  We present a quantum algorithm for simulating complex many-body systems and
finding their ground states, combining the use of tensor networks and density
matrix renormalization group (DMRG) techniques. The algorithm is based on von
Neumann's measurement prescription, which serves as a conceptual building block
for quantum phase estimation. We describe the implementation and simulation of
the algorithm, including the estimation of resources required and the use of
matrix product operators (MPOs) to represent the Hamiltonian. We highlight the
potential applications of the algorithm in simulating quantum spin systems and
electronic structure problems.
