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One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully translationally invariant. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Renyi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning.

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

Exact diagonalization is a well-established method for simulating small quantum systems. Its applicability is limited by the exponential growth of the so-called Hamiltonian matrix that needs to be diagonalized. Physical symmetries are usually utilized to reduce the matrix dimension, and distributed-memory parallelism is employed to explore larger systems. This paper focuses on the implementation the core distributed algorithms, with a special emphasis on the matrix-vector product operation. Instead of the conventional MPI+X paradigm, Chapel is chosen as the language for these distributed algorithms. We provide a comprehensive description of the algorithms and present performance and scalability tests. Our implementation outperforms the state-of-the-art MPI-based solution by a factor of 7--8 on 32 compute nodes or 4096 cores and exhibits very good scaling on up to 256 nodes or 32768 cores. The implementation has 3 times fewer software lines of code than the current state of the art while remaining fully generic., Comment: 11 pages, 9 figures

Magnetic skyrmions are vortex-like quasiparticles characterized by long lifetime and remarkable topological properties. That makes them a promising candidate for the role of information carriers in magnetic information storage and processing devices. Although considerable progress has been made in studying skyrmions in classical systems, little is known about the quantum case: quantum skyrmions cannot be directly observed by probing the local magnetization of the system, and the notion of topological protection is elusive in the quantum realm. Here, we explore the potential robustness of quantum skyrmions in comparison to their classical counterparts. We theoretically analyze the dynamics of a quantum skyrmion subject to local projective measurements and demonstrate that the properties of the skyrmionic quantum state change very little upon external perturbations. We further show that by performing repetitive measurements on a quantum skyrmion, it can be completely stabilized through an analog of the quantum Zeno effect., Comment: 7+eps pages, 7 figures; v2: fixed mistake in the definition of rescaled time \tau after Eq.(6)

Twisted bilayer graphene is an exciting platform for exploring correlated quantum phases, extremely tunable with respect to both the single-particle bands and the interaction profile of electrons. Here, we investigate the phase diagram of twisted bilayer graphene as described by an extended Hubbard model on the honeycomb lattice with two fermionic orbitals (valleys) per site. Besides the special extended {\it cluster interaction} $Q$, we incorporate the effect of gating through an onsite Hubbard-interaction $U$. Within Quantum Monte Carlo (QMC), we find valence-bond-solid, N\'eel-valley antiferromagnetic or charge-density wave phases. Further, we elucidate the competition of these phases by noticing that the cluster interaction induces an exotic constraint on the Hilbert space, which we dub {\it the cluster rule}, in analogy to the famous pyrochlore spin-ice rule. Formulating the perturbative Hamiltonian by projecting into the cluster-rule manifold, we perform exact diagonalization and construct the fixed-point states of the observed phases. Finally, we compute the local electron density patterns as signatures distinguishing these phases, which could be observed with scanning tunneling microscopy. Our work capitalizes on the notion of cluster constraints in the extended Hubbard model of twisted bilayer graphene, and suggests a scheme towards realization of several symmetry-breaking insulating phases in a twisted-bilayer graphene sheet., Comment: 10 pages, 6 figures

The non-trivial phase structure of the eigenstates of many-body quantum systems severely limits the applicability of quantum Monte Carlo, variational, and machine learning methods. Here, we study real-valued signful ground-state wave functions of frustrated quantum spin systems and, assuming that the tasks of finding wave function amplitudes and signs can be separated, show that the signs can be easily bootstrapped from the amplitudes. We map the problem of finding the sign structure to an auxiliary classical Ising model defined on a subset of the Hilbert space basis. We show that the Ising model does not exhibit significant frustrations even for highly frustrated parental quantum systems, and is solvable with a fully deterministic $O(K\log K)$-time combinatorial algorithm (where $K$ is the Ising model size). Given the ground state amplitudes, we reconstruct the signs of the ground states of several frustrated quantum models, thereby revealing the hidden simplicity of many-body sign structures., Comment: 11 pages, 9 figures in the main text; 9 pages, 4 figures in the supplemental information

In narrow-band systems, correlated contribution to effective hopping becomes important, and one needs to carefully consider three types of hopping processes: between doubly and singly occupied sites, between singly occupied and empty sites, and between doubly occupied and empty or two singly occupied sites. All three hopping parameters cannot vanish simultaneously, and one should specify for which of these processes the band becomes flat. By means of exact diagonalization of finite systems we demonstrate that three hoppings play qualitatively different roles in many-body effects, in particular, in the formation of half-metallic ferromagnetic (Nagaoka) states., Comment: v3: minor corrections after acceptance for publication; v2: fix definitions of hoppings, update figures, add connection to real materials; v1: 5 pages, 1 figure in the main text, 1 figure in the supplemental information

