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arXiv:2010.03594 · Physical Review Applied

Quantum-Enhanced Barcode Decoding and Pattern Recognition

Leonardo Banchi, Quntao Zhuang, Stefano Pirandola

Published Dec 8, 2020• 28 citations
arXivHTMLPDF

Abstract

Quantum hypothesis testing is one of the most fundamental problems in quantum information theory, with crucial implications in areas like quantum sensing, where it has been used to prove quantum advantage in a series of binary photonic protocols, e.g., for target detection or memory cell readout. In this work, we generalize this theoretical model to the multipartite setting of barcode decoding and pattern recognition. We start by defining a digital image as an array or grid of pixels, each pixel corresponding to an ensemble of quantum channels. Specializing each pixel to a black and white alphabet, we naturally define an optical model of a barcode. In this scenario, we show that the use of quantum entangled sources, combined with suitable measurements and data processing, greatly outperforms classical coherent-state strategies for the tasks of barcode data decoding and classification of black and white patterns. Moreover, introducing relevant bounds, we show that the problem of pattern recognition is significantly simpler than barcode decoding, as long as the minimum Hamming distance between images from different classes is large enough. Finally, we theoretically demonstrate the advantage of using quantum sensors for pattern recognition with the nearest-neighbor classifier, a supervised learning algorithm, and numerically verify this prediction for handwritten digit classification.

DOI
10.1103/physrevapplied.14.064026

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Quantum hypothesis testing is one of the most fundamental problems in quantum information theory, with crucial implications in areas like quantum sensing, where it has been used to prove quantum advantage in a series of binary photonic protocols, e.g., for target detection or memory cell readout. In this work, we generalize this theoretical model to the multipartite setting of barcode decoding and pattern recognition. We start by defining a digital image as an array or grid of pixels, each pixel corresponding to an ensemble of quantum channels. Specializing each pixel to a black and white alphabet, we naturally define an optical model of a barcode. In this scenario, we show that the use of quantum entangled sources, combined with suitable measurements and data processing, greatly outperforms classical coherent-state strategies for the tasks of barcode data decoding and classification of black and white patterns. Moreover, introducing relevant bounds, we show that the problem of pattern recognition is significantly simpler than barcode decoding, as long as the minimum Hamming distance between images from different classes is large enough. Finally, we theoretically demonstrate the advantage of using quantum sensors for pattern recognition with the nearest-neighbor classifier, a supervised learning algorithm, and numerically verify this prediction for handwritten digit classification.
Quantum hypothesis testing is one of the most fundamental problems in quantum information theory, with crucial implications in areas like quantum sensing, where it has been used to prove quantum advantage in a series of binary photonic protocols, e.g., for target detection or memory cell readout. In this work, we generalize this theoretical model to the multi-partite setting of barcode decoding and pattern recognition. We start by defining a digital image as an array or grid of pixels, each pixel corresponding to an ensemble of quantum channels. Specializing each pixel to a black and white alphabet, we naturally define an optical model of barcode. In this scenario, we show that the use of quantum entangled sources, combined with suitable measurements and data processing, greatly outperforms classical coherent-state strategies for the tasks of barcode data decoding and classification of black and white patterns. Moreover, introducing relevant bounds, we show that the problem of pattern recognition is significantly simpler than barcode decoding, as long as the minimum Hamming distance between images from different classes is large enough. Finally, we theoretically demonstrate the advantage of using quantum sensors for pattern recognition with the nearest neighbor classifier, a supervised learning algorithm, and numerically verify this prediction for handwritten digit classification.
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It is well known that for certain tasks, quantum computing outperforms classical computing. A growing number of contributions try to use this advantage in order to improve or extend classical machine learning algorithms by methods of quantum information theory. This paper gives a brief introduction into quantum machine learning using the example of pattern classification. We introduce a quantum pattern classification algorithm that draws on Trugenberger's proposal for measuring the Hamming distance on a quantum computer (CA Trugenberger, Phys Rev Let 87, 2001) and discuss its advantages using handwritten digit recognition as from the MNIST database.
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Quantum hypothesis testing has been greatly advanced for the binary discrimination of two states, or two channels. In this setting, we already know that quantum entanglement can be used to enhance the discrimination of two bosonic channels. Here, we remove the restriction of binary hypotheses and show that entangled photons can remarkably boost the discrimination of multiple bosonic channels. More precisely, we formulate a general problem of channel-position finding where the goal is to determine the position of a target channel among many background channels. We prove that, using entangled photons at the input and a generalized form of conditional nulling receiver at the output, we may outperform any classical strategy. Our results can be applied to enhance a range of technological tasks, including the optical readout of sparse classical data, the spectroscopic analysis of a frequency spectrum, and the determination of the direction of a target at fixed range.