The problem of the neural network optimization is local minima and flat areas. According to quantum-inspired methods, quantum mechanics, superposition, entanglement and interference are inspirational in order to possibly surpass these constraints in a more efficient manner. Variational quantum algorithms use parameterized quantum circuits parameterized quantum circuits (ansatz) to optimize weights. Quantum kernel methods also take advantage of quantum embeddings in order to transform features better. Hybrid quantum-classical systems incorporate quantum-inspired processing with already known reliability of optimization. There are, however, serious weaknesses that limit implementation. There are exponentially decreasing gradients due to the barren plateau phenomenon that makes it hard to train at scale. The modern quantum machines have a 0.1-1% error and a microsecond coherence time. The overheads in state preparation, the cost of measurement, circuit depth, and poor qubit connectivity are still impediments. The quantum-inspired classical algorithms, which include the tensor networks and optimization heuristics and run-on standard computers, are the most effective in the near future. These come with small advances in certain areas without involving quantum hardware. Although both quantum kernel methods and variational approaches show theoretical potential, the advantages are still small (relative to the advantages of optimized classical methods). Recent evaluations show that quantum benefits are more constrained than originally claimed them to be. Real quantum applications benefits in neural network optimization may only happen 10-20 years ahead, notwithstanding failure resistant quantum hardware and algorithm developments.
The problem of the neural network optimization is local minima and flat areas. According to quantum-inspired methods, quantum mechanics, superposition, entanglement and interference are inspirational in order to possibly surpass these constraints in a more efficient manner. Variational quantum algorithms use parameterized quantum circuits parameterized quantum circuits (ansatz) to optimize weights. Quantum kernel methods also take advantage of quantum embeddings in order to transform features better. Hybrid quantum-classical systems incorporate quantum-inspired processing with already known reliability of optimization. There are, however, serious weaknesses that limit implementation. There are exponentially decreasing gradients due to the barren plateau phenomenon that makes it hard to train at scale. The modern quantum machines have a 0.1-1% error and a microsecond coherence time. The overheads in state preparation, the cost of measurement, circuit depth, and poor qubit connectivity are still impediments. The quantum-inspired classical algorithms, which include the tensor networks and optimization heuristics and run-on standard computers, are the most effective in the near future. These come with small advances in certain areas without involving quantum hardware. Although both quantum kernel methods and variational approaches show theoretical potential, the advantages are still small (relative to the advantages of optimized classical methods). Recent evaluations show that quantum benefits are more constrained than originally claimed them to be. Real quantum applications benefits in neural network optimization may only happen 10-20 years ahead, notwithstanding failure resistant quantum hardware and algorithm developments.
Quantum computing offers new algorithmic primitives—superposition, entanglement, and interference—that can accelerate or qualitatively change parts of the machine-learning pipeline. This article surveys optimization of neural networks using quantum techniques, focusing on three avenues: (i) quantum-accelerated linear algebra and sampling to speed up gradient and Hessian-vector computations; (ii) hybrid variational algorithms where parameterized quantum circuits (PQCs) act as feature maps or layers within classical networks; and (iii) quantum-aware optimizers such as the quantum natural gradient (QNG) that respect the geometry of quantum states. We synthesize theoretical results with NISQ-era constraints (noise, barren plateaus, trainability), propose design patterns for end-to-end systems, and present an illustrative comparison of convergence between classical SGD and a hybrid QNG setup. The analysis indicates that, for structured data and appropriately shallow, problem-matched ansätze, hybrid methods can improve sample efficiency and generalization while remaining hardware-feasible.
Computer vision is confronted with increasing computational bottlenecks and memory requirements hard to scale by normal convolutional neural networks. Quantum-inspired architectures are inspired by quantum mechanics, superposition, entanglement as well as interference to redesign visual information processing in a more efficient way. Quantum convolutional neural networks are one of the biggest improvements as they apply parameterized quantum circuits to explore several input states at a time. Quantum-inspired pruning algorithms have lowered the processing time, and quantum optical neural networks have used the wave nature of light to have parallel characteristics of features. Tensor network architectures are based on quantum physics and can be used to convert high-dimensional image data into information-rich elements and model multi-scale interactions. Hybrid quantum-classical systems can be described as using quantum-inspired processing and the reliability of established deep learning. Attention systems ensure that quantum circuits are dedicated to informative parts of an image, whereas knowledge transfer of classical models stabilizes quantum training. Nonetheless, basic constraints limit applications: the barren plateau problem, measurement overhead, preparation complexity of states and decoherence are all major challenges. The existing applications include quantum-inspired classical algorithms to physical hardware experiments. Thorough benchmarking demonstrates that the classical approaches can be much more effective than the quantum ones. Frameworks such as PennyLane extend accessibility, although best practice and careful consideration of the architecture involving the integration of quantum-inspired and classical computing is critical to realistic computer vision systems.
