Tensor Network Computations That Capture Strict Variationality, Volume Law Behavior, and the Efficient Representation of Neural Network States.

We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the conceptual advantages of tensor network states while removing computational restrictions arising from the need to converge approximate contractions. We use tensor network functions to compute strict variational estimates of the energy on loopy graphs, analyze their expressive power for ground states, show that we can capture aspects of volume law time evolution, and provide a mapping of general feed-forward neural nets onto efficient tensor network functions.

Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance.

A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli dynamics and tensor network algorithms, can simulate these observables orders of magnitude faster than the quantum experiment and can also be systematically converged beyond the experimental accuracy. Our most accurate technique combines a mixed Schrödinger and Heisenberg tensor network representation with the Bethe free entropy relation of belief propagation to compute expectation values with an effective wave function-operator sandwich bond dimension >16,000,000, achieving an absolute accuracy, without extrapolation, in the observables of <0.

Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry.

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.

Using Hyperoptimized Tensor Networks and First-Principles Electronic Structure to Simulate the Experimental Properties of the Giant {Mn} Torus.

The single-molecule magnet {Mn} is a challenge to theory because of its high nuclearity. We directly compute two experimentally accessible observables, the field-dependent magnetization up to 75 T and the temperature-dependent heat capacity, using parameter-free theory. In particular, we use first-principles calculations to derive short- and long-range exchange interactions and compute the exact partition function of the resulting classical Potts and Ising spin models for all 84 Mn = 2 spins to obtain observables.

Quantum Delocalized Interactions.

Classical mechanics obeys the intuitive logic that a physical event happens at a definite spatial point. Entanglement, however, breaks this logic by enabling interactions without a specific location. In this work we study these delocalized interactions.

Machine-Learning-Assisted Many-Body Entanglement Measurement.

Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of quantum correlations in many-body systems. However, in an experiment, the only way of measuring entanglement in a generic mixed state is through reconstructive quantum tomography, requiring an exponential number of measurements in the system size. Here, we propose a machine-learning-assisted scheme to measure the entanglement between arbitrary subsystems of size N_{A} and N_{B}, with O(N_{A}+N_{B}) measurements, and without any prior knowledge of the state.