Matrix product state simulations on a quantum computer

Matrix product states (MPS) afford a compressed representation of many states that are relevant to physical systems. While many classical algorithms have been developed to compute the properties of physical systems using MPS as an ansatz, in many cases of practical interest these algorithms still require exponential resources (for example in the size of the system, or in the evolution time when out of equilibrium). We discuss near-term prospects for using small and non-error-corrected quantum computers to aid in MPS simulations.