Internal:Quantum Edge Detection

Quantum Hadamard Edge Detection (QHED)

The Quantum Hadamard Edge Detection (QHED) algorithm presented by [2] is a method of providing full boundary gradient across a 1D mapping of a 2D image. The presented means of achieving this image processing would require a circuit of exponential depth in regards to the number of qubits used for the data encoding portion. This leads to quantum decoherence leaving our output data indistinguishable from noise. Reference [1] describes the D-NISQ model which could be a means to practically apply the QHED algorithm. When decomposing a large image to a series of more manageable sub images we receive errors across the boarders of the sub images. These errors stem from the classically computed preprocessing method (2D to 1D mapping) shown in [2].

QHED Circuit

500px|thumb|none|Figure 1 QHED circuit providing full boundary gradient.

References

[1] Acampora, Giovanni, et al. “D-NISQ: A Reference Model for Distributed Noisy Intermediate-Scale Quantum Computers.” Information Fusion, vol. 89, 2023, pp. 16–28., https://doi.org/10.1016/j.inffus.2022.08.003.

[2] .-W. Yao, H. Wang, Z. Liao, M.-C. Chen, J. Pan, J. Li, K. Zhang, X. Lin, Z. Wang, Z. Luo, et al., Quantum image processing and its application to edge detection: Theory and experiment, Physical Review X 7 (3) (2017). doi:10.1103/physrevx.7.031041.

[3]I. F. Araujo, D. K. Park, F. Petruccione, A. J. da Silva, A divide-and-conquer algo- rithm for quantum state preparation, Scientific Reports 11 (1) (2021). doi:10.1038/ s41598-021-85474-1.