Density matrix emulation of quantum recurrent neural networks for multivariate time series prediction
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,...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2025-01-01
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| Series: | Machine Learning: Science and Technology |
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| Online Access: | https://doi.org/10.1088/2632-2153/ad9431 |
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| author | J D Viqueira D Faílde M M Juane A Gómez D Mera |
| author_facet | J D Viqueira D Faílde M M Juane A Gómez D Mera |
| author_sort | J D Viqueira |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-41a5718ee5564d02b9054814d669cbe5 |
| institution | DOAJ |
| issn | 2632-2153 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj-art-41a5718ee5564d02b9054814d669cbe52025-08-20T03:02:54ZengIOP PublishingMachine Learning: Science and Technology2632-21532025-01-016101502310.1088/2632-2153/ad9431Density matrix emulation of quantum recurrent neural networks for multivariate time series predictionJ D Viqueira0https://orcid.org/0000-0002-0041-6802D Faílde1https://orcid.org/0000-0002-7685-4331M M Juane2https://orcid.org/0009-0005-0692-7098A Gómez3https://orcid.org/0000-0001-7272-8488D Mera4https://orcid.org/0000-0002-0639-6574Galicia Supercomputing Center (CESGA) , 15705 Santiago de Compostela, Spain; Computer Graphics and Data Engineering (COGRADE), Departamento de Electrónica e Computación, Universidade de Santiago de Compostela , 15782 Santiago de Compostela, SpainGalicia Supercomputing Center (CESGA) , 15705 Santiago de Compostela, SpainGalicia Supercomputing Center (CESGA) , 15705 Santiago de Compostela, SpainGalicia Supercomputing Center (CESGA) , 15705 Santiago de Compostela, SpainComputer Graphics and Data Engineering (COGRADE), Departamento de Electrónica e Computación, Universidade de Santiago de Compostela , 15782 Santiago de Compostela, SpainQuantum 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.https://doi.org/10.1088/2632-2153/ad9431quantum computingmachine learningtime series prediction |
| spellingShingle | J D Viqueira D Faílde M M Juane A Gómez D Mera Density matrix emulation of quantum recurrent neural networks for multivariate time series prediction Machine Learning: Science and Technology quantum computing machine learning time series prediction |
| title | Density matrix emulation of quantum recurrent neural networks for multivariate time series prediction |
| title_full | Density matrix emulation of quantum recurrent neural networks for multivariate time series prediction |
| title_fullStr | Density matrix emulation of quantum recurrent neural networks for multivariate time series prediction |
| title_full_unstemmed | Density matrix emulation of quantum recurrent neural networks for multivariate time series prediction |
| title_short | Density matrix emulation of quantum recurrent neural networks for multivariate time series prediction |
| title_sort | density matrix emulation of quantum recurrent neural networks for multivariate time series prediction |
| topic | quantum computing machine learning time series prediction |
| url | https://doi.org/10.1088/2632-2153/ad9431 |
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