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IEEE International Conference on Quantum Computing and Engineering (QCE)

Enforcing Fading Memory of Noisy Quantum Echo State Networks

Francesco Monzani, Emanuele Ricci, Luca Nigro, Enrico Prati

Published Sep 15, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.1109/qce60285.2024.10363

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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 identify a noise model that ensures the functioning of an echo state network employing a gate-based quantum computer for reservoir computing applications. Energy dissipation induced by amplitude damping drastically improves the short-term memory capacity and expressivity of the network, by simultaneously providing fading memory and richer dynamics. There is an ideal dissipation rate that ensures the best operation of the echo state network around γ∼γ\simγ∼ 0.03. Nevertheless, these beneficial effects are stable as the intensity of the applied noise increases. The improvement of the learning is confirmed by emulating a realistic noise model applied to superconducting qubits, paving the way for the application of reservoir computing methods in current non-fault-tolerant quantum computers.
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.
Reservoir computing promises a fast method for handling large amounts of temporal data. This hinges on constructing a good reservoir--a dynamical system capable of transforming inputs into a high-dimensional representation while remembering properties of earlier data. In this work, we introduce a reservoir based on recurrent quantum feature maps where a fixed quantum circuit is reused to encode both current inputs and a classical feedback signal derived from previous outputs. We evaluate the model on the Mackey-Glass time-series prediction task using our recently introduced CP feature map, and find that it achieves lower mean squared error than standard classical baselines, including echo state networks and multilayer perceptrons, while maintaining compact circuit depth and qubit requirements. We further analyze memory capacity and show that the model effectively retains temporal information, consistent with its forecasting accuracy. Finally, we study the impact of realistic noise and find that performance is robust to several noise channels but remains sensitive to two-qubit gate errors, identifying a key limitation for near-term implementations.
Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we approach sequential modeling by applying a reservoir computing (RC) framework to quantum recurrent neural networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea to this RC approach is that the QRNN with randomly initialized weights is treated as a dynamical system and only the final classical linear layer is trained. Our numerical simulations show that the QRNN-RC can reach results comparable to fully trained QRNN models for several function approximation and time series prediction tasks. Since the QRNN training complexity is significantly reduced, the proposed model trains notably faster. In this work we also compare to corresponding classical RNN-based RC implementations and show that the quantum version learns faster by requiring fewer training epochs in most cases. Our results demonstrate a new possibility to utilize quantum neural network for sequential modeling with greater quantum hardware efficiency, an important design consideration for noisy intermediate-scale quantum (NISQ) computers.
Recent advancements in artificial neural networks have enabled impressive tasks on classical computers, but they demand significant computational resources. While quantum computing offers potential beyond classical systems, the advantages of quantum neural networks (QNNs) remain largely unexplored. In this work, we present and examine a quantum circuit (QC) that implements and aims to improve upon the classical echo-state network (ESN), a type of reservoir-based recurrent neural networks (RNNs), using quantum computers. Typically, ESNs consist of an extremely large reservoir that learns high-dimensional embeddings, enabling prediction of complex system trajectories. Quantum echo-state networks (QESNs) aim to reduce this need for prohibitively large reservoirs by leveraging the unique capabilities of quantum computers, potentially allowing for more efficient and higher performing time-series prediction algorithms. The proposed QESN can be implemented on any digital quantum computer implementing a universal gate set, and does not require any sort of stopping or re-initialization of the circuit, allowing continuous evolution of the quantum state over long time horizons. We conducted simulated QC experiments on the chaotic Lorenz system, both with noisy and noiseless models, to demonstrate the circuit's performance and its potential for execution on noisy intermediate-scale quantum (NISQ) computers.
Quantum reservoir computing (QRC) offers a promising paradigm for harnessing quantum systems for machine learning tasks, especially in the era of noisy intermediate-scale quantum devices. While information-theoretical benchmarks like short-term memory capacity (STMC) are widely used to evaluate QRC performance, they fail to provide insights into the physical mechanisms underlying these quantum neural networks. We establish a quantitative connection between the optical absorption spectrum of a quantum reservoir and its memory performance, revealing that optimal STMC aligns directly with maximal absorption, providing a physical explanation for the previously reported "sweet-spot" behavior in QRC performance as a function of dissipation. This connection bridges quantum information theory with experimentally accessible physical properties, opening pathways for targeted engineering of quantum reservoir computers with optimized performance for specific tasks.