Single-Photon Image Classification
This work provides a simplified, accessible quantum computing model for educational purposes, though it is incremental as it focuses on a toy problem with limited practical application.
The paper tackles image classification using single-photon detection with quantum-inspired optical transformations, achieving theoretical accuracies of 41.27% on MNIST and 36.14% on Fashion-MNIST, compared to classical maximum likelihood estimates of 21.27% and 18.27%, respectively.
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. Instead, we demonstrate the existence of a lower performance and much lower effort island on the accuracy-vs-qubits graph that may well be experimentally accessible with room temperature optics. This high temperature "quantum computing toy model" is nevertheless interesting to study as it allows rather accessible explanations of key concepts in quantum computing, in particular interference, entanglement, and the measurement process. We specifically study the problem of classifying an example from the MNIST and Fashion-MNIST datasets, subject to the constraint that we have to make a prediction after the detection of the very first photon that passed a coherently illuminated filter showing the example. Whereas a classical set-up in which a photon is detected after falling on one of the $28\times 28$ image pixels is limited to a (maximum likelihood estimation) accuracy of $21.27\%$ for MNIST, respectively $18.27\%$ for Fashion-MNIST, we show that the theoretically achievable accuracy when exploiting inference by optically transforming the quantum state of the photon is at least $41.27\%$ for MNIST, respectively $36.14\%$ for Fashion-MNIST. We show in detail how to train the corresponding transformation with TensorFlow and also explain how this example can serve as a teaching tool for the measurement process in quantum mechanics.