Variational preparation of normal matrix product states on quantum computers

Preparing matrix product states (MPSs) on quantum computers is an essential routine in the simulation of many-body physics. However, widely-used schemes based on staircase circuits are often too deep to execute on current hardware. Here we demonstrate that MPSs with short-range correlations can be prepared with shallow circuits by leveraging heuristics from approximate quantum compiling (AQC). We achieve this with ADAPT-AQC, an adaptive-ansatz preparation algorithm, and introduce a generalised initialisation procedure for the existing AQC-Tensor algorithm. We first compare these methods for the task of preparing a molecular electronic structure ground state. We then use them to prepare an antiferromagnetic (AFM) ground state of the 50-site Heisenberg XXZ spin chain near the AFM-XY phase boundary. Through the execution of circuits with up to 59 CZ depth and 1251 CZ gates, we perform a global quench and observe the relaxation of magnetic ordering in a parameter regime previously inaccessible due to deep ground state preparation circuits. Our results demonstrate how the integration of quantum and classical resources can push the boundary of what can be studied on quantum computers.