



01610nas a2200157   4500008004100000245005700041210005600098260001400154520112700168100002001295700002301315700002901338700002301367700002501390856003701415       2022                        eng d00aSimulation Complexity of Many-Body Localized Systems0 aSimulation Complexity of ManyBody Localized Systems  c5/25/20223 a<p>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.&nbsp;</p>1 aEhrenberg, Adam1 aDeshpande, Abhinav1 aBaldwin, Christopher, L.1 aAbanin, Dmitry, A.1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2205.12967