Quantum Neural Networks (QNNs) represent a compelling convergence of quantum mechanics and machine learning, yet their practical deployment remains constrained by noise, limited qubit counts, and the cost of full quantum execution. Hybrid quantum-classical (HQC) training offers a pragmatic path forward: parameterized quantum circuits (PQCs) process information in exponentially large Hilbert spaces while classical optimizers update parameters via gradient methods accessible on today's hardware. We present a modular HQC training framework, formalising the parameter-shift rule for hardware-compatible gradient estimation, characterising the barren-plateau phenomenon through a variance-decay analysis, and introducing noise-aware training strategies for NISQ devices. Empirical results from state-vector and shot-based simulation confirm measurable quantum advantage on quantum-structured tasks, with the phase classification benchmark improving +12.1% over a classical MLP baseline. The accompanying open-source library provides a clean abstraction between quantum simulation and classical optimisation, serving as a foundation for near-term quantum machine learning research.
This chapter offers a clear and accessible introduction to the field of quantum-inspired neural computing. This area combines ideas from quantum mechanics with traditional neural network models to create new possibilities in machine learning and optimization metaheuristic algorithms. Unlike actual quantum computing, quantum-inspired approaches work on classical computers but borrow key concepts like superposition, entanglement, and probabilistic behaviour to improve how neural networks learn and process information. The study begins by explaining why researchers are interested in using quantum principles in neural networks. It then introduces the basic mathematical ideas behind these concepts, such as quantum states and transformations, and shows how they can be used to design more powerful and flexible learning systems. It focuses on discussing current models, outlining the distinctions between quantum-inspired and true quantum systems, and evaluating the potential benefits and challenges of this approach. In addition, Quantum-inspired neural computing introduces a novel framework that bridges classical artificial intelligence with principles derived from quantum mechanics. By simulating quantum behaviours on classical hardware, it opens new avenues for developing more adaptive and efficient learning models. This emerging approach offers promising advantages in areas such as optimization, parallel processing, and high-dimensional data representation. Finally, despite its potential, the field faces notable limitations and challenges. These include the lack of limited theoretical formalization, and difficulties in scaling models for complex real-world applications. Moreover, distinguishing genuine quantum-inspired advantages from conservative algorithmic improvements remains an current research apprehension.
Computational methods are central to modern physics, yet many problems, especially those involving Quantum Many-Body Systems (QMBSs), remain challenging at scale. The core difficulty of simulating QMBSs is the exponential growth of the solution space with system size. This renders exact treatments intractable and pushes approximate methods to their limits when tackling two- and higher-dimensional systems and long-time dynamics. Quantum computers offer a quantum-native platform for representing and manipulating such systems. Recent algorithmic and technological advancements have enabled experiments on quantum processors in the quantum utility regime, a scale at which exact classical reproduction is no longer feasible. This represents the first step towards realizing quantum advantage, where quantum computers solve specific, practically relevant problems more efficiently than any classical approach. While advancing towards the goal of quantum advantage, useful computations on quantum processors are expected to be realised through hybrid quantum-classical algorithms, which combine quantum experiments and classical computational resources. A prominent example are variational quantum algorithms, where a Parametrized Quantum Circuit (PQC) prepares a trial quantum state whose parameters are iteratively updated by a classical optimisation routine to minimize a target cost function (e.g., the energy of a target Hamiltonian). However, the optimisation of such PQCs is affected by trainability issues, such as barren plateaus in the parameter landscape, which can render the optimisation increasingly difficult for larger system sizes. This motivates the development of novel hybrid approaches overcoming the limits of PQCs. In this thesis, we introduce a new class of approaches based on hybrid Tensor Networks (TNs). A hybrid TN is obtained by integrating quantum states prepared on a quantum processor within TNs -- one of the state-of-the-art approaches for simulating quantum systems. We first show how hybrid TNs can be used for ground-state searches within a variational setting. Then, we further extend the framework to non-variational hybrid TN ansätze for which the quantum tensors are prepared via quantum annealing and subsequently post-processed by classical TNs. In the context of quantum machine learning, which also relies on PQCs, we further investigate heuristic best practices that mitigate the same exponential concentration effects in kernel-based models for anomaly detection. Another class of hybrid algorithms are quantum error-mitigation workflows, where classical post-processing is used to reconstruct expectation values from noise-affected circuit executions. Such methods generally feature a trade-off between the bias and the variance: the price to pay for mitigating noise in a bias-free fashion is that the number of measurements usually grows exponentially with the depth of the circuit in order to achieve a fixed accuracy. In this thesis, we develop a low-resource error-mitigation strategy that reduces the measurement overhead in practical digital Hamiltonian-simulation workflows. We apply this method to Trotterized dynamics in a lattice-gauge-theory model, enabling the extraction of expectation values with improved accuracy at time-scales that allow the observation of post-collision scattering dynamics.
