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's 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.

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.

Quantum reservoir computing algorithms recently emerged as a standout approach in the development of successful methods for the noisy intermediate-scale quantum (NISQ) era because of its superb performance and compatibility with current quantum devices. By harnessing the properties and dynamics of a quantum system, quantum reservoir computing effectively uncovers hidden patterns in data. However, the design of the quantum reservoir is crucial to this end in order to ensure an optimal performance of the algorithm. In this work, we introduce a precise quantitative method with strong physical foundations based on the Krylov evolution to assess the wanted good performance in machine-learning tasks. Our results show that the Krylov approach to complexity strongly correlates with quantum reservoir performance, making it a powerful tool in the quest for optimally designed quantum reservoirs, which will pave the road to the implementation of successful quantum machine-learning methods.

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 Schrödinger 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.