Quantum Simulations of complex many-body systems:from theory to algorithms

Laurent Sanchez-Palencia

Johannes Grotendorst, A Muramatsu, D. Marx

Jincheng Zhang

This paper explores the application of the multi-body quantum field theory (MBFT) framework to simulate specific physical systems, introducing a novel "non-ordinary field" concept to capture inherent nonlinear interactions within the system. Traditional field theory methods often struggle with the complexity of these interactions, and MBFT offers a potential solution. We propose a novel simulation algorithm designed to efficiently handle non-linear interactions and leverage the concept of a non-ordinary field to provide more accurate and detailed simulations. The paper details the algorithm's design, its potential benefits, and the challenges and future directions for research in this area. The core claim is that this approach can significantly improve the accuracy and resolution of simulations of complex physical systems by directly incorporating the underlying non-linear dynamics.

Laurent Sanchez-Palencia

Adam Ehrenberg, Abhinav Deshpande, Christopher L. Baldwin +2 more

We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of motion (LIOMs), we demonstrate a transition in the classical complexity of simulating such systems as a function of evolution time. On one side, we construct a quasipolynomial-time tensor-network-inspired algorithm for strong simulation of 1D MBL systems (i.e., calculating the expectation value of arbitrary products of local observables) evolved for any time polynomial in the system size. On the other side, we prove that even weak simulation, i.e. sampling, becomes formally hard after an exponentially long evolution time, assuming widely believed conjectures in complexity theory. Finally, using the consequences of our classical simulation results, we also show that the quantum circuit complexity for MBL systems is sublinear in evolution time. This result is a counterpart to a recent proof that the complexity of random quantum circuits grows linearly in time.

Laurent Sanchez-Palencia