Recent advances in neural network quantum states (NQS) have enabled high-accuracy predictions for complex quantum many-body systems such as strongly correlated electron systems. However, the computational cost remains prohibitive, making exploration of the diverse parameters of interaction strengths and other physical parameters inefficient. While transfer learning has been proposed to mitigate this challenge, achieving generalization to large-scale systems and diverse parameter regimes remains difficult. To address this limitation, we propose a novel curriculum learning framework based on transfer learning for NQS. This facilitates efficient and stable exploration across a vast parameter space of quantum many-body systems. In addition, by interpreting NQS transfer learning through a perturbative lens, we demonstrate how prior physical knowledge can be flexibly incorporated into the curriculum learning process. We also propose Pairing-Net, an architecture to practically implement this strategy for strongly correlated electron systems, and empirically verify its effectiveness. Our results show an approximately 200-fold speedup in computation and a marked improvement in optimization stability compared to conventional methods.

In quantum many-body systems, measurements can induce qualitative new features, but their simulation is hindered by the exponential complexity involved in sampling the measurement results. We propose to use machine learning to assist the simulation of measurement-induced quantum phenomena. In particular, we focus on the measurement-altered quantum criticality protocol and generate local reduced density matrices of the critical chain given random measurement results. Such generation is enabled by a physics-preserving conditional diffusion generative model, which learns an observation-indexed probability distribution of an ensemble of quantum states, and then samples from that distribution given an observation.

Neural-network quantum states (NQSs), variationally optimized by combining traditional methods and deep learning techniques, is a new way to find quantum many-body ground states and gradually becomes a competitor of traditional variational methods. However, there are still some difficulties in the optimization of NQSs, such as local minima, slow convergence, and sign structure optimization. Here, we split a quantum many-body variational wave function into a multiplication of a real-valued amplitude neural network and a sign structure, and focus on the optimization of the amplitude network while keeping the sign structure fixed. The amplitude network is a convolutional neural network (CNN) with residual blocks, namely a ResNet. Our method is tested on three typical quantum many-body systems. The obtained ground state energies are lower than or comparable to those from traditional variational Monte Carlo (VMC) methods and density matrix renormalization group (DMRG). Surprisingly, for the frustrated Heisenberg $J_1$-$J_2$ model, our results are better than those of the complex-valued CNN in the literature, implying that the sign structure of the complex-valued NQS is difficult to be optimized. We will study the optimization of the sign structure of NQSs in the future.

The dual tasks of quantum Hamiltonian learning and quantum Gibbs sampling are relevant to many important problems in physics and chemistry. In the low temperature regime, algorithms for these tasks often suffer from intractabilities, for example from poor sample- or time-complexity. With the aim of addressing such intractabilities, we introduce a generalization of quantum natural gradient descent to parameterized mixed states, as well as provide a robust first-order approximating algorithm, Quantum-Probabilistic Mirror Descent. We prove data sample efficiency for the dual tasks using tools from information geometry and quantum metrology, thus generalizing the seminal result of classical Fisher efficiency to a variational quantum algorithm for the first time. Our approaches extend previously sample-efficient techniques to allow for flexibility in model choice, including to spectrally-decomposed models like Quantum Hamiltonian-Based Models, which may circumvent intractable time complexities. Our first-order algorithm is derived using a novel quantum generalization of the classical mirror descent duality. Both results require a special choice of metric, namely, the Bogoliubov-Kubo-Mori metric. To test our proposed algorithms numerically, we compare their performance to existing baselines on the task of quantum Gibbs sampling for the transverse field Ising model. Finally, we propose an initialization strategy leveraging geometric locality for the modelling of sequences of states such as those arising from quantum-stochastic processes. We demonstrate its effectiveness empirically for both real and imaginary time evolution while defining a broader class of potential applications.

Three RIKEN theoretical physicists have used neural networks to investigate the way atoms and electrons interact with each other at finite temperatures. This knowledge will help inform the development of future quantum technologies for advanced computation. Many of a material's properties, both conventional and exotic, originate from atoms and electrons interacting with each other according to the laws of quantum mechanics. Understanding these so-called quantum many-body systems is critical for predicting and controlling these properties. In addition, this knowledge will be vital for developing practically useful devices such as quantum computers.

We introduce a machine learning model, the q-CNN model, sharing key features with convolutional neural networks and admitting a tensor network description. As examples, we apply q-CNN to the MNIST and Fashion MNIST classification tasks. We explain how the network associates a quantum state to each classification label, and study the entanglement structure of these network states. In both our experiments on the MNIST and Fashion-MNIST datasets, we observe a distinct increase in both the left/right as well as the up/down bipartition entanglement entropy during training as the network learns the fine features of the data. More generally, we observe a universal negative correlation between the value of the entanglement entropy and the value of the cost function, suggesting that the network needs to learn the entanglement structure in order the perform the task accurately. This supports the possibility of exploiting the entanglement structure as a guide to design the machine learning algorithm suitable for given tasks.

Machine learning techniques have so far proved to be very promising for the analysis of data in several fields, with many potential applications. However, researchers have found that applying these methods to quantum physics problems is far more challenging due to the exponential complexity of many-body systems. Quantum many-body systems are essentially microscopic structures made up of several interacting particles. While quantum physics studies have focused on the collective behavior of these systems, using machine learning in these investigations has proven to be very difficult. With this in mind, a team of researchers at Harvard University recently developed a quantum circuit-based algorithm inspired by convolutional neural networks (CNNs), a popular machine learning technique that has achieved remarkable results in a variety of fields.

Machine learning techniques have so far proved to be very promising for the analysis of data in several fields, with many potential applications. However, researchers have found that applying these methods to quantum physics problems is far more challenging due to the exponential complexity of many-body systems. Quantum many-body systems are essentially microscopic structures made up of several interacting particles. While quantum physics studies have focused on the collective behavior of these systems, using machine learning in these investigations has proven to be very difficult. With this in mind, a team of researchers at Harvard University recently developed a quantum circuit-based algorithm inspired by convolutional neural networks (CNNs), a popular machine learning technique that has achieved remarkable results in a variety of fields.

Machine learning has been used to beat a human competitor in a game of Go (1), a game that has long been viewed as the most challenging of board games for artificial intelligence. Research is now under way to investigate whether machine learning can be used to solve long outstanding problems in quantum science. Carleo and Troyer used an artificial neural network to represent the wave function of a quantum many-body system and to make the neural network'learn' what the ground state (or dynamics) of the system is. Their approach is found to perform better than the current state-of-the-art numerical simulation methods.