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 qubits 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.

Reference:
arXiv:1908.07958

冉仕举, 2010年本科毕业于北京师范大学物理学系；2015年博士毕业于中国科学院大学物理学院；2015至2018年于西班牙光子科学研究所从事博士后研究，并于2017年获Fundacio-Catalunya独立博士后研究员fellowship；2018年入职首都师范大学物理系。研究方向是强关联系统的数值计算与量子模拟、量子机器学习模型与算法，主要使用的理论工具是张量网络。张量网络是一种起源于量子信息科学的强大的数值工具，其不但可用于高效处理量子多体系统，最近还被用于发展量子多体态空间的机器学习模型，实现基于量子理论的人工智能。