Minimalistic and Scalable Quantum Reservoir Computing Enhanced with Feedback

Abstract: Quantum Reservoir Computing (QRC) leverages quantum systems to perform complex computational tasks with exceptional efficiency and reduced energy consumption. We introduce a minimalistic QRC framework utilizing only a few two-level atoms in a single-mode optical cavity, combined with continuous quantum measurements. To achieve high computational expressivity with minimal hardware, we include two critical elements: reservoir feedback and polynomial regression. Reservoir feedback modifies the reservoir's dynamics without altering its hardware, while polynomial regression enhances output resolution by nonlinearly extending expressions. We evaluate QRC's memory retention and nonlinear data processing through two tasks: predicting chaotic time-series data via the Mackey-Glass task and classifying sine-square waveforms. Our results demonstrate significant QRC performance with minimal reservoirs containing as few as five atoms, further enhanced by feedback mechanisms and polynomial regression. This framework fulfills QRC's objectives to minimize hardware size and energy consumption, marking a significant advancement in integrating quantum physics with machine learning technology.