Variational preparation of normal matrix product states on quantum computers

Preparing matrix product states (MPS) on quantum computers is an important routine in the study of many-body physics due to their mapping to the ground states of gapped local Hamiltonians. Of the available methods, preparation schemes involving variational optimisation have shown great promise in producing shallow circuits amenable to current hardware. In this work, we consider how this extends to normal MPS, which have short-range correlations. Inspired by approximate quantum compiling, our main contribution is the development of an adaptive preparation scheme in which each two-qubit unitary is added based on the current state of optimisation. For random MPS we find that our algorithm outperforms other protocols, producing shallower circuits with fewer two-qubit gates. Following this, we apply our method to study the dynamics of non-integrable spin systems following a global quench over a phase transition. Due to reduced depth preparing the ground state, we are able to study the relaxation of magnetic ordering for 50 qubits on real quantum hardware. Excitingly, our results demonstrate how efficient use of classical resources can push the boundary of what can be studied on quantum computers.