In the current noisy intermediate-scale quantum (NISQ)era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parameterized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parameterized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a back groundin probability and linear algebra. It first describes the necessary background, concepts, and tools necessary to describe quantum operations and measurements. Then,it covers parameterized quantum circuits, the variation alquantum eigensolver, as well as unsupervised and supervised quantum machine learning formulations.
In the current noisy intermediate-scale quantum (NISQ)era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parameterized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parameterized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a back groundin probability and linear algebra. It first describes the necessary background, concepts, and tools necessary to describe quantum operations and measurements. Then,it covers parameterized quantum circuits, the variation alquantum eigensolver, as well as unsupervised and supervised quantum machine learning formulations.
In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parametrized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parametrized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra. It first describes the necessary background, concepts, and tools necessary to describe quantum operations and measurements. Then, it covers parametrized quantum circuits, the variational quantum eigensolver, as well as unsupervised and supervised quantum machine learning formulations.
This monograph is motivated by a number of recent developments that appear to define a possible new role for researchers with an engineering profile. First, there are now several software libraries – such as IBM’s Qiskit, Google’s Cirq, and Xanadu’s PennyLane – that make programming quantum algorithms more accessible, while also providing cloud-based access to actual quantum computers. Second, a new framework is emerging for programming quantum algorithms to be run on current quantum hardware: quantum machine learning. In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parametrized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parametrized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra. It first describes the background, concepts, and tools necessary to describe quantum operations and measurements. Then, it covers parametrized quantum circuits, the variational quantum eigensolver, as well as unsupervised and supervised quantum machine learning formulations.
Parameterized quantum circuits (PQC) have emerged as a quantum analogue of deep neural networks and can be trained for discriminative or generative tasks and can be trained with gradient-based optimization on near-term quantum devices [1], [2], [3]. In the current era of quantum computing, known as the noisy intermediate scale quantum (NISQ) era [4], these devices contain a moderate number of qubits (< 100), and algorithmic performance is strongly impacted by hardware noise. Additionally, the training of PQCs are hybrid algorithms, in which the computational workflow is split between quantum and classical computing platforms.
Quantum computing has emerged as one of the most influential paradigms capable of transforming computational processes that struggle under classical limitations. In recent years, hybrid quantum–classical algorithms have gained significant attention for their ability to leverage the strengths of both architectures, especially within the Noisy Intermediate-Scale Quantum (NISQ) era. This research paper explores a quantum-enhanced optimization framework designed to improve machine learning model performance through parameterized quantum circuits (PQCs). The goal of this study is to provide a practical, scalable approach that can be integrated into existing machine learning workflows without requiring fully developed fault-tolerant quantum hardware. The proposed framework uses classical preprocessing to encode data into quantum states, followed by quantum transformations that explore richer feature spaces due to quantum superposition and entanglement. A classical optimizer then updates the quantum circuit parameters based on measurement results, forming an end-to-end feedback loop. This hybrid model aims to demonstrate improved optimization efficiency, reduction in loss-function plateaus, and better generalization for specific ML tasks involving small to medium-sized datasets. This paper provides a comprehensive investigation of methodology, literature background, and experimental reasoning with statistical analysis, along with conceptual diagrams illustrating system architecture and circuit layouts. The outcomes further strengthen the viability of hybrid quantum–classical computation as a promising direction for advanced machine learning systems.
Supervised quantum machine learning (QML) applies quantum resources to classical tasks such as classification and regression. We examine methods feasible on current Noisy Intermediate-Scale Quantum (NISQ) hardware, including variational (parameterized) quantum circuits (VQCs/PQCs), quantum kernel methods, data encodings, and hybrid quantumclassical workflows, and we summarize recent experiments in quantum-native and low-data regimes. We clarify theory on generalization and trainability and identify practical blockers: noise and depth limits, encoding overheads, missing standardized benchmarks, and unsettled conditions for advantage. Our main contribution is a ten-year outlook from 2025 to 2035 that maps hardware progress, error mitigation, benchmarking, quantum data generation, federated learning & privacy, and AutoQML to potential enterprise use cases. The roadmap draws on a qualitative synthesis of publication trends, milestone experiments, prior surveys, and practitioner insights. Near-term gains are most likely in niche applications and hybrid deployments; broader adoption depends on scalable error-corrected hardware, shared benchmarks, interdisciplinary training, and calibrated expectations.
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 .