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arXiv:1804.11326 · Nature

Supervised learning with quantum-enhanced feature spaces

Vojtěch Havlíček, Antonio D. Corcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, Jay Gambetta

Published Mar 13, 2019• 2,584 citations
arXivHTMLPDF
DOI
10.1038/s41586-019-0980-2

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The kernel trick in supervised learning signifies transformations of an inner product by a feature map, which then restructures training data in a larger Hilbert space according to an endowed inner product. A quantum feature map corresponds to an instance with a Hilbert space of quantum states by fueling quantum resources to machine learning algorithms. In this work, we point out that the quantum state space is specific such that a measurement postulate characterizes an inner product and that manipulation of quantum states prepared from classical data cannot enhance the distinguishability of data points. We present a feature map for quantum data as a probabilistic manipulation of quantum states to improve supervised learning algorithms.
Many existing quantum supervised learning (SL) schemes consider data given a priori in a classical description. With only noisy intermediate-scale quantum (NISQ) devices available in the near future, their quantum speedup awaits the development of quantum random access memories (qRAMs) and fault-tolerant quantum computing. There, however, also exist a multitude of SL tasks whose data are acquired by sensors, e.g., pattern classification based on data produced by imaging sensors. Solving such SL tasks naturally requires an integrated approach harnessing tools from both quantum sensing and quantum computing. We introduce supervised learning assisted by an entangled sensor network (SLAEN) as a means to carry out SL tasks at the physical layer. The entanglement shared by the sensors in SLAEN boosts the performance of extracting global features of the object under investigation. We leverage SLAEN to construct an entanglement-assisted support-vector machine for data classification and entanglement-assisted principal component analyzer for data compression. In both schemes, variational circuits are employed to seek the optimum entangled probe states and measurement settings to maximize the entanglement-enabled {enhancement}. We observe that SLAEN enjoys an appreciable entanglement-enabled performance gain, even in the presence of loss, over conventional strategies in which classical data are acquired by separable sensors and subsequently processed by classical SL algorithms. SLAEN is realizable with available technology, opening a viable route toward building NISQ devices that offer unmatched performance beyond what the optimum classical device is able to afford.