Noisy, intermediate-scale quantum (NISQ) computing devices have become an industrial reality in the last few years, and cloud-based interfaces to these devices are enabling the exploration of near-term quantum computing on a range of problems.As NISQ devices are too noisy for many of the algorithms with a known quantum advantage, discovering impactful applications for near-term devices is the subject of intense research interest.We explore a quantum-assisted machine learning (QAML) workflow using NISQ devices through the perspective of tensor networks (TNs), which offer a robust platform for designing resource-efficient and expressive machine learning models to be dispatched on quantum devices.In particular, we lay out a framework for designing and optimizing TN-based QAML models using classical techniques, and then compiling these models to be run on quantum hardware, with demonstrations for generative matrix product state (MPS) models.We put forth a generalized canonical form for MPS models that aids in compilation to quantum devices, and demonstrate greedy heuristics for compiling with a given topology and gate set that outperforms known generic methods in terms of the number of entangling gates, e.g., CNOTs, in some cases by an order of magnitude.We present an exactly solvable benchmark problem for assessing the performance of MPS QAML models and also present an application for the canonical MNIST handwritten digit dataset.The impacts of hardware topology and day-to-day experimental noise fluctuations on model performance are explored by analyzing both raw experimental counts and statistical divergences of inferred distributions.We also present parametric studies of depolarization and readout noise impacts on model performance using hardware simulators.
Noisy, intermediate-scale quantum (NISQ) computing devices have become an industrial reality in the last few years, and cloud-based interfaces to these devices are enabling the exploration of near-term quantum computing on a range of problems.As NISQ devices are too noisy for many of the algorithms with a known quantum advantage, discovering impactful applications for near-term devices is the subject of intense research interest.We explore a quantum-assisted machine learning (QAML) workflow using NISQ devices through the perspective of tensor networks (TNs), which offer a robust platform for designing resource-efficient and expressive machine learning models to be dispatched on quantum devices.In particular, we lay out a framework for designing and optimizing TN-based QAML models using classical techniques, and then compiling these models to be run on quantum hardware, with demonstrations for generative matrix product state (MPS) models.We put forth a generalized canonical form for MPS models that aids in compilation to quantum devices, and demonstrate greedy heuristics for compiling with a given topology and gate set that outperforms known generic methods in terms of the number of entangling gates, e.g., CNOTs, in some cases by an order of magnitude.We present an exactly solvable benchmark problem for assessing the performance of MPS QAML models and also present an application for the canonical MNIST handwritten digit dataset.The impacts of hardware topology and day-to-day experimental noise fluctuations on model performance are explored by analyzing both raw experimental counts and statistical divergences of inferred distributions.We also present parametric studies of depolarization and readout noise impacts on model performance using hardware simulators.
The development of near-term quantum computers, referred to as Noisy Intermediate-Scale Quantum (NISQ) computers, has progressed rapidly in the past few years resulting in several quantum computers which vary in their underlying technology and physical constraints. The performance of these computers also varies from one quantum algorithm to another. To enable efficient selection of the quantum computer that provides the highest output fidelity for a given application, an accurate noise modeling of each quantum hardware is required. However, noise modeling for a given application is a complex problem because of the unknown interaction between the quantum circuit parameters and the noise parameters of NISQ devices. We propose the use of Machine Learning (ML) to model the performance of different quantum computers at the application level. The ML models predict the output fidelity of the quantum application executed on different quantum computers given their publicly available physical constraints. We use a diverse training dataset to cover the key features for application-level benchmarking of the quantum hardware. Our results obtained from different superconducting quantum devices show that our proposed ML models enable cost-effective quantum computer selection for different quantum applications with different fidelity metrics.
Abstract Machine learning is a promising application of quantum computing, but challenges remain for implementation today because near-term devices have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks, that could already have benefits with such near-term devices. The result is a unified framework in which classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes in which, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a hybrid quantum-classical optimization procedure that could be carried out on quantum hardware today, and testing the noise resilience of the trained model.
