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arXiv:2505.02491 · npj Quantum Information

Non-Markovianity and memory enhancement in quantum reservoir computing

Antonio Sannia, Ricard Ravell Rodríguez, Gian Luca Giorgi, Roberta Zambrini

Published May 8, 2026• 4 citations
arXivHTMLPDF

Abstract

Featuring memory of past inputs is a fundamental requirement for machine learning models processing time-dependent data. In quantum reservoir computing, all architectures proposed so far rely on Markovian dynamics, which, as we prove, inherently lead to an exponential decay of past information, thereby limiting long-term memory capabilities. We demonstrate that non-Markovian dynamics can overcome this limitation, enabling extended memory retention. By analytically deriving memory bounds and supporting our findings with numerical simulations, we show that non-Markovian reservoirs can outperform their Markovian counterparts, particularly in tasks that require a coexistence of short- and long-term correlations. We introduce an embedding approach that allows a controlled transition from Markovian to non-Markovian evolution, providing a path for practical implementations. Our results establish quantum non-Markovianity as a key resource for enhancing memory in quantum machine learning architectures, with broad implications in quantum neural networks.

DOI
10.1038/s41534-026-01257-4

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Featuring memory of past inputs is a fundamental requirement for machine learning models processing time-dependent data. In quantum reservoir computing, all architectures proposed so far rely on Markovian dynamics, which, as we prove, inherently lead to an exponential decay of past information, thereby limiting long-term memory capabilities. We demonstrate that non-Markovian dynamics can overcome this limitation, enabling extended memory retention. By analytically deriving memory bounds and supporting our findings with numerical simulations, we show that non-Markovian reservoirs can outperform their Markovian counterparts, particularly in tasks that require a coexistence of short- and long-term correlations. We introduce an embedding approach that allows a controlled transition from Markovian to non-Markovian evolution, providing a path for practical implementations. Our results establish quantum non-Markovianity as a key resource for enhancing memory in quantum machine learning architectures, with broad implications in quantum neural networks.
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The control of open-system dynamics provides a powerful mechanism for using quantum information to process sequential tasks. While quantum reservoir computing typically relies on Markovian dissipation to process sequential data, the computational role of non-Markovian memory effects remains largely unexplored. We introduce a framework for quantum reservoir computing where non-Markovianity is explicitly modeled and regulated using fractional derivatives. By employing fractional time subordination, we generate tunable, heavy-tailed relaxation dynamics that govern the information backflow between the system and its environment. Non-Markovian information backflow regulates the overall temporal retention of the system, maximizing short-term linear memory capacity. Within an optimal operating regime, fractional non-Markovianity redistributes the reservoir memory towards recent inputs, improving both linear memory capacity and nonlinear prediction accuracy at short delays, at the expense of long-range temporal retention. System-environment interaction proves being not merely a requirement for quantum reservoir computing, but an active resource that embeds memory retention directly into the quantum evolution.
Quantum Reservoir Computing (QRC) processes temporal data by retaining a memory of past inputs in the recurrent state of a quantum system, whereas a Quantum Extreme-Learning Machine (QELM) discards that memory, resetting the system at every step so that only the most recent input shapes the response. The two are usually treated as separate computational paradigms. We show that they are the two limits of a single architecture, connected by the input-encoding length, that is, the number of qubits overwritten with fresh data at each step. When a single qubit is re-encoded the system operates as a standard QRC, when the whole register is re-encoded it operates as a QELM, and intermediate lengths interpolate between them. The overwritten qubits hold the recent past in an explicit register, while the remaining qubits are never reset and carry older inputs forward in their evolving quantum state, so the encoding length redistributes memory between explicit and recurrent storage at fixed system size. Tuning the reservoir Hamiltonian and the evolution time with Bayesian optimization at each encoding length, we find that recurrent quantum memory is essential when a task must reach far into the past, and dispensable when the relevant history is short, where the memoryless reset limit already suffices. For every task the best reservoirs operate at the edge of chaos, where they perform as well as a densely connected reservoir with random all-to-all couplings of the same size, indicating that what temporal processing requires is the dynamical regime rather than the connectivity.
We propose a Hamiltonian-level framework for non-Markovian quantum reservoir computing directly tailored for analog hardware implementations. By dividing the reservoir into a system block and an environment block and evolving their joint state under a unified Hamiltonian, our architecture naturally embeds memory backflow by harnessing entanglement-induced information backflow with tunable coupling strengths. Numerical benchmarks on short-term memory tasks demonstrate that operating in non-Markovian regimes yields significantly slower memory decay compared to the Markovian limit. Further analyzing the echo-state property (ESP), showing that the non-Markovian quantum reservoir evolves from two different initial states, they do not converge to the same trajectory even after a long time, strongly suggesting that the ESP is effectively violated. Our work provides the first demonstration in quantum reservoir computing that strong non-Markovianity can fundamentally violate the ESP, such that conventional linear-regression readouts fail to deliver stable training and inference. Finally, we experimentally showed that, with an appropriate time-evolution step size, the non-Markovian reservoir exhibits superior performance on higher-order nonlinear autoregressive moving-average(NARMA) tasks.
Reservoir computing is a versatile paradigm in computational neuroscience and machine learning that uses recurrent neural networks to process time-dependent inputs. We leverage noise in gate-based quantum computers to enforce the fading memory property of a quantum circuit acting as a reservoir. We test the learning architecture on standard bench-marking tasks, such as NARMA and short-term memory tasks, by providing numerical evidence supporting the existence of an optimal noise regime that enhances predictive performances. This critical behavior indicates the presence of a regime in which several network capabilities, such as short-term memory capacity and expressivity, are maximized. Our results pave the way for the efficient use of current noisy quantum devices in quantum machine learning applications.
We use a Quantum Extreme Learning Machine for characterizing and estimating parameters of quantum dynamics generated by a tunable collision model. The input to the learning protocol consists of quantum states produced by successive system environment interactions, while the reservoir is implemented as a disordered many body quantum system evolving under a fixed Hamiltonian. We systematically explore how extending the QELM feature space, through the inclusion of temporal information and additional observables, affects estimation performance. Our results demonstrate that temporal extensions of the feature vector consistently and significantly enhance estimation accuracy relative to the baseline protocol. Notably, incorporating memory from earlier time steps yields the most substantial and robust improvements, whereas extensions based solely on additional observables offer only marginal gains. Crucially, the advantage conferred by temporal memory becomes increasingly pronounced as the dynamics become more strongly non Markovian, indicating that environmental memory effects serve as a constructive resource for learning.