8/19/2023 0 Comments Compact machines quantum entangler![]() Furthermore, classical or quantum physical systems are also amenable to be used as the dynamical system 13– 15, paving the way to harvesting computational power from essentially random physical systems with fading memory and complex dynamics. ![]() ![]() This is known as reservoir computing (RC), which is a powerful approach to solving temporal tasks thanks to a remarkably low training cost 10, 11 combined with state-of-the-art performance 12. Under typically mild conditions the input time series can be used to drive random dynamical systems such that their internal variables become such fading memory functions, which can then be combined to approximate the desired ouput by training a simple, even linear readout function. This is possible in particular for tasks that can be solved by so called fading memory functions, which are functions well approximated by continuous functions of only a finite number of past inputs 9. When successful, online time series processing facilitates, e.g., the processing of arbitrarily long sequences of data since the inputs are continuously processed into outputs. Such tasks are also known as temporal tasks. Instead, the objective is to realize the time dependent function which for a given timestep and input time series up to that step returns the corresponding element of the output time series. In online time series processing both the given data and desired transformed data are functions of time, which separates it from approaches such as first recording the data and later processing it. Tasks where one time series need to be transformed into another include time series forecasting 1, 2, pattern generation 3, 4 and pattern recognition 5– 8. Finally, we discuss partial generalizations where only the input or only the output time series is quantum. We illustrate its power by generalizing two paradigmatic benchmark tasks from classical reservoir computing to quantum information and introducing a task without a classical analogue where a random system is trained to both create and distribute entanglement between systems that never directly interact. Here we propose a reservoir computing inspired approach to online processing of time series consisting of quantum information, sidestepping the measurement problem. Extracting the output from a quantum system without disturbing its state too much is problematic however, and can be expected to become a bottleneck in such approaches. Recently the use of random quantum systems has been proposed, leveraging the complexity of quantum dynamics for classical time series processing. It has reached state-of-the-art performance in tasks such as chaotic time series prediction and continuous speech recognition thanks to its unique combination of high computational power and low training cost which sets it aside from alternatives such as traditionally trained recurrent neural networks, and furthermore is amenable to implementations in dedicated hardware, potentially leading to extremely compact and efficient reservoir computers. Reservoir computing is a powerful machine learning paradigm for online time series processing.
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