Theory of the Edge-of-Chaos Advantage in Quantum Reservoir Computing
Abstract
Numerical studies suggest that quantum reservoir computing performs optimally near the edge of chaos, a behavior commonly attributed to a balance between memory retention and nonlinear information processing. Here we develop an explicit quantum reservoir model and rigorously analyze its chaotic regime and integrable point. In the chaotic regime, we show that Gaussian-unitary-ensemble statistics lead to rapid memory loss: learning performance decays exponentially with the storage time required by a temporal task. This decay limits the ability of chaotic reservoirs to learn long-range temporal dependencies. At the integrable point, described by a free-fermion model, we prove that amplitude encoding and a linear readout of fermionic two-point correlations cannot learn a representative class of nonlinear tasks coupling present and past inputs. Introducing interactions alleviates this obstruction. By identifying distinct limitations on memory retention in the chaotic regime and nonlinear processing at the integrable point, our analysis provides a theoretical basis for the observed edge-of-chaos advantage and guides the design of quantum reservoirs for temporal learning.
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BibTeX
@misc{cao2026theory,
title = {{Theory of the Edge-of-Chaos Advantage in Quantum Reservoir Computing}},
author = {Shuaifan Cao and Wei Xia and Xiaopeng Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05213},
eprint = {2610.05213},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05213},
}
RIS
TY - UNPB
TI - Theory of the Edge-of-Chaos Advantage in Quantum Reservoir Computing
AU - Shuaifan Cao
AU - Wei Xia
AU - Xiaopeng Li
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05213
UR - https://arxiv.org/abs/2610.05213
AB - Numerical studies suggest that quantum reservoir computing performs optimally near the edge of chaos, a behavior commonly attributed to a balance between memory retention and nonlinear information processing. Here we develop an explicit quantum reservoir model and rigorously analyze its chaotic regime and integrable point. In the chaotic regime, we show that Gaussian-unitary-ensemble statistics lead to rapid memory loss: learning performance decays exponentially with the storage time required by a temporal task. This decay limits the ability of chaotic reservoirs to learn long-range temporal dependencies. At the integrable point, described by a free-fermion model, we prove that amplitude encoding and a linear readout of fermionic two-point correlations cannot learn a representative class of nonlinear tasks coupling present and past inputs. Introducing interactions alleviates this obstruction. By identifying distinct limitations on memory retention in the chaotic regime and nonlinear processing at the integrable point, our analysis provides a theoretical basis for the observed edge-of-chaos advantage and guides the design of quantum reservoirs for temporal learning.
ER -