Processing of digital images is continuously gaining in volume and relevance, with concomitant demands\non data storage, transmission, and processing power. Encoding the image information in quantum-mechanical\nsystems instead of classical ones and replacing classical with quantum information processing may alleviate\nsome of these challenges. By encoding and processing the image information in quantum-mechanical\nsystems, we here demonstrate the framework of quantum image processing, where a pure quantum state\nencodes the image information: we encode the pixel values in the probability amplitudes and the pixel\npositions in the computational basis states. Our quantumimage representation reduces the required number of\nqubits compared to existing implementations, and we present image processing algorithms that provide\nexponential speed-up over their classical counterparts. For the commonly used task of detecting the edge of an\nimage, we propose and implement a quantum algorithm that completes the task with only one single-qubit\noperation, independent of the size of the image. This demonstrates the potential of quantum image processing\nfor highly efficient image and video processing in the big data era.
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