RT Journal Article
T1 Density matrix emulation of quantum recurrent neural networks for multivariate time series prediction
A1 Viqueira, José Daniel
A1 Faílde, Daniel
A1 Juane, Mariamo Mussa
A1 Gómez, Andrés
A1 Mera Pérez, David
K1 Quantum computing
K1 Machine learning
K1 Time series prediction
AB 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 noisy intermediate-scale quantum 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.
PB IOPScience
SN 2632-2153
YR 2025
FD 2025-01-30
LK https://hdl.handle.net/10347/43392
UL https://hdl.handle.net/10347/43392
LA eng
NO Viqueira, J. D., Faílde, D., Juane, M. M., Gómez, A., & Mera, D. (2025). Density matrix emulation of quantum recurrent neural networks for multivariate time series prediction. Machine Learning: Science and Technology, 6(1), 015023.
NO This work was supported by Axencia Galega de Innovación through the Grant Agreement ‘Despregamento dunha infraestructura baseada en tecnoloxías cuánticas da información que permita impulsar a I+D+I en Galicia’ within the program FEDER Galicia 2014-2020. This work was partially supported by the Galician Government under Grant ED431B 2024/44. A Gómez, D Faílde and M M Juane were supported by MICIN through the European Union NextGenerationEU recovery plan (PRTR-C17.I1), and by the Galician Regional Government through the ‘Planes Complementarios de I+D+I con las Comunidades Autónomas’ in Quantum Communication. J. D. Viqueira was supported by Axencia Galega de Innovación (Xunta de Galicia) through the ‘Programa de axudas á etapa predoutoral’. Simulations on this work were performed using Galicia Supercomputing Center (CESGA) FinisTerrae III supercomputer with financing from the Programa Operativo Plurirregional de Espa˜na 2014-2020 of ERDF, ICTS-2019-02-CESGA-3, and the Qmio quantum infrastructure, with financing from the European Union, through the Programa Operativo Galicia 2014-2020 of ERDF_REACT EU, as part of the European Union’s response to the COVID-19 pandemic.
DS Minerva
RD 23 abr 2026