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arXiv:2505.22575 · Chaos An Interdisciplinary Journal of Nonlinear Science

Minimal quantum reservoirs with Hamiltonian encoding

Gerard McCaul, Juan Sebastian Totero Gongora, Wendy Otieno, Sergey E. Savel'ev, Alexandre M. Zagoskin, Alexander G. Balanov

Published Sep 1, 2025• 11 citations
arXivHTMLPDF

Abstract

We investigate a minimal architecture for quantum reservoir computing based on Hamiltonian encoding, in which input data are injected via modulation of system parameters rather than state preparation. This approach circumvents many of the experimental overheads typically associated with quantum machine learning, enabling computation without feedback, memory, or state tomography. We demonstrate that such a minimal quantum reservoir, despite lacking intrinsic memory, can perform nonlinear regression and prediction tasks when augmented with post-processing delay embeddings. Our results provide a conceptually and practically streamlined framework for quantum information processing, offering a clear baseline for future implementations on near-term quantum hardware.

DOI
10.1063/5.0282921

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We investigate a minimal architecture for quantum reservoir computing based on Hamiltonian encoding, in which input data are injected via modulation of system parameters rather than state preparation. This approach circumvents many of the experimental overheads typically associated with quantum machine learning, enabling computation without feedback, memory, or state tomography. We demonstrate that such a minimal quantum reservoir, despite lacking intrinsic memory, can perform nonlinear regression and prediction tasks when augmented with post-processing delay embeddings. Our results provide a conceptually and practically streamlined framework for quantum information processing, offering a clear baseline for future implementations on near-term quantum hardware.
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Quantum learning provides a versatile paradigm for information processing by exploiting the intrinsic representational capacity of high-dimensional Hilbert spaces. Here, we investigate a Hamiltonian-encoding framework for quantum reservoir computing that simultaneously addresses three key challenges in quantum learning: trainability, hardware efficiency, and information stability. In this framework, input data are directly mapped onto a fixed Hamiltonian and transformed into expressive nonlinear features through quantum dynamical evolution. By employing the reservoir-computing paradigm, the approach naturally circumvents the barren plateau problem in quantum learning landscapes. We validate the framework across two complementary platforms: an analog superconducting array processor and a digital gate-based quantum circuit implementation. Despite their fundamentally different realizations, both platforms exhibit comparable representational power and achieve competitive learning performance, establishing a unified framework for cross-platform quantum learning. While both implementations achieve comparable performance, the analog processor may offer a more hardware-efficient realization by bypassing the temporal overhead of gate-based decomposition and thereby making more effective use of finite coherence times, albeit at the expense of universality. Furthermore, we find that finite dissipation suppresses quantum-scrambling-induced instabilities at long evolution times and can enhance learning performance, revealing a constructive role for environmental coupling in stabilizing quantum learning dynamics. Collectively, these results establish Hamiltonian-encoded reservoir computing as a compact, expressive, and hardware-efficient paradigm for quantum learning on current-generation quantum platforms.
A distinctive feature of Quantum Reservoir Computing (QRC) is the ability to directly embed quantum input states into the reservoir dynamics. However, the resulting output is fundamentally linear for a single input state, preventing QRC from naturally computing nonlinear functionals such as purity or entropy. We overcome this limitation with a quantum-classical hybrid architecture combining a qubit quantum reservoir with a classical echo state network (ESN), allowing both nonlinear functional approximation and effective temporal processing. We systematically study performance under two information regimes: full-tomography and partial information (single-axis measurements), with the latter demonstrating that the hybrid system outperforms its standalone components in both linear and nonlinear tasks due to the enhanced information retrieval provided by the quantum reservoir. Building on these results, we apply an online monitoring protocol that explicitly accounts for measurement back-action and finite measurement ensembles, enabling a realistic assessment of performance under experimental conditions. These results establish hybrid quantum-classical reservoir computing (HRC) architectures as a practical and scalable route for enhanced quantum machine learning on near-term qubit hardware.
Reservoir computing (RC) is an effective method for predicting chaotic systems by using a high-dimensional dynamic reservoir with fixed internal weights, while keeping the learning phase linear, which simplifies training and reduces computational complexity compared to fully trained recurrent neural networks (RNNs). Quantum reservoir computing (QRC) uses the exponential growth of Hilbert spaces in quantum systems, allowing for greater information processing, memory capacity, and computational power. However, the original QRC proposal requires coherent injection of inputs multiple times, complicating practical implementation. We present a hybrid quantum-classical approach that implements memory through classical post-processing of quantum measurements. This approach avoids the need for multiple coherent input injections and is evaluated on benchmark tasks, including the chaotic Mackey-Glass time series prediction. We tested our model on two physical platforms: a fully connected Ising model and a Rydberg atom array. The optimized model demonstrates promising predictive capabilities, achieving a higher number of steps compared to previously reported approaches.
We investigate quantum reservoir computing (QRC) using a hybrid qubit-boson system described by the Jaynes-Cummings (JC) Hamiltonian and its dispersive limit (DJC). These models provide high-dimensional Hilbert spaces and intrinsic nonlinear dynamics, making them powerful substrates for temporal information processing. We systematically benchmark both reservoirs through linear and nonlinear memory tasks, demonstrating that they exhibit an unusual superior nonlinear over linear memory capacity. We further test their predictive performance on the Mackey-Glass time series, a widely used benchmark for chaotic dynamics, and show comparable forecasting ability. We also investigate how memory and prediction accuracy vary with reservoir parameters and show the role of higher-order bosonic observables and time multiplexing in enhancing expressivity, even in minimal spin-boson configurations. Our results establish JC- and DJC-based reservoirs as versatile platforms for time-series processing and as elementary units that overcome the setting of equivalent qubit pairs and offer pathways toward tunable, high-performance quantum machine learning architectures.
Quantum reservoir computing (QRC) harnesses quantum systems to tackle intricate computational problems with exceptional efficiency and minimized energy usage. This paper presents a QRC framework that utilizes a minimalistic quantum reservoir, consisting of only a few two-level atoms within an optical cavity. The system is inherently scalable, as newly added atoms automatically couple with the existing ones through the shared cavity field. We demonstrate that the quantum reservoir outperforms traditional classical reservoir computing in both memory retention and nonlinear data processing through two tasks, namely, the prediction of time-series data using the Mackey-Glass task and the classification of sine-square waveforms. Our results show significant performance improvements with an increasing number of atoms, facilitated by nondestructive, continuous quantum measurements and polynomial regression techniques. These findings confirm the potential of QRC as a practical and efficient solution to addressing complex computational challenges in quantum machine learning.