The convergence of machine learning (ML) and quantum computing is quickly becoming a game-changing new frontier in computational science. The most intriguing area of overlap may be quantum optimization, which seeks to reduce the exponentially increasing complexity and computational cost of ML algorithms. As they grow larger and more complicated, traditional optimization methods, particularly in high-dimensional and non-convex space, will inevitably hit performance limits. Quantum optimization is the whole new paradigm that leverages quantum mechanical effects like superposition, entanglement, and tunnelling to explore solution spaces more efficiently. The chapter outlines the theory, practice, and potential of hybrid quantum-classical optimization algorithms for machine learning. The most brilliant research direction in the current NISQ (noisy intermediate-scale quantum) era is mixed systems leveraging classical computing capability augmented by quantum capacity. In such designs, computationally intensive subroutines like optimization for global optima or escape from local minima are left to quantum processors and data preprocessing, iterative refinement, and model testing are performed by classical processors. We start by defining the fundamental principles of quantum computing and acquainting readers with the fundamentals like qubits, quantum gates, and quantum circuits. These are the building blocks for quantum algorithms, which hopefully can be utilized for optimization, for example, the QAOA (quantum approximate optimization algorithm), the VQE (variational quantum Eigensolver), and quantum annealing. They all build to optimize the problems in some way differently: QAOA through parameterized quantum circuits, VQE through approximations of ground states of the Hamiltonians, and quantum annealing through quantum evolution to low-energy solutions. We then form a loop between these quantum algorithms and regular machine learning tasks. Optimization impacts virtually all ML phases, from training neural networks, where one reduces loss functions; feature selection, where one aims to discover the most relevant subset of input variables; and hyperparameter optimization, which often involves expensive search procedures over extremely large combinatorial spaces. Quantum optimization techniques can therefore, in principle, accelerate such procedures through computational complexity reduction and enhancing solutions over challenging landscapes. Realistic simulations and case studies emphasize the degree to which hybrid quantum-classical algorithms have been employed in solving ML problems, that is, QSVMs, quantum-enhanced clustering, and quantum reinforcement learning. Despite their experimental nature, these applications already show encouraging results in terms of improved performance metrics as well as reduction in time-to-solution compared to classical-only solutions. Notwithstanding that, this new field is not bereft of real challenges. Quantum hardware suffers from hard limits on qubit fidelity, decoherence, and scalability in the current times. Furthermore, quantum circuit integration into broad ML pipelines requires novel architectures and software platforms. As a counter to those issues, this chapter surveys recent advances in quantum programming languages, simulators, and hybrid platforms like PennyLane, Qiskit, and TensorFlow Quantum. We conclude by looking to the future possibility that quantum optimization will revolutionize the machine learning landscape. As hardware improves and algorithmic complexity increases, the possibility of quantum-powered learning systems solving hard problems becomes increasingly accessible. From speeding up deep network training to enabling new types of unsupervised learning, quantum optimization holds the potential to recast computational tractability in machine learning. This chapter is an all-encompassing introduction and state-of-the-art work for students, researchers, and practitioners interested in using quantum optimization for practical ML applications. It sets the foundation for understanding how to pursue hybrid approaches (how they may be applied today in the real world and bracing oneself for disruption in the future).