Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and they require solving the grand-challenge problem of the many-electron Schrödinger equation. An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bulk material, embodying several central themes of modern condensed-matter physics and chemistry while retaining a connection to the paradigmatic Hubbard model. Here, we report a combined application of cutting-edge computational methods to determine the properties of the hydrogen chain in its quantummechanical ground state. Varying the separation between the nuclei leads to a rich phase diagram, including a Mott phase with quasi-long-range antiferromagnetic order, electron density dimerization with power-law correlations, an insulator-to-metal transition, and an intricate set of intertwined magnetic orders.

We analyze the dynamical phases of the current-biased 1D and multi-lane open asymmetric simple exclusion processes (ASEP), using matrix product states and the density matrix renormalization group (DMRG) algorithm. In the 1D ASEP, we present a systematic numerical study of the current cumulant generating function and its derivatives, which serve as dynamical phase order parameters. We further characterize the microscopic structure of the phases from local observables and the entanglement spectrum. In the multi-lane ASEP, which may be viewed as finite width 2D strip, we use the same approach and find the longitudinal current-biased dynamical phase behavior to be sensitive to transverse boundary conditions. Our results serve to illustrate the potential of tensor networks in the simulation of classical nonequilibrium statistical models.

Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem.

The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman. Since the original suggestion, concrete proposals have appeared for simulating molecular and materials chemistry through quantum computation, as a potential "killer application" [1,2, 3, 4, 5]. Indications of potential exponential quantum advantage in artificial tasks [6, 7, 8, 9] have increased interest in this application, thus, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation. We conclude that evidence for such an advantage across chemical space has yet to be found. While quantum computers may still prove useful for quantum chemistry, it may be prudent to assume exponential speedups are not generically available for this problem. MainThe most common task in quantum chemistry is computing the ground electronic energy. The exponential quantum advantage hypothesis for this task is that for a large set of relevant ("generic") chemical problems, this may be completed exponentially more quickly (as a function of system size) on a quantum versus classical computer. Here we examine this hypothesis.We proceed using numerical experiments supported by theoretical analysis. Numerics is needed because while much theoretical analysis is known, its relevance to problems of chemical interest is often unclear. To limit scope, we focus on fault-tolerant quantum algorithmsthe most advantageous setting for quantum computing, not limited by noise or hardware. Rigorously, computing the ground-state of even simple Hamiltonians can be exponentially hard on a quantum computer [10]. However, such Hamiltonians might not be relevant to generic chemistry, and thus the specific exponential quantum advantage (EQA) hypothesis considered here, is that generic chemistry involves Hamiltonians which are polynomially easy for quantum algorithms (with respect to ground-state preparation) and simultaneously still exponentially hard classically, even using the best classical heuristics. Numerically, we thus focus on the evidence for quantum state preparation being exponentially easier than classical heuristic solution in typ-

We demonstrate the power of 2D tensor networks for obtaining large deviation functions of dynamical observables in a classical nonequilibrium setting. Using these methods, we analyze the previously unstudied dynamical phase behavior of the fully 2D asymmetric simple exclusion process with biases in both the x and y directions. We identify a dynamical phase transition, from a jammed to a flowing phase, and characterize the phases and the transition, with an estimate of the critical point and exponents.