Quantum edge detection on an amplitude-encoded image
Detect the edges of a digital image: the pixel positions at which the image values change sharply. Processing digital images keeps growing in volume, with matching demands on data storage, transmission and processing power.
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Detect the edges of a digital image: the pixel positions at which the image values change sharply. Processing digital images keeps growing in volume, with matching demands on data storage, transmission and processing power. The whole image is carried by a single pure quantum state: the authors encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states, so the register's basis states carry the position index and its amplitudes carry the picture. They state that this representation reduces the required number of qubits compared to existing implementations, and that the image processing algorithms they present provide exponential speed-up over their classical counterparts. Edge detection is then reduced to one operation on one qubit, a count that does not grow with the picture; the abstract's own wording is that the algorithm completes the task with only one single-qubit operation, independent of the size of the image. The paper reports more than a proposal — it says the algorithm was both proposed and implemented — and its title names theory and experiment together.
Circuit & simulation
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algorithm
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readout
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What this takes and returns
TakesNothingWhat joins here
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ReturnsNothingWhat joins here
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How it works
The whole image is carried by a single pure quantum state: the authors encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states, so the register's basis states carry the position index and its amplitudes carry the picture. They state that this representation reduces the required number of qubits compared to existing implementations, and that the image processing algorithms they present provide exponential speed-up over their classical counterparts. Edge detection is then reduced to one operation on one qubit, a count that does not grow with the picture; the abstract's own wording is that the algorithm completes the task with only one single-qubit operation, independent of the size of the image. The paper reports more than a proposal — it says the algorithm was both proposed and implemented — and its title names theory and experiment together. The Classiq library carries this subject under applications · image_processing. Reported cost: One single-qubit operation for the edge-detection step, independent of the size of the image; for the image processing algorithms the paper presents, an exponential speed-up over their classical counterparts. The qubit claim is comparative rather than absolute — the representation reduces the required number of qubits compared to existing implementations — and the abstract states no gate count for preparing the encoded image or for reading the result back out..
Implementation
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quantum-edge-detection.txt
ALGORITHM: Quantum edge detection on an amplitude-encoded image
PROBLEM: Detect the edges of a digital image: the pixel positions at which the image values change sharply. Processing digital images keeps growing in volume, with matching demands on data storage, transmission and processing power.
IDEA: The whole image is carried by a single pure quantum state: the authors encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states, so the register's basis states carry the position index and its amplitudes carry the picture. They state that this representation reduces the required number of qubits compared to existing implementations, and that the image processing algorithms they present provide exponential speed-up over their classical counterparts. Edge detection is then reduced to one operation on one qubit, a count that does not grow with the picture; the abstract's own wording is that the algorithm completes the task with only one single-qubit operation, independent of the size of the image. The paper reports more than a proposal — it says the algorithm was both proposed and implemented — and its title names theory and experiment together.
REPORTED COST: One single-qubit operation for the edge-detection step, independent of the size of the image; for the image processing algorithms the paper presents, an exponential speed-up over their classical counterparts. The qubit claim is comparative rather than absolute — the representation reduces the required number of qubits compared to existing implementations — and the abstract states no gate count for preparing the encoded image or for reading the result back out.
BASIS: abstract of arXiv:1801.01465: "we propose and implement a quantum algorithm that completes the task with only one single-qubit operation, independent of the size of the image"; the speed-up clause is "we present image processing algorithms that provide exponential speed-up over their classical counterparts"; the qubit clause is "Our quantum image representation reduces the required number of qubits compared to existing implementations". That abstract states no running time, gate count, circuit depth or error bound, and the Classiq index entry read for this record gives the directory path and its file name only, with no bound of any kind.
DEMONSTRATED BY: the Classiq library entry applications/image_processing/quantum_hadamard_edge_detection
PRIMARY SOURCE: Xi-Wei Yao, Hengyan Wang, Zeyang Liao, Ming-Cheng Chen, Jian Pan, Jun Li, Kechao Zhang, Xingcheng Lin, Zhehui Wang, Zhihuang Luo, Wenqiang Zheng, Jianzhong Li, Meisheng Zhao, Xinhua Peng, Dieter Suter (2018), Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment — https://arxiv.org/abs/1801.01465
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Quantum vs classical
Classical baseline
Compare Quantum image processing with the strongest classical method for the same instance, input budget, and output metric.
Quantum claim
This reference exposes a quantum circuit pattern; it does not imply an application-level speedup without a matched benchmark.
How to compare
Report input loading, circuit depth, repetitions, classical preprocessing, post-processing, and wall-clock time together.
Declared gaps
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Literature & references
Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment2018 · Xi-Wei Yao, Hengyan Wang, Zeyang Liao, Ming-Cheng Chen, Jian Pan, Jun Li, Kechao Zhang, Xingcheng Lin, Zhehui Wang, Zhihuang Luo, Wenqiang Zheng, Jianzhong Li, Meisheng Zhao, Xinhua Peng, Dieter Suter
Primary source. It sets out the quantum image representation this record describes — pixel values in the probability amplitudes, pixel positions in the computational basis states — claims a reduced qubit requirement against existing implementations and an exponential speed-up for the image processing algorithms it presents, and reports the edge-detection algorithm as both proposed and implemented, completing the task with one single-qubit operation independent of image size. Consult it for the state-preparation and readout procedures, for which single-qubit operation is used, and for the experiment's platform, image sizes and accuracy, none of which the abstract states.