benchmarks, and found the algorithm achieves better performance under multiple diverse datasets. In addition, we investigated the noise impact on the extended QACO and evaluated its operation possibility on current available noisy intermediate scale quantum(NISQ) devices. Our work shows that the combination of the clustering algorithm with QACO effectively improved its problem solving scale, which makes its practical application possible in current NISQ era of quantum computing.
Quantum computing has emerged as a transformative paradigm capable of addressing computational challenges beyond the reach of classical systems.In the current era of Noisy Intermediate-Scale Quantum (NISQ) devices, practical quantum hardware is characterized by limited qubit counts, short coherence times, gate errors, and the absence of full error correction.Despite these constraints, significant progress has been made in developing quantum machine learning (QML) techniques tailored to operate on near-term quantum processors.This paper presents a comprehensive review of Quantum Machine Learning in the context of NISQ computing.We first outline the fundamental principles of quantum computing, including qubits, superposition, entanglement, and quantum parallelism, followed by a detailed discussion of the NISQ computing model and its hardware limitations.The review then examines hybrid quantum-classical learning frameworks, variational quantum algorithms, quantum data encoding strategies, and noise mitigation techniques that enable practical implementation on existing platforms.Emerging applications across healthcare, finance, cybersecurity, climate modeling, and materials science are also surveyed to highlight the real-world potential of QML.Furthermore, key challenges such as scalability, trainability issues, and algorithmic robustness are analyzed, along with current research efforts aimed at overcoming these barriers.The paper concludes by identifying promising future directions for advancing QML toward quantum advantage.This review aims to provide researchers and practitioners with a structured understanding of the capabilities, limitations, and opportunities of quantum machine learning in the NISQ era .
Quantum machine learning has emerged as a promising approach to enhance computational efficiency by leveraging the principles of quantum computing. However, the limitations of current Noisy Intermediate-Scale Quantum (NISQ) devices, such as noise, limited qubit availability, and circuit depth constraints, restrict the implementation of fully quantum models. To address these challenges, this study focuses on the design, implementation, and performance evaluation of hybrid quantum-classical machine learning (HQML) models. The proposed approach integrates parameterized quantum circuits with classical optimization techniques to enable efficient learning within NISQ environments. The study employs standard benchmark datasets, including Iris, Breast Cancer, and MNIST, to evaluate the performance of the hybrid model. The results indicate that the HQML model achieves competitive accuracy on small and medium-sized datasets while maintaining balanced precision, recall, and F1-score. However, performance declines for complex datasets due to hardware limitations and noise effects. Additionally, the hybrid model demonstrates a lower number of parameters compared to classical deep learning models but requires higher training time due to iterative quantum-classical optimization. The findings highlight that hybrid quantum-classical models provide a practical and scalable approach for utilizing quantum computing in the current technological landscape. Although challenges related to noise, scalability, and computational overhead persist, advancements in quantum hardware and algorithm design are expected to improve performance. This study contributes to the growing field of quantum machine learning by providing a systematic framework for evaluating hybrid models on NISQ devices and identifying key areas for future research.