Fisher-Orthogonal Memory in Quantum Reservoir Computing

Abstract:Quantum reservoir computing processes temporal information through driven many-body dynamics, but its performance is ultimately limited by how accurately past inputs can be extracted from finite measurements. Here we formulate this limitation as a local multiparameter estimation problem and introduce a delay-space quantum Fisher information matrix to quantify the distinguishability of memory traces. This perspective identifies Fisher-orthogonal memory as a measurement-efficient design principle: different delays should perturb the reservoir state along statistically independent directions. We first analyze the single-qubit limit using the Gill--Massar bound, revealing an optimal write-store-routing trade-off. Guided by this structure, we construct solvable multi-qubit reservoirs based on Clifford routing orbits and Singer-cycle Pauli algebra. The resulting dynamics yield diagonal, analytically programmable Fisher memory matrices with controlled dissipation profiles. Under finite-shot local Pauli readout, these reservoirs retain sharp memory windows and substantially improve over optimized random Ising reservoirs for both linear delay reconstruction and nonlinear product-delay tasks. The nonlinear advantage is traced to second-order response channels that inherit the same Pauli-routing structure. Our results provide an analytically controlled route toward measurement-efficient quantum reservoir computing.

arXiv:2607.29219 [quant-ph]

(or arXiv:2607.29219v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.29219 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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