  Preparation of a target quantum many-body state on quantum simulators is one
of the significant steps in quantum science and technology. With a small number
of qubits, a few quantum states, such as the Greenberger-Horne-Zeilinger state,
have been prepared, but fundamental difficulties in systems with many qubits
remain, including the Lieb-Robinson bounds for the number of quantum
operations. Here, we provide one algorithm with an implementation of a deep
learning process and achieve to prepare the target ground states with many
qubits. Our strategy is to train a machine-learning model and predict
parameters with many qubits by utilizing a pattern of quantum states from the
corresponding quantum states with small numbers of qubits. For example, we
demonstrate that our algorithm with the Quantum Approximate Optimization Ansatz
can effectively generate the ground state for a 1D XY model with 64 spins. We
also demonstrate that the reduced density operator of two qubits can be
utilized to capture the pattern of quantum many-body states such as correlation
lengths even for quantum critical states.
