Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment

Processing of digital images is continuously gaining in volume and relevance, with concomitant demands on data storage, transmission and processing power. Encoding the image information in quantum-mechanical systems instead of classical ones and replacing classical with quantum information processing may alleviate some of these challenges. By encoding and processing the image information in quantum-mechanical systems, we here demonstrate the framework of quantum image processing, where a pure quantum state encodes the image information: we encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states. Our quantum image representation reduces the required number of qubits compared to existing implementations, and we present image processing algorithms that provide exponential speed-up over their classical counterparts. For the commonly used task of detecting the edge of an image, we propose and implement a quantum algorithm that completes the task with only one single-qubit operation, independent of the size of the image. This demonstrates the potential of quantum image processing for highly efficient image and video processing in the big data era.Comment: 13 pages, including 9 figures and 5 appendixe

A Compact Source for Quantum Image Processing with Four-wave Mixing in Rubidium-85

We have built a compact light source for bright squeezed twin-beams at 795\,nm based on four-wave-mixing in atomic $^{85}$Rb vapor. With a total optical power of 400\,mW derived from a free running diode laser and a tapered amplifier to pump the four-wave-mixing process, we achieve 2.1\,dB intensity difference squeezing of the twin beams below the standard quantum limit, without accounting for losses. Squeezed twin beams generated by the type of source presented here could be used as reference for the precise calibration of photodetectors. Transferring the quantum correlations from the light to atoms in order to generate correlated atom beams is another interesting prospect. In this work we investigate the dispersion that is generated by the employed four-wave-mixing process with respect to bandwidth and dependence on probe detuning. We are currently using this squeezed light source to test the transfer of spatial information and quantum correlations through media of anomalous dispersion.Comment: 6 pages, 4 figure

Quantum Radio Astronomy: Data Encodings and Quantum Image Processing

We explore applications of quantum computing for radio interferometry and astronomy using recent developments in quantum image processing. We evaluate the suitability of different quantum image representations using a toy quantum computing image reconstruction pipeline, and compare its performance to the classical computing counterpart. For identifying and locating bright radio sources, quantum computing can offer an exponential speedup over classical algorithms, even when accounting for data encoding cost and repeated circuit evaluations. We also propose a novel variational quantum computing algorithm for self-calibration of interferometer visibilities, and discuss future developments and research that would be necessary to make quantum computing for radio astronomy a reality.Comment: 10 pages, 8 figure

Optical Phase-Space-Time-Frequency Tomography

We present a new approach for constructing optical phase-space-time-frequency tomography (OPSTFT) of an optical wave field. This tomography can be measured by using a novel four-window optical imaging system based on two local oscillator fields balanced heterodyne detection. The OPSTFT is a Wigner distribution function of two independent Fourier Transform pairs, i.e., phase-space and time-frequency. From its theoretical and experimental aspects, it can provide information of position, momentum, time and frequency of a spatial light field with precision beyond the uncertainty principle. We simulate the OPSTFT for a light field obscured by a wire and a single-line absorption filter. We believe that the four-window system can provide spatial and temporal properties of a wave field for quantum image processing and biophotonics.Comment: 11 pages, 6 figure

Quantum image classification using principal component analysis

We present a novel quantum algorithm for classification of images. The algorithm is constructed using principal component analysis and von Neuman quantum measurements. In order to apply the algorithm we present a new quantum representation of grayscale images.Comment: 9 page