Taking advantage of noise in quantum reservoir computing

Delayed self-feedback echo state network for long-term dynamics of hyperchaotic systems

Analyzing the long-term behavior of hyperchaotic systems poses formidable challenges in the field of nonlinear science. This paper proposes a data-driven model called the delayed self-feedback echo state network (self-ESN) specifically designed for the evolution behavior of hyperchaotic systems. Self-ESN incorporates a delayed self-feedback term into the dynamic equation of a reservoir to reflect the finite transmission speed of neuron signals. Delayed self-feedback establishes a connection between the current and previous m time steps of the reservoir state and provides an effective means to capture the dynamic characteristics of the system, thereby significantly improving memory performance. In addition, the concept of local echo state property (ESP) is introduced to relax the conventional ESP condition, and theoretical analysis is conducted on guiding the selection of feedback delay and gain to ensure the local ESP. The judicious selection of feedback gain and delay in self-ESN improves prediction accuracy and overcomes the challenges associated with obtaining optimal parameters of the reservoir in conventional ESN models. Numerical experiments are conducted to assess the long-term prediction capabilities of the self-ESN across various scenarios, including a 4D hyperchaotic system, a hyperchaotic network, and an infinite-dimensional delayed chaotic system. The experiments involve reconstructing bifurcation diagrams, predicting the chaotic synchronization, examining spatiotemporal evolution patterns, and uncovering the hidden attractors. The results underscore the capability of the proposed self-ESN as a strategy for long-term prediction and analysis of the complex systems.

Heterogeneous reservoir computing in second-order Ta2O5/HfO2 memristors

Multiple switching modes in a Ta2O5/HfO2 memristor are studied experimentally and numerically through a reservoir computing (RC) simulation to reveal the importance of nonlinearity and heterogeneity in the RC framework. Unlike most studies, where homogeneous reservoirs are used, heterogeneity is introduced by combining different behaviors of the memristor units. The chosen memristor for the reservoir units is based on a Ta2O5/HfO2 bilayer, in which the conductances of the Ta2O5 and HfO2 layers are controlled by the oxygen vacancies and deep/shallow traps, respectively, providing both volatile and non-volatile resistive switching modes. These several control parameters make the second-order Ta2O5/HfO2 memristor system present different behaviors in agreement with its history-dependent conductance and allow the fine-tuning of the behavior of each reservoir unit. The heterogeneity in the reservoir units improves the pattern recognition performance in the heterogeneous memristor RC system with a similar physical structure.

Reconstructing bifurcation diagrams of chaotic circuits with reservoir computing

Model-free reconstruction of bifurcation diagrams of Chua's circuits using the technique of parameter-aware reservoir computing is investigated. We demonstrate that (1) reservoir computer can be utilized as a noise filter to restore the system dynamics from noisy signals; (2) for a single Chua circuit, a machine trained by the noisy time series measured at several sampling states is capable of reconstructing the whole bifurcation diagram of the circuit with a high precision; and (3) for two coupled chaotic Chua circuits with mismatched parameters, the machine trained by the noisy time series measured at several coupling strengths is able to anticipate the variation of the synchronization degree of the coupled circuits with respect to the coupling strength over a wide range. Our studies verify the capability of the technique of parameter-aware reservoir computing in learning the dynamics of chaotic circuits from noisy signals, signifying the potential application of this technique in reconstructing the bifurcation diagram of real-world chaotic systems.

Optimizing quantum noise-induced reservoir computing for nonlinear and chaotic time series prediction

Quantum reservoir computing is strongly emerging for sequential and time series data prediction in quantum machine learning. We make advancements to the quantum noise-induced reservoir, in which reservoir noise is used as a resource to generate expressive, nonlinear signals that are efficiently learned with a single linear output layer. We address the need for quantum reservoir tuning with a novel and generally applicable approach to quantum circuit parameterization, in which tunable noise models are programmed to the quantum reservoir circuit to be fully controlled for effective optimization. Our systematic approach also involves reductions in quantum reservoir circuits in the number of qubits and entanglement scheme complexity. We show that with only a single noise model and small memory capacities, excellent simulation results were obtained on nonlinear benchmarks that include the Mackey-Glass system for 100 steps ahead in the challenging chaotic regime.

Binding affinity predictions with hybrid quantum-classical convolutional neural networks

Central in drug design is the identification of biomolecules that uniquely and robustly bind to a target protein, while minimizing their interactions with others. Accordingly, precise binding affinity prediction, enabling the accurate selection of suitable candidates from an extensive pool of potential compounds, can greatly reduce the expenses associated to practical experimental protocols. In this respect, recent advances revealed that deep learning methods show superior performance compared to other traditional computational methods, especially with the advent of large datasets. These methods, however, are complex and very time-intensive, thus representing an important clear bottleneck for their development and practical application. In this context, the emerging realm of quantum machine learning holds promise for enhancing numerous classical machine learning algorithms. In this work, we take one step forward and present a hybrid quantum-classical convolutional neural network, which is able to reduce by 20% the complexity of the classical counterpart while still maintaining optimal performance in the predictions. Additionally, this results in a significant cost and time savings of up to 40% in the training stage, which means a substantial speed-up of the drug design process.