Condensed Matter

Neural quantum states (NQSs) have emerged as a novel promising numerical method to solve the quantum many-body problem. However, it has remained a central challenge to train modern large-scale deep network architectures to desired quantum state accuracy, which would be vital in utilizing the full power of NQSs and making them competitive or superior to conventional numerical approaches. Here, we propose a minimum-step stochastic reconfiguration (MinSR) method that reduces the optimization complexity by orders of magnitude while keeping similar accuracy as compared to conventional stochastic reconfiguration. MinSR allows for accurate training on unprecedentedly deep NQS with up to 64 layers and more than 105 parameters in the spin-1/2 Heisenberg J1-J2 models on the square lattice. We find that this approach yields better variational energies as compared to existing numerical results and we further observe that the accuracy of our ground state calculations approaches different levels of machine precision on modern GPU and TPU hardware. The MinSR method opens up the potential to make NQS superior as compared to conventional computational methods with the capability to address yet inaccessible regimes for two-dimensional quantum matter in the future.

Our universe is quantum, but our everyday experience is classical. Where is the boundary between quantum and classical worlds? How does classical reality emerge in quantum many-body systems? Does the collapse of the quantum states involve intelligence? These are fundamental questions that have puzzled physicists and philosophers for centuries. The recent development of quantum information science and artificial intelligence offers new opportunities to investigate these old problems. In this talk, we present our preliminary research on using a transformer-based language model to process randomized measurement data collected from Schrödinger’s cat quantum state. We show that the classical reality emerges in the language model due to the information bottleneck: although our training data contains the full quantum information of Schrödinger’s cat, a weak language model can only learn the classical reality of the cat from the data. Our study opens up a new avenue for using the big data generated on noisy intermediate-scale quantum (NISQ) devices to train generative models for representation learning of quantum operators, which might be a step toward our ultimate goal of creating an artificial intelligence quantum physicist.

Recurrent neural networks (RNNs), originally developed for natural language processing, hold great promise for accurately describing strongly correlated quantum many-body systems. In this talk, we will illustrate how to use 2D RNNs to investigate two prototypical quantum many-body Hamiltonians exhibiting topological order. Specifically, we will demonstrate that RNN wave functions can effectively capture the topological order of the toric code and a Bose-Hubbard spin liquid on the kagome lattice by estimating their topological entanglement entropies. Overall, we will show that RNN wave functions constitute a powerful tool for studying phases of matter beyond Landau's symmetry-breaking paradigm.

Recently, machine learning has become a powerful tool for detecting quantum phases. While the sole information about the presence of transition is valuable, the lack of interpretability and knowledge on the detected order parameter prevents this tool from becoming a customary element of a physicist's toolbox. Here, we report designing a special convolutional neural network with adaptive kernels, which allows for fully interpretable and unsupervised detection of local order parameters out of spin configurations measured in arbitrary bases. With the proposed architecture, we detect relevant and simplest order parameters for the one-dimensional transverse-field Ising model from any combination of projective measurements in the x, y, or z basis. Moreover, we successfully tackle the bilinear-biquadratic spin-1 model with a nontrivial nematic order. We also consider extending the proposed approach to detecting topological order parameters. This work can lead to integrating machine learning methods with quantum simulators studying new exotic phases of matter.

The field of artificial intelligence (AI) has experienced major developments over the last decade. Within AI, of particular interest is the paradigm of reinforcement learning (RL), where autonomous agents learn to accomplish a given task via feedback exchange with the world they are placed in, called an environment. Thanks to impressive advances in quantum technologies, the idea of using quantum physics to boost the performance of RL agents has been recently drawing the attention of many scientists. In my talk I will focus on the bridge between RL and quantum mechanics, and show how RL has proven amenable to quantum enhancements. I will provide an overview of the most recent results — for example, the development of agents deciding faster on their next move [1]— and I will then focus on how the learning time of an agent can be reduced using quantum physics. I will show that such a reduction can be achieved and quantified only if the agent and the environment can also interact quantumly, that is, if they can communicate via a quantum channel [2]. This idea has been implemented on a quantum platform that makes use of single photons as information carriers. The achieved speed-up in the agent’s learning time, compared to the fully classical picture, confirms the potential of quantum technologies for future RL applications. [1] Sriarunothai, T. et al. Quantum Science and Technology 4, 015014 (2018). [2] Saggio, V. et al. Nature 591, 229–233 (2021).

Dense hydrogen, the most abundant matter in the visible universe, exhibits a range of fascinating physical phenomena such as metallization and high-temperature superconductivity, with significant implications for planetary physics and nuclear fusion research. Accurate prediction of the equations of state and phase diagram of dense hydrogen has long been a challenge for computational methods. In this talk, we present a deep generative model-based variational free energy approach to tackle the problem of dense hydrogen, overcoming the limitations of traditional computational methods. Our approach employs a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model the electron wavefunction at given proton positions. The joint optimization of these two neural networks leads to a comparable variational free energy to previous coupled electron-ion Monte Carlo calculations. Our results suggest that hydrogen in planetary conditions is even denser than previously estimated using Monte Carlo and ab initio molecular dynamics methods. Having reliable computation of the equation of state for dense hydrogen, and in particular, direct access to its entropy and free energy, opens new opportunities in planetary modeling and high-pressure physics research.