  Quantum computing offers potential solutions for finding ground states in
condensed-matter physics and chemistry. However, achieving effective ground
state preparation is also computationally hard for arbitrary Hamiltonians. It
is necessary to propose certain assumptions to make this problem efficiently
solvable, including preparing a trial state of a non-trivial overlap with the
genuine ground state. Here, we propose a classical-assisted quantum ground
state preparation method for quantum many-body systems, combining Tensor
Network States (TNS) and Monte Carlo (MC) sampling as a heuristic method to
prepare a trial state with a non-trivial overlap with the genuine ground state.
We extract a sparse trial state by sampling from TNS, which can be efficiently
prepared by a quantum algorithm on early fault-tolerant quantum computers. Our
method demonstrates a polynomial improvement in scaling of overlap between the
trial state and genuine ground state compared to random trial states, as
evidenced by numerical tests on the spin-$1/2$ $J_1$-$J_2$ Heisenberg model.
Furthermore, our method is a novel approach to hybridize a classical numerical
method and a quantum algorithm and brings inspiration to ground state
preparation in other fields.

Quantum Physics