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Machine learning with classical data

There has been significant recent interest in exploring the interplay between quantum computing and machine learning. Quantum resources and quantum algorithms have been studied in all major parts of the traditional machine learning pipeline: (1) the data set; (2) data processing and analysis; (3) the machine learning model leading to a hypothesis family; and (4) the learning algorithm (see [1, 2, 3] for reviews). In this section we predominantly focus on quantum approaches for the latter three categories—that is, here we mostly consider quantum algorithms applied to classical data. These approaches include algorithms hinging on the quantum linear system solver (or quantum linear algebra more generally) as the source for possible quantum speedup over classical learning algorithms. These also include quantum neural networks (using the framework of variational quantum algorithms) and quantum kernels, where the classical machine learning model is replaced with a quantum model. Additionally, in this section we discuss quantum algorithms that aim to speed up data analysis tasks, namely tensor principal component analysis (TPCA) and topological data analysis.

Quantum machine learning is an active area of research. As such, we expect the conclusions made in this section to evolve over time, as new results are discovered. At present, our evaluation suggests that few of the considered quantum machine learning algorithms show any promise of quantum advantage in the intermediate future. This conclusion stems from a number of factors, including issues of loading classical data into the quantum device and extracting classical data via tomography, and the success of classical "dequantized\" algorithms [4]. More specialized tasks, such as tensor PCA and topological data analysis may provide larger polynomial speedups (i.e., better than quadratic) in some regimes, but their application scope is less broad. Finally, other techniques such as quantum neural networks and quantum kernel methods contain heuristic elements which make it challenging to perform concrete analytic end-to-end resource estimates [5].

Bibliography

  1. Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd. Quantum machine learning. Nature, 549:195–202, 2017. arXiv: https://arxiv.org/abs/1611.09347. doi:10.1038/nature23474.

  2. M Cerezo, Guillaume Verdon, Hsin-Yuan Huang, Lukasz Cincio, and Patrick J Coles. Challenges and opportunities in quantum machine learning. Nature Computational Science, 2(9):567–576, 2022. arXiv: https://arxiv.org/abs/2303.09491. doi:https://doi.org/10.1038/s43588-022-00311-3.

  3. Carlo Ciliberto, Mark Herbster, Alessandro Davide Ialongo, Massimiliano Pontil, Andrea Rocchetto, Simone Severini, and Leonard Wossnig. Quantum machine learning: a classical perspective. Proceedings of the Royal Society A, 474(2209):20170551, 2018. arXiv: https://arxiv.org/abs/1707.08561. doi:https://doi.org/10.1098/rspa.2017.0551.

  4. Ewin Tang. A quantum-inspired classical algorithm for recommendation systems. In Proceedings of the 51st ACM Symposium on the Theory of Computing (STOC), 217–228. 2019. arXiv: https://arxiv.org/abs/1807.04271. doi:10.1145/3313276.3316310.

  5. Maria Schuld and Nathan Killoran. Is quantum advantage the right goal for quantum machine learning? PRX Quantum, 3(3):030101, 2022. arXiv: https://arxiv.org/abs/2203.01340. URL: https://link.aps.org/doi/10.1103/PRXQuantum.3.030101, doi:10.1103/PRXQuantum.3.030101.