Preparation of initial states with open and periodic boundary conditions on quantum devices using matrix product states

Abstract: We present a framework for preparing quantum states from matrix product states (MPS) with open and periodic boundary conditions on quantum devices. The MPS tensors are mapped to unitary gates, which are subsequently decomposed into native gates on quantum hardware. States with periodic boundary conditions (pbc) can be represented efficiently as quantum circuits using ancilla qubits and post-selection after measurement. We derive an exact expression for the success rate of this probabilistic approach, which can be evaluated a priori. The applicability of the method is demonstrated in two examples. First, we prepare the ground state of the Heisenberg model with pbc and simulate dynamics under a quenched Hamiltonian. The volume-law entanglement growth in the time evolution challenges classical algorithms but can potentially be overcome on quantum hardware. Second, we construct quantum circuits that generate excited states of the Schwinger model with high fidelities. Our approach provides a scalable method for preparing states on a quantum device, enabling efficient simulations of strongly correlated systems on near-term quantum computers.