Liouvillian Response for Temporal Information in Quantum Reservoir Computing

Abstract:Open quantum systems offer a physical substrate for temporal information processing in quantum reservoir computing, yet the microscopic mechanisms linking their dynamics to computational performance remain unclear. Here we establish a microscopic response-to-performance framework that connects Liouvillian dynamics directly to task performance. We decompose observable Volterra weights as $W^{(q)}=BH^{(q)}$, separating internal input-history pathways from their readout visibility, and show that a dynamical response contributes to a task only if it is input-generated, readout-visible, target-correlated, and resolvable above the regularization scale. This framework reveals how Liouvillian modes govern the retention and propagation of task-relevant information, while symmetries determine which components remain visible to the readout. It further establishes how distinct covariance modes encode different temporal information structures and how system parameters and processing protocols can reshape their contributions to improve QRC performance. Thermalization drives the reservoir from processing that retains input history to a response dominated by the most recent input before regularization suppresses the residual information. We finally show that weak measurement can activate task-relevant covariance modes by lifting symmetry-imposed channel equivalence, whereas delayed feedback creates controlled return pathways for historical information. These results establish a microscopic connection between open-system dynamics and computational performance, providing principles for engineering task-relevant information flow in quantum reservoirs.

arXiv:2609.23429 [quant-ph]

(or arXiv:2609.23429v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.23429 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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