We derive a material-realistic real-space many-body Hamiltonian for twisted bilayer graphene from first principles, including both single-particle hopping terms for $p_z$ electrons and long-range Coulomb interactions. By disentangling low- and high-energy subspaces of the electronic dispersion, we are able to utilize state-of-the-art constrained Random Phase Approximation calculations to reliably describe the non-local background screening from the high-energy $s$, $p_x$, and $p_y$ electron states for arbitrary twist angles. The twist-dependent low-energy screening from $p_z$ states is subsequently added to obtain a full screening model. We use this approach to study real-space plasmonic patterns in electron-doped twisted bilayer graphene supercells and find, next to classical dipole-like modes, also twist-angle-dependent plasmonic quantum-dot-like excitations with $s$ and $p$ symmetries. Based on their inter-layer charge modulations and their footprints in the electron energy loss spectrum, we can classify these modes into "bright" and "dark" states, which show different dependencies on the twist angle., Comment: 9 pages, 8 figures

We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable variables (e.g. states of neurons) and trainable variables (e.g. weight matrix). Non-trainable variables are rapidly driven towards stochastic equilibrium and trainable variables are slowly driven towards learning equilibrium described by a scale-invariant distribution on a wide range of scales. Our results suggest that the scale invariance observed in many physical and biological systems might be due to some kind of learning dynamics and support the claim that the universe might be a neural network., Comment: 11 pages, 4 figures

Exact diagonalization (ED) is one of the most reliable and established numerical methods of quantum many-body theory. The main limiting factor of the method is the exponential scaling of Hilbert space dimension with system size. Fortunately, by symmetry considerations the effective dimension can be reduced by multiple orders of magnitude. Here, we present lattice-symmetries, a package for working with such symmetry-adapted quantum many-body bases and operators. It supports bases for spin-1/2 particles with arbitrary user-defined symmetries and generic 1-, 2-, 3-, and 4-point operators. As an example application we discuss SpinED program which allows to easily diagonalize clusters of at least 42 sites on a single node thus making large-scale ED easily accessible to people with no background in numerical methods and computational physics., Comment: v2: submitted version, published in Journal of Open Source Software; extended discussion of similar software, added a note on architecture limitations, minor grammar corrections; v1: 4 pages, 1 figure

The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a RVB-like many-variable Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to $4\times 4^3$ and $4 \times 3^3$ spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin-liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets., Comment: 9 pages, 5 figures

Neural quantum states (NQS) are a novel class of variational many-body wave functions that are very flexible in approximating diverse quantum states. Optimization of an NQS ansatz requires sampling from the corresponding probability distribution defined by squared wave function amplitude. For this purpose we propose to use kinetic sampling protocols and demonstrate that in many important cases such methods lead to much smaller autocorrelation times than Metropolis-Hastings sampling algorithm while still allowing to easily implement lattice symmetries (unlike autoregressive models). We also use Uniform Manifold Approximation and Projection algorithm to construct two-dimensional isometric embedding of Markov chains and show that kinetic sampling helps attain a more homogeneous and ergodic coverage of the Hilbert space basis., Comment: v2: 8 pages, 11 figures, UMAP analysis of typical NQS added, revtex; comments are welcome!

Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wavefunction structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility., Comment: 9+6 pages, 5+7 figures, v3: added results for larger systems, improved discussion, added new references

We introduce NetKet, a comprehensive open source framework for the study of many-body quantum systems using machine learning techniques. The framework is built around a general and flexible implementation of neural-network quantum states, which are used as a variational ansatz for quantum wave functions. NetKet provides algorithms for several key tasks in quantum many-body physics and quantum technology, namely quantum state tomography, supervised learning from wave-function data, and ground state searches for a wide range of customizable lattice models. Our aim is to provide a common platform for open research and to stimulate the collaborative development of computational methods at the interface of machine learning and many-body physics.

Recent progress in the fabrication of materials has made it possible to create arbitrary non-periodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the plasmonic properties of electron gases in complex geometries such as fractals. In this work, we study the plasmonic properties of Sierpinski carpets and gaskets, two prototypical fractals with different ramification, by fully calculating their dielectric functions. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum scale., Comment: 5 pages, 4 figures, comments are welcome