Abstract Decades of exponential scaling in high-performance computing (HPC) efficiency is coming to an end. Transistor-based logic in complementary metal-oxide semiconductor (CMOS) technology is approaching physical limits beyond which further miniaturization will be impossible. Future HPC efficiency gains will necessarily rely on new technologies and paradigms of computing. The Ising model shows particular promise as a future framework for highly energy-efficient computation. Ising systems are able to operate at energies approaching thermodynamic limits for energy consumption of computation. Ising systems can function as both logic and memory. Thus, they have the potential to significantly reduce energy costs inherent to CMOS computing by eliminating costly data movement. The challenge in creating Ising-based hardware is in optimizing useful circuits that produce correct results on fundamentally nondeterministic hardware. The contribution of this paper is a novel machine learning approach, a combination of deep neural networks and random forests, for efficiently solving optimization problems that minimize sources of error in the Ising model. In addition, we provide a process to express a Boltzmann probability optimization problem as a supervised machine learning problem.
Abstract Decades of exponential scaling in high-performance computing (HPC) efficiency is coming to an end. Transistor-based logic in complementary metal-oxide semiconductor (CMOS) technology is approaching physical limits beyond which further miniaturization will be impossible. Future HPC efficiency gains will necessarily rely on new technologies and paradigms of computing. The Ising model shows particular promise as a future framework for highly energy-efficient computation. Ising systems are able to operate at energies approaching thermodynamic limits for energy consumption of computation. Ising systems can function as both logic and memory. Thus, they have the potential to significantly reduce energy costs inherent to CMOS computing by eliminating costly data movement. The challenge in creating Ising-based hardware is in optimizing useful circuits that produce correct results on fundamentally nondeterministic hardware. The contribution of this paper is a novel machine learning approach, a combination of deep neural networks and random forests, for efficiently solving optimization problems that minimize sources of error in the Ising model. In addition, we provide a process to express a Boltzmann probability optimization problem as a supervised machine learning problem.
Ising machines have received growing interest as efficient and hardware-friendly solvers for combinatorial optimization problems (COPs). They search for the absolute or approximate ground states of the Ising model with a proper annealing process. In contrast to Ising machines built with superconductive or optical circuits, complementary metal-oxide-semiconductor (CMOS) Ising machines offer inexpensive fabrication, high scalability, and easy integration with mainstream semiconductor chips. As low-energy and CMOS-compatible emerging technologies, spintronics and phase-transition devices offer functionalities that can enhance the scalability and sampling performance of Ising machines. In this article, we survey various approaches in the process flow for solving COPs using CMOS, hybrid CMOS-spintronic, and phase-transition devices. First, the methods for formulating COPs as Ising problems and embedding Ising formulations to the topology of the Ising machine are reviewed. Then, Ising machines are classified by their underlying operational principles and reviewed from a perspective of hardware implementation. CMOS solutions are advantageous with denser connectivity, whereas hybrid CMOS-spintronic and phase-transition device-based solutions show great potential in energy efficiency and high performance. Finally, the challenges and prospects are discussed for the Ising formulation, embedding process, and implementation of Ising machines.
Combinatorial optimization problems are difficult to solve due to the space explosion in an exhaustive search. Using Ising model-based solvers can efficiently find near-optimal solutions by minimizing the energy of a nonlinear Hamiltonian system. In contrast to Ising machines based on quantum mechanics, classical Ising machines using conventional technologies, such as the complementary metal-oxide-semiconductor, offer efficient implementations with competitive performance. In this paper, we briefly review recently developed simulation algorithms of classical Ising machines. These algorithms are classified by considering various inherent mechanisms in the simulation of physical phenomena. Then, strategies to improve the simulation efficiency are discussed by generalizing their characteristics and behaviours. These simulation algorithms are key for improving the efficiency of classical Ising machines in solving combinatorial optimization problems.
Analog Ising machines (AIMs) have emerged as a promising paradigm for combinatorial optimization, utilizing physical dynamics to solve Ising problems with high energy efficiency. However, the performance of traditional optimization and sampling algorithms on these platforms is often limited by inherent measurement noise. We introduce BRAIN (Boltzmann Reinforcement for Analog Ising Networks), a distribution learning framework that utilizes variational reinforcement learning to approximate the Boltzmann distribution. By shifting from state-by-state sampling to aggregating information across multiple noisy measurements, BRAIN is resilient to Gaussian noise characteristic of AIMs. We evaluate BRAIN across diverse combinatorial topologies, including the Curie-Weiss and 2D nearest-neighbor Ising systems. We find that under realistic 3\% Gaussian measurement noise, BRAIN maintains 98\% ground state fidelity, whereas Markov Chain Monte Carlo (MCMC) methods degrade to 51\% fidelity. Furthermore, BRAIN reaches the MCMC-equivalent solution up to 192x faster under these conditions. BRAIN exhibits O(N1.55) scaling up to 65,536 spins and maintains robustness against severe measurement uncertainty up to 40\%. Beyond ground state optimization, BRAIN accurately captures thermodynamic phase transitions and metastable states, providing a scalable and noise-resilient method for utilizing analog computing architectures in complex optimizations.
