Condensed Matter

Quantum Hall phases are the most exotic experimentally established quantum phases of matter.Recently they have been discovered at zero external magnetic field in two dimensional moire materials. I will describe recent work (with Xue-Yang Song and Ya-Hui Zhang) on their proximate phases and associated phase transitions that is motivated by the high tunability of thede moire systems. These phase transitions (and some of the proximate phases) are exotic as well, and realize novel ‘beyond Landau’ criticality that have been explored theoretically for many years. I will show that these moiré platforms provide a great experimental opportunity to study these unconventional phase transitions and related unconventional phases, thereby opening a new direction for research in quantum matter.

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Zoom link : https://pitp.zoom.us/j/97483204701?pwd=S2x4ck9tNHFjM0RiTDNWNFhaMk9SUT09

We study the Petz map, which is a universal recovery channel of a tripartite quantum state upon erasing one party, in quantum many-body systems. The fidelity of the recovered state with the original state quantifies how much information shared by the two parties is not mediated by one of the party, and has a universal lower bound in terms of the conditional mutual information (CMI). I will study this quantity in two different contexts. First, in a CFT ground state, we show that the fidelity is universal, which means it only depends on the central charge and the cross ratio. We compute this universal function numerically and show that it is consistently better than the naive CMI bound. Secondly, we show that for two broad classes of the states, the CMI lower bound is saturated. These include stabilizer states (in any dimensions) and the ground state of 2+1D topological order.

Zoom link: https://pitp.zoom.us/j/92623435839?pwd=N1JIdkUwWHFkZGpqb1p1V3NKYy91QT09

The notorious exponential complexity of quantum problems can be avoided for systems with limited correlations. For example, states of one-dimensional systems with bounded entanglement are approximable by matrix product states. We consider fermionic systems, where correlations can be defined as deviations from Gaussian states. Heuristically, one expects a link between compact non-Gaussian ansatzes and bounded fermionic correlations. This connection, however, has not been rigorously demonstrated. Our work resolves this conceptual gap.

We focus on pure states with a fixed number of fermions. Generalizing the so-called Plücker relations, we introduce k-particle correlation measures ω_k. The vanishing of ω_k at a constant k defines a class H_k of states with limited correlations. These sets H_k are nested, ranging from Gaussian for k=1 to the full n-fermion Hilbert space H for k=n+1. States in H_{k=O(1)} can be represented using a non-Gaussian ansatz of polynomial size. Classes H_k have physical meaning, containing all truncated perturbation series around Gaussian states. We also identify non-perturbative examples of states in H_{k=O(1)}, by a numerical study of excited states in the 1D Hubbard model. Finally, we discuss the information-theoretic implications of our results for the widely used coupled-cluster ansatz.

Zoom Link: TBD

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.

How do you control something you can not look at? For controlling quantum systems, information on the system’s state could come through weak measurements. Such measurements provide some information, but will inevitably also perturb the system, meaning there is noise both in the state estimation as well as in the measurement. We study a simple single particle quantum setup (the quantum equivalent of the instability problem known as the cartpole problem) and investigate several control methods including reinforcement learning, and compare their performance.

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.

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.

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).