Emergent Recursive Kernels in Quantum Reservoir Computing
Abstract
Learning with a quantum reservoir can be far simpler than simulating its dynamics. We show that a quantum reservoir governed by a fixed evolution, consisting of an input coupling followed by an independently sampled Haar unitary, admits an exact recursive kernel in the large-dimension limit at fixed history length. Memory orthogonality and factorization of propagated overlaps reduce each kernel evaluation to a scalar recurrence, linear in history length and independent of reservoir size. We establish self-averaging around this limit and connect the kernel coefficients to out-of-time-ordered correlators. Our analysis of finite-dimensional effects shows that the computational simplicity of the Haar kernel does not come at the expense of expressive power. Moreover, we demonstrate how the kernel can be tuned for different learning tasks by adjusting properties such as memory retention and temporal interaction order. On the NARMA10 benchmark, the tuned kernel achieves lower prediction error than the tested Ising and Sachdev--Ye--Kitaev reservoirs.
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BibTeX
@misc{wang2026emergent,
title = {{Emergent Recursive Kernels in Quantum Reservoir Computing}},
author = {Ce Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34430},
eprint = {2610.34430},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34430},
}
RIS
TY - UNPB
TI - Emergent Recursive Kernels in Quantum Reservoir Computing
AU - Ce Wang
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34430
UR - https://arxiv.org/abs/2610.34430
AB - Learning with a quantum reservoir can be far simpler than simulating its dynamics. We show that a quantum reservoir governed by a fixed evolution, consisting of an input coupling followed by an independently sampled Haar unitary, admits an exact recursive kernel in the large-dimension limit at fixed history length. Memory orthogonality and factorization of propagated overlaps reduce each kernel evaluation to a scalar recurrence, linear in history length and independent of reservoir size. We establish self-averaging around this limit and connect the kernel coefficients to out-of-time-ordered correlators. Our analysis of finite-dimensional effects shows that the computational simplicity of the Haar kernel does not come at the expense of expressive power. Moreover, we demonstrate how the kernel can be tuned for different learning tasks by adjusting properties such as memory retention and temporal interaction order. On the NARMA10 benchmark, the tuned kernel achieves lower prediction error than the tested Ising and Sachdev--Ye--Kitaev reservoirs.
ER -