High dimensional data in machine learning (ML) however is not yet fully tapped due curse of dimensionality, sensitivity to local minima and computational burden. In this paper, we will introduce and test a new QIGS algorithm for such problems on classical computer. The efficiency of QIGS is demonstrated to be benefiting from the amplitude–phase hybrid probabilistic encoding and gradient-assisted update for optimizing entangling operations, which can effectively balance global exploration and local exploitation. We test this experiment on synthetic benchmark functions (Rastrigin, Rosenbrock, Ackley up to 5,000 dimensions) and real-world data sets (genomic profiles with 20,531 features and BERT-based sentiment embeddings with 768 features). It is also shown that QIGS achieves a classification accuracy of 94.2% on the genomic data (Adam: 91.5%, SGD: 90.7%, PSO: 89.8%) and reduces the number of iterations for convergence by 35–40% compared to fastest baseline on synthetic benchmarks. In addition, on the BERT representations QIGS got a training loss of 0.083 in 120 iterations (vs Adam's loss of 0.091 in 180 iterations). These results establish that QIGS is not only a faster converging algorithm, but also one which produces solutions of higher quality for many problems, thereby making it an accessible segue between classical optimization and the future of quantum-inspired machine learning.
High dimensional data in machine learning (ML) however is not yet fully tapped due curse of dimensionality, sensitivity to local minima and computational burden. In this paper, we will introduce and test a new QIGS algorithm for such problems on classical computer. The efficiency of QIGS is demonstrated to be benefiting from the amplitude–phase hybrid probabilistic encoding and gradient-assisted update for optimizing entangling operations, which can effectively balance global exploration and local exploitation. We test this experiment on synthetic benchmark functions (Rastrigin, Rosenbrock, Ackley up to 5,000 dimensions) and real-world data sets (genomic profiles with 20,531 features and BERT-based sentiment embeddings with 768 features). It is also shown that QIGS achieves a classification accuracy of 94.2% on the genomic data (Adam: 91.5%, SGD: 90.7%, PSO: 89.8%) and reduces the number of iterations for convergence by 35–40% compared to fastest baseline on synthetic benchmarks. In addition, on the BERT representations QIGS got a training loss of 0.083 in 120 iterations (vs Adam's loss of 0.091 in 180 iterations). These results establish that QIGS is not only a faster converging algorithm, but also one which produces solutions of higher quality for many problems, thereby making it an accessible segue between classical optimization and the future of quantum-inspired machine learning.
High-dimensional medical datasets pose a persistent challenge for artificial intelligence because traditional classification algorithms often incur escalating computational costs and reduced predictive accuracy. As healthcare systems generate increasingly complex clinical records, imaging outputs, and genomic profiles, scalable analytic methods that balance precision and efficiency are critical. This study proposes a Quantum-Inspired Optimization (QIO) framework for efficient and accurate classification of high-dimensional healthcare data. Leveraging the exploratory power of variational quantum algorithms, specifically techniques analogous to the Quantum Approximate Optimization Algorithm, the framework integrates quantum-style search strategies with classical computation to achieve global optimization and numerical stability. Publicly available medical datasets with hundreds of features were used to evaluate the approach. Classification models were trained and tested across varying feature dimensionalities, and performance was assessed using accuracy, runtime, and scalability metrics. Empirical results demonstrate that QIO achieves up to 95.4% classification accuracy and reduces computational time by 40% compared with state-of-the-art classical baselines. The method demonstrates stable convergence and clear decision boundaries even as feature dimensionality grows, highlighting its resilience to the curse of dimensionality. These results indicate that QIO can enable fast and reliable healthcare analytics in data-rich clinical environments. Future research may examine domain-specific adaptations, real-time deployment, and integration with emerging quantum hardware to enhance the impact of quantum-inspired artificial intelligence further.
