A quantum edge detection algorithm based on the sequency-ordered Walsh-Hadamard transform and a quantum high-pass filter achieves O(log N) circuit depth when state preparation is excluded.
On sequency-complete and sequency-ordered matrices
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abstract
The concept of sequency holds a fundamental significance in signal analysis using Walsh basis functions. In this study, we closely examine the concept of sequency and explore the properties of sequency-complete and sequency-ordered matrices. We obtain results on cardinalities of sets containing sequency-complete and sequency-ordered matrices of arbitrary sizes. We present methods for obtaining interesting classes of sequency-complete and sequency-ordered matrices of arbitrary sizes. We also provide results on the sequencies of columns in tensor products involving two or more matrices.
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Quantum algorithm for edge detection in digital grayscale images
A quantum edge detection algorithm based on the sequency-ordered Walsh-Hadamard transform and a quantum high-pass filter achieves O(log N) circuit depth when state preparation is excluded.