Hybridizing machine learning (ML) with quantum computing has become an attractive strategy to increase computational power on Noisy Intermediate Scale Quantum (NISQ) devices. Although these can be potentially quantum advantage devices, their qubit numbers and noise are bounded and there are challenges when it comes to practical quantum circuit realization. This work concentrates on the creation of optimized quantum circuits via ML-based strategies, to enhance the performance of the circuits, to reduce the error rate and to accommodate the particular noise profile of the hardware of NISQ devices. The resulting suboptimal mappings with little or no consideration of noise and hardware topology in traditional quantum compilers can ruin the fidelity of quantum algorithm. Leveraging machine learning, and specifically reinforcement and supervised learning methods, our method learns to optimize compilation strategy for specific quantum hardware architecture. The paper proposes a framework that uses machine learning models to predict qubit mappings, gate decompositions, and transpilation paths that minimize gate depth and error accumulation. We also investigate transfer learning methods for propagating the learned compilation strategies to novel NISQ machines. Such methods are empirically validated on both simulated and real quantum hardware backends, providing evidence of circuit depth, execution time and error reductions. The results show that ML-assisted compilation can achieve better success probabilities for benchmark quantum algorithms like VQE and QAOA than conventional compilers. Furthermore, the work examines the interpretability of ML models providing hardware-aware optimization recommendations and understanding the noise patterns and methods of error correction. Our work highlights the key role of ML for transferring between theoretical quantum algorithms and their practical NISQ implementations. This integration boosts the immediate applicability of existing quantum devices and provides a basis for adaptive and scalable likelihood-based compilation for the era of fault-tolerant quantum computation. Our results motivate further investigation of hybrid classical-quantum workflows, in which ML iteratively improves compilation in accordance with changing hardware noise and capabilities. By improving quantum circuit compilation onNISQ computers, this work is taking steps toward the realization of quantum advantage in application scenarios such as optimization, cryptography, and quantum simulation without needing to wait for fully fault-tolerant large-scale quantum computers.
As medium-scale quantum computers progress, the application of quantum algorithms across diverse fields like simulating physical systems, chemistry, optimization, and cryptography becomes more prevalent. However, these quantum computers, known as Noisy Intermediate Scale Quantum (NISQ), are susceptible to noise, prompting the search for applications that can capitalize on quantum advantage without extensive error correction procedures. Since, Machine Learning (ML), particularly Deep Learning (DL), faces challenges due to resource-intensive training and algorithmic opacity. Therefore, this study explores the intersection of quantum computing and ML, focusing on computer vision tasks. Specifically, it evaluates the effectiveness of hybrid quantum-classical algorithms, such as the data re-uploading scheme and the patch Generative Adversarial Networks (GAN) model, on small-scale quantum devices. Through practical implementation and testing, the study reveals comparable or superior performance of these algorithms compared to classical counterparts, highlighting the potential of leveraging quantum algorithms in ML tasks.
Abstract The arrival of noisy intermediate-scale quantum (NISQ) devices defines an era in which quantum utility is fundamentally constrained by finite coherence times, limited qubit counts, gate infidelities, restricted connectivity, and measurement noise. Within this regime, hybrid quantum-classical frameworks have emerged as the dominant operational paradigm, particularly for quantum machine learning (QML). This review identifies a fundamental trade-off between expressivity, trainability, and noise resilience that governs the performance and scalability of NISQ-era QML systems. To contextualize these challenges, we introduce the resource-constrained iterative routing framework, a hardware-aware conceptual architecture that integrates topology-aware classical compression and distributed quantum orchestration to maintain circuit depths within device-dependent limits while routing representations toward symmetry-constrained Hilbert subspaces to mitigate noise-induced barren plateaus. Furthermore, we shift the discussion of quantum advantage away from asymptotic fault-tolerant complexity toward the notion of operational NISQ advantage based on finite-resource scaling, trainability preservation, and sampling complexity. We evaluate the practical resource efficiency of variational quantum algorithms, quantum kernel methods, and quantum neural networks across superconducting, trapped-ion, neutral-atom, and photonic platforms. The review also examines reproducibility challenges, emphasizing benchmarking against optimized classical baselines, and discusses strategies for managing the sampling overhead of error mitigation alongside distributed execution and quantum circuit compilation. Ultimately, NISQ in Practice positions hybrid QML as a physically constrained computational paradigm while outlining a pathway from contemporary noisy workflows toward early fault-tolerant quantum architectures.
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 .