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The reservoir learning power across quantum many-body localization transition
跨量子多体定位转换的水库学习能力
量子多体局在遷移全体の貯水池学習力
양자 다물체 국소화 전환 전반에 걸친 저장소 학습 능력
El poder de aprendizaje del reservorio a través de la transición de localización cuántica de muchos cuerpos
La puissance d'apprentissage du réservoir à travers la transition de localisation quantique à plusieurs corps
Способность к обучению резервуара при квантовом переходе локализации многих тел
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, 15 June 2022
Abstract

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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