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.

Figure 1 Example of 1024x1024 Medical image decomposed into 256x256 sub images.

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]. The circuit is constructed classically (mathematically determining a series of gates which will produce the highest probable desired output) with the actual execution performed on the newly constructed quantum circuit itself.

Quantum Computation Layer

The states created in the second layer now act as the input to the quantum algorithm itself. If carried out in parallel, each quantum device will execute their respective inputs across the qHED circuit. If performed iteratively, the quantum devices will have to be reset after each execution.

Figure 1 Generalized qHED Circuit with input vector f and output vector g.

Quantum Information Fusion

The D-NISQ model considers the measurement portion of the circuit as the first part of the quantum information layer. Multiple measurements of output states are collected to develop a probability distribution for each sub problem. That probability distribution is mapped as a solution to the respective sub problem. In the case of qHED, the probability amplitudes (pixel values) of basis states (pixels mapped to 1D space) represent the image edge values. In this case, a reverse mapping of 1D to 2D is required. From there, the sub problems are recombined into the final result.

Quantum Utility Scale Repository

https://github.com/ebill007/Quantum-Utility-Scale

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.