Speaker
Description
Image reconstruction is a critical problem in Optics, particularly in Ghost Imaging experiments [1, 2]. While enabling non-local quantum imaging without state collapse, it requires $\approx 2N^2$ measurements for an $N \times N$ image [3], causing challenges in reconstruction speed and fidelity. Classical reconstruction methods remain computationally intensive.
To address this, we propose U-NET Classical and Quantum Convolutional Neural Network (CNN) algorithms [4] to reconstruct low-sampled images in the Hadamard transform domain. Instead of processing pixel-domain images, the CNNs take under sampled Hadamard coefficients as inputs to reconstruct the complete coefficient set.
The Quantum CNN (QCNN) adapts a novel classical U-Net architecture, implementing convolutional and pooling layers via Variational Quantum Circuits. By utilizing quantum superposition and entanglement, the QCNN exploits intrinsic patterns within the Hadamard coefficient space. Simulations indicate enhanced reconstruction speed and higher fidelity compared to equivalent classical models.
This paper details the classical and quantum CNN architectures, the Hadamard-to-quantum state encoding scheme, variational layers, and the classical optimization loop. We present simulation results on the MNIST dataset and experimental results from the Wits Structured Light Lab. The networks demonstrate full Hadamard coefficient reconstruction from various undersampling levels, followed by an inverse CNN to generate high-fidelity pixel-domain images. These findings highlight the potential of quantum machine learning to significantly advance computational imaging techniques.
References: Moodley and Forbes analysing resolution [1], Padgett and Boyd providing introductions [2], Sephton et al. revealing embedded phase profiles [3], and Cong et al. introducing the quantum convolutional neural network framework architecture utilized herein [4].
| Topic | Quantum algorithms for machine learning applications |
|---|---|
| Additional Topic | Quantum state reconstruction from data |