In chaotic dynamical systems, extreme events manifest in time series as unpredictable large-amplitude peaks. Although deterministic, extreme events appear seemingly randomly, which makes their forecasting difficult. By learning the dynamics from observables (data), reservoir computers can time-accurately predict extreme events and chaotic dynamics, but they may require many degrees of freedom (large reservoirs). In this paper, by exploiting quantum-computer ansätze and entanglement, we design reservoir computers with compact reservoirs and accurate prediction capabilities. First, we propose the recurrence-free quantum reservoir computer (RF-QRC) architecture. By developing ad-hoc quantum feature maps and removing recurrent connections, the RF-QRC has quantum circuits with small depths. This allows the RF-QRC to scale well with higher-dimensional chaotic systems, which makes it suitable for hardware implementation. Second, we forecast the temporal chaotic dynamics and their long-term statistics of low- and higher-dimensional dynamical systems. We find that RF-QRC requires smaller reservoirs than classical reservoir computers. Third, we apply the RF-QRC to the time prediction of extreme events in a model of a turbulent shear flow with turbulent bursts. We find that the RF-QRC has a longer predictability than the classical reservoir computer. The results and analyses indicate that quantum-computer ansätze offer nonlinear expressivity and computational scalability, which are useful for forecasting chaotic dynamics and extreme events. This work opens new opportunities for using quantum machine learning on near-term quantum computers.
Quantum reservoir computing for predicting and characterizing chaotic maps
University of Electronic Science and Technology of China（电子科技大学）；Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿研究院）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（电子科技大学量子物理与光子量子信息教育部重点实验室）；School of Life Science and Technology, University of Electronic Science and Technology of China（电子科技大学生命科学与技术学院）；Institute of Science Tokyo（东京科学大学）；Center for Mind/Brain Sciences (CIMeC), University of Trento（特伦托大学心智/脑科学中心）；Shimmer Center, Tianfu Jiangxi Laboratory（天府江西实验室闪烁中心）
Theory of the Edge-of-Chaos Advantage in Quantum Reservoir Computing
Fudan University（复旦大学）；Shanghai Qi Zhi Institute（上海人工智能实验室）；The Chinese University of Hong Kong（香港中文大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Hefei National Laboratory（合肥国家实验室）
The reservoir memory effects can lead to information backflow and recurrence of the previously lost quantum correlations. We establish connections between the direction of information flow and variation of the geometric quantum discords (GQDs) measured respectively by the trace distance, the Hellinger distance, and the Bures distance for two qubits subjecting to the bosonic structured reservoirs, and unveil their dependence on a factor whose derivative signifies the (non-)Markovianity of the dynamics. By considering the reservoirs with Lorentzian and Ohmic-like spectra, we further demonstrated…
Optimal training of finitely-sampled quantum reservoir computers for forecasting of chaotic dynamics
Imperial College London（伦敦帝国理工学院）；City St George’s, University of London（伦敦大学城市圣乔治学院）；The Alan Turing Institute（艾伦·图灵研究所）；Politecnico di Torino（都灵理工大学）
Leveraging Metrologically Useful States in Quantum Reservoir Networks
Naval Surface Warfare Center Panama City Division（海军水面武器中心巴拿马城分部）；The Johns Hopkins Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；Qodex Quantum（Qodex量子）；University of South Carolina - Columbia（南卡罗来纳大学哥伦比亚分校）
Reservoir Computing Using Measurement-Controlled Quantum Dynamics
Artificial Intelligence and Cyber Futures Institute, Charles Sturt University（查尔斯斯特大学人工智能与网络未来学院）；Cyber Futures Institute, Charles Sturt University（查尔斯斯特大学网络未来学院）
