A computational model of adiabatic evolutionary quantum system (or AEQS, pronounced "eeh-ks") was introduced in [Yamakami,2022] as a sort of quantum annealing and its underlying input-driven Hamiltonians are generated quantum-algorithmically by various forms of quantum automata families (including 1qqaf's). We study an efficient way to accomplish certain machine learning tasks by training these AEQSs quantumly. When AEQSs are controlled by 1qqaf's, it suffices in essence to find an optimal 1qqaf that approximately solves a target relational problem. For this purpose, we develop a basic idea of approximately utilizing well-known quantum algorithms for quantum counting, quantum amplitude estimation, and quantum approximation. We then provide a rough estimation of the efficiency of our quantum learning algorithms for AEQSs.
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(A4, 11pt, 10 pages) A preliminary report was presented at the 22nd International Conference on Unconventional Computation and Natural Computation (UCNC 2025), Nice, France, September 1--5, 2025
A computational model of adiabatic evolutionary quantum system (or AEQS, pronounced "eeh-ks") was introduced in [Yamakami,2022] as a sort of quantum annealing and its underlying input-driven Hamiltonians are generated quantum-algorithmically by various forms of quantum automata families (including 1qqaf's). We study an efficient way to accomplish certain machine learning tasks by training these AEQSs quantumly. When AEQSs are controlled by 1qqaf's, it suffices in essence to find an optimal 1qqaf that approximately solves a target relational problem. For this purpose, we develop a basic idea of approximately utilizing well-known quantum algorithms for quantum counting, quantum amplitude estimation, and quantum approximation. We then provide a rough estimation of the efficiency of our quantum learning algorithms for AEQSs.
Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing algorithm. Adiabatic evolution of quantum systems have been studied as a potential means that physically realizes quantum computation. Up to now, all the research on adiabatic quantum systems has dealt with polynomial time-bounded computation and little attention has been paid to, for instance, adiabatic quantum systems consuming only constant memory space. Such quantum systems can be modeled in a form similar to quantum finite automata. This exposition dares to ask a bold question of how to make adiabatic quantum computation fit into the rapidly progressing framework of quantum automata theory. As our answer to this eminent but profound question, we first lay out a fundamental platform to carry out adiabatic evolutionary quantum systems (AEQSs) with limited computational resources (in size, energy, spectral gap, etc.) and then establish how to construct such AEQSs by operating suitable families of quantum finite automata. We further explore fundamental structural properties of decision problems (as well as promise problems) solved quickly by the appropriately constructed AEQSs.
Variational Quantum Classifiers (VQCs) stand out as one of the most popular classification approaches within the Quantum Machine Learning (QML) community. They serve as an accessible entry point for newcomers to QML world, particularly those with a background in classical machine learning, due to their workflow similarity to conventional neural networks. In essence, VQCs boast a layered structure conducive to training via a classical optimizer. Recently, Evolutionary Algorithms (EAs) have emerged as a suitable methodology for this training goal. However, current quantum tools provide implementations for various gradient-based optimizers and just one EA tailored for VQC training. Moreover, it is important to note that access to this toolset remains largely confined to expert users. This highlights the necessity for platforms that facilitate the utilization of EAs for VQC training by non-experts in quantum or evolutionary computing. This work introduces a web application designed to implement quantum classifiers to be trained on user-supplied datasets by means of a set of EAs, which can be customized by users. The capabilities of the proposed web application are shown in the experimental session, where a VQC is trained to classify a well-known dataset using a variety of EAs.
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).
This study examines the relationship between machine learning and quantum computing, emphasizing the potential benefits of quantum algorithms for classification, optimization and clustering problems. Through a comprehensive literature review of peer-reviewed journal articles and preprints from 2014 to 2024, Quantum K-Means Clustering, Quantum Support Vector Machines (QSVMs), and Quantum Approximate Optimization Algorithms (QAOA) and Quantum Annealing are among the important quantum algorithms identified in the study. Although the theoretical potential of these algorithms is substantial, present hardware constraints, such as noise, de-coherence, and qubit count limitations, make practical implementation difficult. The review also highlights the ongoing challenges in quantum error correction and the nascent stage of quantum hardware development, which prevent large-scale machine learning tasks from being fully realized. Even so, hybrid quantum-classical models are a plausible route forward for near-term utility. These results suggest that to leverage quantum machine learning to its full potential, further progress in quantum hardware, error correction codes, and hybrid algorithms is required. Future studies should focus on designing more robust quantum error correction methods, further developing hybrid systems and exploring new areas of machine learning, such as reinforcement learning and generative models.
We develop a hybrid quantum-classical algorithm to solve an optimal population transfer problem for a molecule subject to a laser pulse. The evolution of the molecular wave function under the laser pulse is simulated on a quantum computer, while the optimal pulse is iteratively shaped via a machine learning (evolutionary) algorithm. A method to encode on the quantum computer the n-electrons wave function is discussed, the circuits accomplishing its quantum simulation are derived and the scalability in terms of number of operations is discussed. Performance on noisy intermediate-scale quantum devices (IBM Q X2) is provided to assess the current technological gap. Furthermore the hybrid algorithm is tested on a quantum emulator to compare performance of the evolutionary algorithm with standard ones. Our results show that such algorithms are able to outperform the optimization with a downhill simplex method and provide performance comparable to more advanced (but quantum-computer unfriendly) algorithms such as Rabitz's or gradient-based optimization.