José Daniel Viqueira

José Daniel Viqueira, Daniel Faílde, Mariamo M. Juane et al.

Quantum Recurrent Neural Networks (QRNNs) are robust candidates for modelling and predicting future values in multivariate time series. However, the effective implementation of some QRNN models is limited by the need for mid-circuit measurements. Those increase the requirements for quantum hardware, which in the current NISQ era does not allow reliable computations. Emulation arises as the main near-term alternative to explore the potential of QRNNs, but existing quantum emulators are not dedicated to circuits with multiple intermediate measurements. In this context, we design a specific emulation method that relies on density matrix formalism. Using a compact tensor notation, we provide the mathematical formulation of the operator-sum representation involved. This allows us to show how the present and past information from a time series is transmitted through the circuit, and how to reduce the computational cost in every time step of the emulated network. In addition, we derive the analytical gradient and the Hessian of the network outputs with respect to its trainable parameters, which are needed when the outputs have stochastic noise due to hardware errors and a finite number of circuit shots (sampling). We finally test the presented methods using a hardware-efficient ansatz and four diverse datasets that include univariate and multivariate time series, with and without sampling noise. In addition, we compare the model with other existing quantum and classical approaches. Our results show how QRNNs can be trained with numerical and analytical gradients to make accurate predictions of future values by capturing non-trivial patterns of input series with different complexities.

Juan M. Murillo, Ignacio García Rodríguez de Guzmán, Enrique Moguel et al.

The first edition of the QuantumX track, held within the XXIX Jornadas de Ingeniería del Software y Bases de Datos (JISBD 2025), brought together leading Spanish research groups working at the intersection of Quantum Computing and Software Engineering. The event served as a pioneering forum to explore how principles of software quality, governance, testing, orchestration, and abstraction can be adapted to the quantum paradigm. The presented works spanned diverse areas (from quantum service engineering and hybrid architectures to quality models, circuit optimization, and quantum machine learning), reflecting the interdisciplinary nature and growing maturity of Quantum Computing and Quantum Software Engineering. The track also fostered community building and collaboration through the presentation of national and Ibero-American research networks such as RIPAISC and QSpain, and through dedicated networking sessions that encouraged joint initiatives. Beyond reporting on the event, this article provides a structured synthesis of the contributions presented at QuantumX, identifies common research themes and engineering concerns, and outlines a set of open challenges and future directions for the advancement of Quantum Software Engineering. This first QuantumX track established the foundation for a sustained research community and positioned Spain as an emerging contributor to the European and global quantum software ecosystem.