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The matrix product state (MPS) belongs to the most important mathematicalmodels in, for example, condensed matter physics and quantum informationsciences. However, to realize an $N$-qubit MPS with large $N$ and largeentanglement on a quantum platform is extremely challenging, since it requireshigh-level qudits or multi-body gates of two-level qubits to carry theentanglement. In this work, an efficient method that accurately encodes a givenMPS into a quantum circuit with only one- and two-qubit gates is proposed. Theidea is to construct the unitary matrix product operators that optimallydisentangle the MPS to a product state. These matrix product operators form thequantum circuit that evolves a product state to the targeted MPS with a highfidelity. Our benchmark on the ground-state MPS's of the strongly-correlatedspin models show that the constructed quantum circuits can encode the MPS'swith much fewer qubits than the sizes of the MPS's themselves. This methodpaves a feasible and efficient path to realizing quantum many-body states andother MPS-based models as quantum circuits on the near-term quantum platforms.

Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates