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

TL;DR

This paper presents an efficient method to encode matrix product states into quantum circuits using only one- and two-qubit gates, enabling practical realization of complex quantum many-body states on near-term quantum devices.

Contribution

The authors develop a novel approach to encode MPS into quantum circuits with minimal qubits, utilizing unitary matrix product operators for high-fidelity state preparation.

Findings

Quantum circuits can encode MPS with fewer qubits than the MPS size.

The method achieves high fidelity in representing ground states of strongly-correlated spin models.

Efficient encoding facilitates realization of complex quantum states on near-term quantum platforms.

Abstract

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.