Stochastic Gradient Descent (SGD) is a cornerstone algorithm in training machine learning models, particularly deep neural networks. However, its performance degrades significantly as the dimensionality of the problem increases, a phenomenon known as the "curse of dimensionality." This paper introduces a novel optimization algorithm, Quantum-Inspired Stochastic Gradient Descent (QISGD), designed to mitigate this issue. QISGD draws inspiration from quantum mechanics, specifically the concepts of superposition and interference, to guide the stochastic updates. The algorithm utilizes a probability distribution that mimics a quantum state, enabling it to explore the loss landscape more effectively and potentially achieve faster convergence in high-dimensional spaces. We present a theoretical framework for QISGD and discuss its key components, including the initialization of the quantum state, the generation of stochastic updates, and the implementation of interference effects. The core idea is to treat the parameters of the model as a quantum state, allowing for a more nuanced exploration of the loss function. We analyze the algorithm's convergence properties and provide insights into its potential advantages over traditional SGD. The primary goal is to demonstrate that quantum-inspired techniques can provide a robust and efficient solution for high-dimensional optimization problems.
The curse of dimensionality in high-dimensional optimization: It is inherently seen that the dimensionality of feature space presents a fundamental challenge to high-dimensional optimization: as dimensionality increases, feature space becomes computationally inefficient, overfitted and model interpretability declines, thus requiring highly robust sparsity-based solutions. To find a solution to these problems, a new quantum-inspired framework of sparse optimization is proposed in this study, which combines probabilistic Q-bit representation and L1-regularized optimization to efficiently consider large solution spaces but with a sparsity constraint. The suggested method builds on quantum-inspired search algorithms such as initiation by superposition and rotation gate updates to the search to improved exploration and exploitation ratio, leading to a better convergence process. Experimental analyses show that the framework produces better optimization accuracy, indicated by much lower Mean Squared Error (MSE) and convergence rates than classical and met heuristic baselines, with the framework also having a higher level of sparsity in the solution space. These results highlight the effectiveness of the proposed method in handling high-dimensional problems, making it particularly suitable for applications in signal processing, machine learning-based feature selection, and large-scale scientific computing tasks.
The training of large-scale machine learning models presents significant computational challenges, primarily due to the inherent complexity of optimization algorithms like stochastic gradient descent (SGD) and its variants. These algorithms often struggle with convergence speed, getting trapped in local minima, and the ability to effectively explore the vast solution space. This paper investigates the potential of quantum-inspired optimization techniques to address these limitations. Specifically, we explore the application of quantum annealing and variational quantum eigensolver (VQE) approaches to accelerate the training and optimization process of large-scale machine learning models. Our core claim is that by mapping the optimization problem to a quantum system, we can leverage quantum computation to overcome the computational bottlenecks associated with classical optimization methods. We propose a framework where the objective function of the machine learning model is translated into a Hamiltonian for a quantum annealer or the cost function for a VQE, enabling a quantum-inspired solution. The results, while theoretical in this initial exploration, demonstrate a potential pathway for significantly reducing training times and improving the overall performance of large-scale machine learning models. Further research is needed to develop efficient hybrid quantum-classical algorithms and explore the practical limitations of this approach.
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).
Quantum computing has inspired new ways to represent and process data, offering perspectives that can also benefit classical machine learning. In this work, we investigate how quantum-inspired data representations can be integrated into classical machine learning classifiers such as Logistic Regression, Support Vector Machines, and Naive Bayes for binary classification tasks. The proposed approach utilizes a simple amplitude-based encoding that normalizes feature vectors and incorporates phase-like transformations, assisting classical models to capture complex interactions and patterns in the data similar to quantum information processing. We evaluate this approach on both synthetic and three other benchmark datasets, comparing standard and quantum-inspired data representations. The results highlights that the quantum-inspired data encoding often matches or improves classifier performance in terms of accuracy, F1-Score, and precision. Additionally, the normalized encoding provides a more structured representation of the data, which can help with interpretability and visualization. These results highlight the potential of quantum-inspired transformations as a practical and effective tool for improving classical machine learning pipelines without requirement of quantum hardware.