Storage, Scrambling, and Loss of Information in the Quantum Reservoir Computing Paradigm
The suitability of a quantum reservoir computing (QRC) platform for a given time-series processing task is closely tied to the dynamical properties of its computational substrate and design. Information is injected into, processed by, and read from this substrate, and finally passed to a linear readout layer which is trained to perform a specific task. In this work we introduce a classical-quantum state derived from the process tensor representing the dynamical part of this process for typical QRC protocols found in the literature. Using this object, mutual informations between physical subsystems and subsets of past inputs can be written as Holevo quantities, which we then use to numerically investigate information saturation in the substrate, fading memory of past inputs, and the local accessibility of injected information for a commonly used QRC platform. We then extract two diagnostics that characterise the nonlocal scrambling of information within, and loss of information from the substrate, and compare these to QRC performance across Hamiltonian parameters and measurement strengths. Finally, we comment on future directions that the framework introduced here opens up for the study and extension of the QRC program.