Affiliation:
1. Barcelona Supercomputing Center
2. Universitat de Barcelona
3. Institute of Fundamental Physics IFF-CSIC
Abstract
We study the computational complexity of simulating the time-dependent expectation value of a local operator in a one-dimensional quantum system by using temporal matrix product states(MPSs) and argue that it is intimately related to that of encoding temporal transition matrices and their partial traces. We show that we can upper-bound the rank of these reduced transition matrices by one of the Heisenberg evolution of local operators, thus making aconnection between two apparently different quantities, the temporal entanglement and the local operator entanglement(OE). As a result, whenever the local OE grows slower than linearly in time, we show that computing time-dependent expectation values of local operators using temporal MPSs is likely advantageous with respect to computing the same quantities using standard MPS techniques.
Published by the American Physical Society
2024
Funder
Consejo Superior de Investigaciones Científicas
'la Caixa' Foundation
Publisher
American Physical Society (APS)