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Scar theory is one of the fundamental pillars in the field of quantum chaos, and scarred functions a superb tool to carry out studies in it. Several methods, usually semiclassical, have been described to cope with these two phenomena. In this paper, we present an alternative method, based on the novel machine learning algorithm known as Reservoir Computing, to calculate such scarred wavefunctions together with the associated eigenstates of the system. The resulting methodology achieves outstanding accuracy while reducing execution times by a factor of ten. As an illustration of the effectiveness of this method, we apply it to the widespread chaotic two-dimensional coupled quartic oscillator., Comment: arXiv admin note: text overlap with arXiv:2310.07455

The emerging technology of quantum reservoir computing (QRC) stands out in the noisy-intermediate scale quantum era (NISQ) for its exceptional efficiency and adaptability. By harnessing the power of quantum computing, it holds a great potential to untangle complex economic markets, as demonstrated here in an application to food price crisis prediction - a critical effort in combating food waste and establishing sustainable food chains. Nevertheless, a pivotal consideration for its success is the optimal design of the quantum reservoirs, ensuring both high performance and compatibility with current devices. In this paper, we provide an efficient criterion for that purpose, based on the complexity of the reservoirs. Our results emphasize the crucial role of optimal design in the algorithm performance, especially in the absence of external regressor variables, showcasing the potential for novel insights and transformative applications in the field of time series prediction using quantum computing.

The field of drug discovery hinges on the accurate prediction of binding affinity between prospective drug molecules and target proteins, especially when such proteins directly influence disease progression. However, estimating binding affinity demands significant financial and computational resources. While state-of-the-art methodologies employ classical machine learning (ML) techniques, emerging hybrid quantum machine learning (QML) models have shown promise for enhanced performance, owing to their inherent parallelism and capacity to manage exponential increases in data dimensionality. Despite these advances, existing models encounter issues related to convergence stability and prediction accuracy. This paper introduces a novel hybrid quantum-classical deep learning model tailored for binding affinity prediction in drug discovery. Specifically, the proposed model synergistically integrates 3D and spatial graph convolutional neural networks within an optimized quantum architecture. Simulation results demonstrate a 6% improvement in prediction accuracy relative to existing classical models, as well as a significantly more stable convergence performance compared to previous classical approaches., Comment: 5 pages, 3 figures

The biggest challenge that quantum computing and quantum machine learning are currently facing is the presence of noise in quantum devices. As a result, big efforts have been put into correcting or mitigating the induced errors. But, can these two fields benefit from noise? Surprisingly, we demonstrate that under some circumstances, quantum noise can be used to improve the performance of quantum reservoir computing, a prominent and recent quantum machine learning algorithm. Our results show that the amplitude damping noise can be beneficial to machine learning, while the depolarizing and phase damping noises should be prioritized for correction. This critical result sheds new light into the physical mechanisms underlying quantum devices, providing solid practical prescriptions for a successful implementation of quantum information processing in nowadays hardware., Comment: 6 pages, 3 figures

One of the main challenges in drug discovery is to find molecules that bind specifically and strongly to their target protein while having minimal binding to other proteins. By predicting binding affinity, it is possible to identify the most promising candidates from a large pool of potential compounds, reducing the number of compounds that need to be tested experimentally. Recently, deep learning methods have shown superior performance than traditional computational methods for making accurate predictions on large datasets. However, the complexity and time-consuming nature of these methods have limited their usage and development. Quantum machine learning is an emerging technology that has the potential to improve many classical machine learning algorithms. In this work we present a hybrid quantum-classical convolutional neural network, which is able to reduce by 20% the complexity of the classical network while maintaining optimal performance in the predictions. Additionally, it results in a significant time savings of up to 40% in the training process, which means a meaningful speed up of the drug discovery process., Comment: 14 pages, 10 figures

Universal fault-tolerant quantum computers require millions of qubits with low error rates. Since this technology is years ahead, noisy intermediate-scale quantum (NISQ) computation is receiving tremendous interest. In this setup, quantum reservoir computing is a relevant machine learning algorithm. Its simplicity of training and implementation allows to perform challenging computations on today available machines. In this Letter, we provide a criterion to select optimal quantum reservoirs, requiring few and simple gates. Our findings demonstrate that they render better results than other commonly used models with significantly less gates, and also provide insight on the theoretical gap between quantum reservoir computing and the theory of quantum states complexity.

Reservoir computing is a machine learning algorithm that excels at predicting the evolution of time series, in particular, dynamical systems. Moreover, it has also shown superb performance at solving partial differential equations. In this work, we adapt this methodology to integrate the time-dependent Schr\"odinger equation, propagating an initial wavefunction in time. Since such wavefunctions are complex-valued high-dimensional arrays the reservoir computing formalism needs to be extended to cope with complex-valued data. Furthermore, we propose a multi-step learning strategy that avoids overfitting the training data. We illustrate the performance of our adapted reservoir computing method by application to four standard problems in molecular vibrational dynamics.