Conventionally, the study of phases in statistical mechan- ics is performed with the help of random sampling tools. Among the most powerful are Monte Carlo simulations consisting of a stochastic importance sampling over state space and evaluation of estimators for physical quantities. The ability of modern machine learning techniques to classify, identify, or in- terpret massive data sets provides a complementary paradigm to the above approach to analyze the exponentially large number of states in statistical physics. In this report, it is demonstrated by application on Ising-type models that deep learning has potential wide applications in solving many-body statis- tical physics problems. In application of supervised learning, we showed that the feed-forward neural network can identify phases and phase transitions in the ferromagnetic Ising model and the convolutional neural network (CNN) is extremely powerful in classifying T = 0 and T = ∞ phases in the Ising gauge model; In application of unsupervised learning, we illustrated that a deep auto-encoder constructed by stacked restricted Boltzmann machines (RBM)\nis closely related to the renormalization group (RG) method well understood in modern physics and our reconstruction of Ising spin configurations in the ferromagnetic Ising model is similar to the hand-written digits reconstruction.
Quantum Machine Learning (QML) has emerged as a transformative paradigm that integrates the computational advantages of quantum computing with the adaptive intelligence of machine learning to solve complex optimization problems in smart computing systems. Traditional optimization techniques often struggle with high-dimensional search spaces, combinatorial complexity, computational overhead, and scalability limitations in applications such as intelligent transportation, healthcare analytics, smart manufacturing, cybersecurity, cloud computing, and Internet of Things (IoT) infrastructures. QML approaches exploit quantum superposition, entanglement, and quantum parallelism to accelerate optimization tasks and enhance predictive performance beyond classical machine learning capabilities. This research proposes a hybrid Quantum Machine Learning optimization framework that combines Variational Quantum Circuits (VQCs), Quantum Neural Networks (QNNs), and classical deep learning models to address resource allocation, task scheduling, energy optimization, and intelligent decision-making in smart computing environments. The proposed framework integrates quantum-enhanced feature extraction, adaptive optimization layers, and reinforcement-based learning mechanisms to improve convergence speed and computational efficiency. Experimental analysis is performed using benchmark optimization datasets and simulated quantum environments to evaluate accuracy, execution time, energy efficiency, and scalability. Comparative results demonstrate that the proposed QML-based framework achieves superior optimization accuracy, reduced computational latency, and improved resource utilization when compared with traditional machine learning and classical metaheuristic optimization methods. Furthermore, the study highlights the practical significance of hybrid quantum-classical architectures in next-generation intelligent systems where large-scale optimization and real-time decision support are critical. The findings suggest that QML can significantly contribute to the advancement of sustainable, adaptive, and high-performance smart computing ecosystems while opening new directions for future quantum-aware intelligent infrastructures.
Use of AI/ML is associated with more and more computing power, which often necessitates the application to guzzle energy and take time to train. The paper presents a Quantum-Enhanced High-Performance Computing (Q-HPC) system that will combine traditional HPC units with quantum-assisted optimization to enhance the model training in addition to the predictive accuracy and energy efficiency. The framework that could be used to work with such large volumes of data is multi- GPU/CPU parallelization, and the optimization of parameters and hyperparameters can be implemented with the help of quantum-inspired algorithms. This will lead to a hybrid computation balancing dynamically the classical and quantum computations. Q-HPC was experimented with multiple AI/ML model types, such as convolutional networks, transformer models, graph neural networks and reinforcement learning agents, in which cases it was observed to traverse to the solution faster, more accurately and used less energy than the traditional HPC. It can also be said that the framework is dynamically adaptable and sustainable, i.e. it could be deployed to a massive diversifying range of tasks of AI/ML. The suggested model is a combination of the performance and scalability of the classical HPC with the optimization performance of quantum computing in order to create a new and valuable approach to the next generation AI. It deals with the issues of performance and environmental concerns of high-performance computing.