Prediction of chaotic dynamics and extreme events: A recurrence-free quantum reservoir computing approach

• URL: http://arxiv.org/abs/2405.03390v2
• Date: Sat, 26 Oct 2024 12:33:00 GMT
• Title: Prediction of chaotic dynamics and extreme events: A recurrence-free quantum reservoir computing approach
• Authors: Osama Ahmed, Felix Tennie, Luca Magri,
• Abstract summary: Reservoir computers can time-accurately predict extreme events and chaotic dynamics, but they may require many degrees of freedom. We design reservoir computers with compact reservoirs and accurate prediction capabilities. This work opens new opportunities for using quantum machine learning on near-term quantum computers.
• Score: 3.7960472831772765
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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 ans\"atze 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 ans\"atze 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.

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