  The matrix product state (MPS) belongs to the most important mathematical
models in, for example, condensed matter physics and quantum information
sciences. However, to realize an $N$-qubit MPS with large $N$ and large
entanglement on a quantum platform is extremely challenging, since it requires
high-level qudits or multi-body gates of two-level qubits to carry the
entanglement. In this work, an efficient method that accurately encodes a given
MPS into a quantum circuit with only one- and two-qubit gates is proposed. The
idea is to construct the unitary matrix product operators that optimally
disentangle the MPS to a product state. These matrix product operators form the
quantum circuit that evolves a product state to the targeted MPS with a high
fidelity. Our benchmark on the ground-state MPS's of the strongly-correlated
spin models show that the constructed quantum circuits can encode the MPS's
with much fewer qubits than the sizes of the MPS's themselves. This method
paves a feasible and efficient path to realizing quantum many-body states and
other MPS-based models as quantum circuits on the near-term quantum platforms.
