(Peer-Reviewed) The reservoir learning power across quantum many-body localization transition
Wei Xia ¹, Jie Zou 邹杰 ¹, Xingze Qiu 邱型泽 ¹ ², Xiaopeng Li 李晓鹏 ¹ ³
¹ State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing, and Department of Physics, Fudan University, Shanghai 200433, China
中国 上海 复旦大学微纳电子器件与量子计算机研究院 应用表面物理国家重点实验室
² Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
中国 深圳 南方科技大学 深圳量子科学与工程研究院
³ Shanghai Qi Zhi Institute, AI Tower, Xuhui District, Shanghai 200232, China
中国 上海 上海西岸国际人工智能中心 上海期智研究院
Frontiers of Physics, 2022-06-15

Harnessing the quantum computation power of the present noisy-intermediate-size-quantum devices has received tremendous interest in the last few years. Here we study the learning power of a one-dimensional long-range randomly-coupled quantum spin chain, within the framework of reservoir computing.

In time sequence learning tasks, we find the system in the quantum many-body localized (MBL) phase holds long-term memory, which can be attributed to the emergent local integrals of motion. On the other hand, MBL phase does not provide sufficient nonlinearity in learning highly-nonlinear time sequences, which we show in a parity check task.

This is reversed in the quantum ergodic phase, which provides sufficient nonlinearity but compromises memory capacity. In a complex learning task of Mackey–Glass prediction that requires both sufficient memory capacity and nonlinearity, we find optimal learning performance near the MBL-to-ergodic transition.

This leads to a guiding principle of quantum reservoir engineering at the edge of quantum ergodicity reaching optimal learning power for generic complex reservoir learning tasks. Our theoretical finding can be tested with near-term NISQ quantum devices.
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