We propose a dynamical scaling analysis improved by a deep learning approach. While Gaussian process regression has been widely employed for estimating scaling parameters, its computational cost for parameter optimization becomes a limitation in dynamical scaling analysis, where large datasets are involved. In contrast, the present method employs a neural network, which significantly reduces the computational cost and enables the use of the entire dataset that was inaccessible with Gaussian process regression. We applied the method to the 2D Ising model and the 2D 3-state Potts model, achieving higher accuracy and computational efficiency than conventional approaches.
We propose a dynamical scaling analysis improved by a deep learning approach. While Gaussian process regression has been widely employed for estimating scaling parameters, its computational cost for parameter optimization becomes a limitation in dynamical scaling analysis, where large datasets are involved. In contrast, the present method employs a neural network, which significantly reduces the computational cost and enables the use of the entire dataset that was inaccessible with Gaussian process regression. We applied the method to the 2D Ising model and the 2D 3-state Potts model, achieving higher accuracy and computational efficiency than conventional approaches.
Determining the universality class of a system exhibiting critical phenomena is one of the central problems in physics. There are several methods to determine this universality class from data. As methods to collapse plots onto scaling functions, polynomial regression, which is less accurate, and Gaussian process regression, which provides high accuracy and flexibility but is computationally expensive, have been proposed. In this paper, we propose a regression method using a neural network. The computational complexity is linear only in the number of data points. We demonstrate the proposed method for the finite-size scaling analysis of critical phenomena in the two-dimensional Ising model and bond percolation problem to confirm the performance. This method efficiently obtains the critical values with accuracy in both cases.
Gaussian process regression (GPR) is a nonparametric supervised learning method, widely valued for its ability to quantify uncertainty. Despite its advantages and broad applications, classical GPR implementations face significant scalability challenges, as they involve matrix operations with a cubic complexity in relation to the dataset size. This computational challenge is further compounded by the demand of optimizing the Gaussian Process (GP) model over its hyperparameters, rendering the total computational cost prohibitive for data intensive problems. To address this issue, we propose a quantum gradient descent algorithm to optimize the GP model. Taking advantage of recent advances in quantum algorithms for linear algebra, our algorithm achieves exponential speedup in computing the gradients of the log marginal likelihood. The entire gradient descent process is integrated into the quantum circuit. Through runtime analysis and error bounds, we demonstrate that our approach significantly improves the scalability of GPR model optimization, making it computationally feasible for large-scale applications.
State-of-the-art quantum algorithms routinely tune dynamically parametrized cost functionals for combinatorics, machine learning, equation solving, and energy minimization. However, large search complexity often demands many (noisy) quantum measurements, leading to the increasing use of classical probability models to estimate which areas in the cost functional landscape are of highest interest. Introducing deep learning based modeling of the landscape, we demonstrate order-of-magnitude increases in accuracy and speed over state-of-the-art Bayesian methods with respect to control of a many-body spin chain. Moreover, once trained, the deep neural network enables the extraction of information at a much faster rate than conventional numerical simulation. This allows for on-the-fly experimental optimizations of circuits with large depth and moderate width and detailed classification of problem complexity and navigability throughout the phase diagram of the landscape.
Part of the challenge for quantum many-body problems comes from the difficulty of representing large-scale quantum states, which in general requires an exponentially large number of parameters. Neural networks provide a powerful tool to represent quantum many-body states. An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to the popularity of deep learning methods. Here, we give a proof that, assuming a widely believed computational complexity conjecture, a deep neural network can efficiently represent most physical states, including the ground states of many-body Hamiltonians and states generated by quantum dynamics, while a shallow network representation with a restricted Boltzmann machine cannot efficiently represent some of those states.One of the challenges in studies of quantum many-body physics is finding an efficient way to record the large system wavefunctions. Here the authors present an analysis of the capabilities of recently-proposed neural network representations for storing physically accessible quantum states.
With Deep learning and quantum computing are emerging technologies with transformative potential in financial risk assessment, optimization, and fraud detection. The integration of these fields can significantly enhance the efficiency and accuracy of financial decision-making processes. However, existing fraud detection methods often suffer from high false positives, slow processing times, and limited adaptability to complex fraud patterns. Traditional machine learning models struggle with scalability and computational efficiency when dealing with large-scale financial data. To address these issues, we propose the Quantum-Inspired Neural Networks for Fraud Detection (Q-INN-FD) framework, which leverages quantum-inspired computing principles to enhance neural network architectures. The framework incorporates quantum-inspired feature encoding, variational quantum circuits, and hybrid classical-quantum learning mechanisms to improve pattern recognition in financial transactions. These techniques enable more efficient fraud detection by enhancing model robustness and reducing computational overhead. The proposed method is applied to financial datasets to detect fraudulent transactions, optimize risk assessment models, and improve decision-making in real-time scenarios. Our findings demonstrate that Q-INN-FD achieves higher accuracy, faster processing, and reduced false positive rates compared to traditional deep learning approaches. This paper highlights the potential of quantum-inspired deep learning for revolutionizing financial security and risk management.
Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example cases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena.