Variational preparation of normal matrix product states on quantum computers

Abstract: Preparing matrix product states (MPSs) on quantum computers is important for a wide class of quantum algorithms including the simulation of many-body physics. However, widely-used schemes based on staircase circuits are often too deep to be run on quantum computers today. In this work, we demonstrate how normal MPSs, which have short-range correlations, can be prepared with shallow circuits using heuristics from approximate quantum compiling (AQC). We achieve this with ADAPT-AQC, an adaptive-ansatz preparation algorithm, as well as with a generalised initialisation scheme for the existing AQC-Tensor algorithm. We subsequently apply these methods to prepare an antiferromagnetic (AFM) ground state of the 50-site Heisenberg XXZ spin chain near the AFM-XY phase boundary and study the dynamics following a global quench. Through the execution of circuits with up to 59 CZ depth and 1251 CZ gates, we obtain the signature relaxation of magnetic ordering for a parameter regime previously inaccessible on quantum hardware due to deep ground state preparation circuits. Overall, our results demonstrate how the close integration of quantum and classical resources can push the boundary of what can be studied on quantum computers.