SINGLE-PHOTON IMAGE CLASSIFICATION

Abstract

Quantum Computing based Machine Learning mainly focuses on quantum computing hardware that is experimentally challenging to realize due to requiring quantum gates that operate at very low temperature. We demonstrate the existence of a "quantum computing toy model" that illustrates key aspects of quantum information processing while being experimentally accessible with room temperature optics. Pondering the question of the theoretical classification accuracy performance limit for MNIST (respectively "Fashion-MNIST") classifiers, subject to the constraint that a decision has to be made after detection of the very first photon that passed through an image-filter, we show that a machine learning system that is permitted to use quantum interference on the photon's state can substantially outperform any machine learning system that can not. Specifically, we prove that a "classical" MNIST (respectively "Fashion-MNIST") classifier cannot achieve an accuracy of better than 22.96% (respectively 21.38% for "Fashion-MNIST") if it must make a decision after seeing a single photon falling on one of the 28 × 28 image pixels of a detector array. We further demonstrate that a classifier that is permitted to employ quantum interference by optically transforming the photon state prior to detection can achieve a classification accuracy of at least 41.27% for MNIST (respectively 36.14% for "Fashion-MNIST"). We show in detail how to train the corresponding quantum state transformation with TensorFlow and also explain how this example can serve as a teaching tool for the measurement process in quantum mechanics.

1. INTRODUCTION

Both quantum mechanics and machine learning play a major role in modern technology, and the emerging field of AI applications of quantum computing may well enable major breakthroughs across many scientific disciplines. Yet, as the majority of current machine learning practitioners do not have a thorough understanding of quantum mechanics, while the majority of quantum physicists only have an equally limited understanding of machine learning, it is interesting to look for "Rosetta Stone" problems where simple and widely understood machine learning ideas meet simple and widely understood quantum mechanics ideas. It is the intent of this article to present a setting in which textbook quantum mechanics sheds a new light on a textbook machine learning problem, and vice versa, conceptually somewhat along the lines of Google's TensorFlow Playground (Smilkov et al. (2017) ,) which was introduced as a teaching device to illustrate key concepts from Deep Learning to a wider audience. Specifically, we want to consider the question what the maximal achievable accuracy on common one-out-of-many image classification tasks is if one must make a decision after the detection of the very first quantum of light (i.e. photon) that passed a filter showing an example image from the test set. In this setting, we do not have a one-to-one correspondence between example images from the training (respectively test) set and classification problems. Instead, every example image defines a probability distribution for the (x, y) detector pixel location on which the first photon passing an image filter lands, the per-pixel probability being the pixel's brightness relative to the accumulated (across all pixels) image brightness. So, from every (28 × 28 pixels) example image, we can sample arbitrarily many photon-detection-event classifier examples, where the features are a pair of integer pixel coordinates, and the label is the digit class. On the MNIST handwritten digit dataset (LeCun and Cortes (2010)), any machine learning system that only gets to see a single such "photon detected at coordinates (x, y)" event as its input features, of the pixel that flashed up are the only input features, is limited in accuracy

