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.
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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
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
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Cited by
[1] Seth Lloyd, Maria Schuld, Aroosa Ijaz, Josh Izaac, and Nathan Killoran, “Quantum embeddings for machine learning”, arXiv:2001.03622.
[2] Sergi Ramos-Calderer, Adrián Pérez-Salinas, Diego García-Martín, Carlos Bravo-Prieto, Jorge Cortada, Jordi Planagumà, and José I. Latorre, “Quantum unary approach to option pricing”, arXiv:1912.01618.
The above citations are from SAO/NASA ADS (last updated successfully 2020-02-06 14:31:00). The list may be incomplete as not all publishers provide suitable and complete citation data.
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Source: https://quantum-journal.org/papers/q-2020-02-06-226/
