Quantum reservoir computing with a superconducting resonator in the semi-classical regime

Quantum reservoir computing is a promising approach to quantum neural networks capable of solving hard learning tasks on both classical and quantum input data [1]. Multiple implementation schemes were proposed, using basis states of a qubit system [2], basis states of a system of coupled quantum oscillators [3], or field-quadratures of a system of parametrically coupled quantum oscillateurs [4] as reservoir neurons. However, experimental realizations were lacking. Here we implement experimentally reservoir computing on a quantum oscillator in the semi-classical regime. We use the fundamental mode of a superconducting resonator as a quantum oscillator, and its field quadratures as reservoir neurons. We sample the two quadratures multiple times for the same input data point in order to increase the number of effective neurons. We encode the input data in the amplitude of the resonant drive, and we set the amplitude range in the Kerr regime, in order to obtain the nonlinearity that is essential for data processing. We test the performance of the superconducting reservoir on a simple benchmark task for reservoir computing, that is sine and square waveform classification. This task specifically tests the memory of the neural network and thus its capacity to process temporal data series. We demodulate each pair of output neurons from a 20 ns oscillator emission. Using 8 samples per data point and thus 16 effective neurons, we obtain > 99% accuracy on this task. This is an improvement in terms of the number of necessary neurons compared to reservoir computing with classical oscillators : with a single spintronic nano-oscillator, this task requires 24 effective neurons [5]. This is the first experimental implementation of reservoir computing with superconducting circuits and an important step towards the experimental realization of quantum reservoir computing with the basis states of coupled quantum oscillators that will fully exploit the quantum nature of this system. [1] S. Ghosh, A. Opala, M. Matuszewski, T. Paterek, and T. C. H. Liew, "Quantum reservoir processing" npj Quantum Information 5, 23 (2019). [2] K. Fujii and K. Nakajima, "Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning", Physical Review Applied 8, 024030 (2017). [3] Julien Dudas, Baptiste Carles, Erwan Plouet, Alice Mizrahi, Julie Grollier, and Danijela Markovic, "Quantum reservoir computing implementation on coherently coupled quantum oscillators" npj Quantum Inf 9, 64 (2023). [4] G. Angelatos, S. Khan, and H. E. T¨ ureci, "Reservoir Computing Approach to Quantum State Measurement Gerasimos", ", Physical Review X 11, 041062 (2021). [5] M. Riou, F. A. Araujo, J. Torrejon, S. Tsunegi, G. Khalsa, D. Querlioz, P. Bortolotti, V. Cros, K. Yakushiji, A. Fukushima, H. Kubota, S. Yuasa, M. D. Stiles, and J. Grollier, "Neuromorphic Computing through Time-Multiplexing with a Spin-Torque Nano-Oscillator", , IEEE Trans Electron Devices, (2017)