Data re-uploading for a universal quantum classifier

Adrián Pérez-Salinas; Alba Cervera-Lierta; Elies Gil-Fuster; José I. Latorre

doi:10.22331/q-2020-02-06-226

Data re-uploading for a universal quantum classifier

Adrián Pérez-Salinas^1,2, Alba Cervera-Lierta^1,2, Elies Gil-Fuster³, and José I. Latorre^1,2,4,5

¹Barcelona Supercomputing Center
²Institut de Ciències del Cosmos, Universitat de Barcelona, Barcelona, Spain
³Dept. Física Quàntica i Astrofísica, Universitat de Barcelona, Barcelona, Spain.
⁴Nikhef Theory Group, Science Park 105, 1098 XG Amsterdam, The Netherlands.
⁵Center for Quantum Technologies, National University of Singapore, Singapore.

Published:	2020-02-06, volume 4, page 226
Eprint:	arXiv:1907.02085v2
Doi:	https://doi.org/10.22331/q-2020-02-06-226
Citation:	Quantum 4, 226 (2020).

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Updated version: The authors have uploaded version v3 of this work to the arXiv which may contain updates or corrections not contained in the published version v2. The authors left the following comment on the arXiv:

19 pages, 9 figures

Abstract

A single qubit provides sufficient computational capabilities to construct a universal quantum classifier when assisted with a classical subroutine. This fact may be surprising since a single qubit only offers a simple superposition of two states and single-qubit gates only make a rotation in the Bloch sphere. The key ingredient to circumvent these limitations is to allow for multiple $\textit{data re-uploading}$. A quantum circuit can then be organized as a series of data re-uploading and single-qubit processing units. Furthermore, both data re-uploading and measurements can accommodate multiple dimensions in the input and several categories in the output, to conform to a universal quantum classifier. The extension of this idea to several qubits enhances the efficiency of the strategy as entanglement expands the superpositions carried along with the classification. Extensive benchmarking on different examples of the single- and multi-qubit quantum classifier validates its ability to describe and classify complex data.

Featured image: Results of a classification problem with increasing depth, i. e.: numbers of layers. Results improve as the circuit gets deeper.

Popular summary

In this paper, we show how to use the computational power of a single qubit to solve non-trivial classification problems. We propose a hybrid classical-quantum algorithm based on re-uploading classical data into the angles of the single-qubit unitary gates multiple times along the circuit. Together with the data points, other parameters are introduced into the circuit and adjusted by classically minimizing a cost function. To construct this cost function, we train the circuit to distribute the data points into different regions of the Bloch sphere, one for each class. A particular division of the Bloch sphere accompanies this strategy for maximizing distinguishability between classes.
This procedure cannot provide any quantum advantage as a single qubit can be simulated classically. However, the capability of handling one qubit might be useful as a small piece of larger circuits. Besides, an extension of the algorithm for more qubits and entanglement is also presented in this work. The multi-qubit role remains unexplored and might be a candidate for quantum advantage. A first step analyzed, there exists a trade-off between the number of qubits needed and the times of data re-uploading for classifying, namely layers.
This algorithm is to be compared with a neural network with one hidden layer. Neural Networks re-upload classical data several times, once per hidden neuron, achieving the same kind of processing as in our quantum classifier. Success rates are also comparable for both models.

► BibTeX data

@article{PerezSalinas2020datareuploading,
  doi = {10.22331/q-2020-02-06-226},
  url = {https://doi.org/10.22331/q-2020-02-06-226},
  title = {Data re-uploading for a universal quantum classifier},
  author = {P{\'{e}}rez-Salinas, Adri{\'{a}}n and Cervera-Lierta, Alba and Gil-Fuster, Elies and Latorre, Jos{\'{e}} I.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {226},
  month = feb,
  year = {2020}
}

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