Internal:Hybrid Computing
Distributed Noisy Intermediate-Scale Quantum Computers (D-NISQ)
The D-NISQ model presented by [1] describes a hierarchical architecture of hybrid classical/quantum processors to break up large computations into smaller sub problems. Resource management of limited qubits and noisy quantum computation make domain decomposition a necessary method to practically use many quantum algorithms. The D-NISQ model has four layers. Consider the application to Quantum Hadamard Edge Detection[2] qHED:
Decomposition Layer
The first layer is performed classically. Consider a 1024x1024 medical image. This comes out to 1,048,576 pixels requiring 20 (2^20) qubits plus 1 ancillary qubit for the QHED algorithm. Additionally, the amplitude encoding process expands exponentially with regards to qubit number. We can divide the image into separate sub images and solve either iteratively or in parallel (multithreading). Each sub image is now considered to be a sub input of the overall problem.
Classical to Quantum Layer
The second layer performs a mapping of classical input data to quantum. In this case, we wish to encode the pixel values into the amplitudes of basis states where those basis states act as the pixels position in 1D space[3].
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.