Dataset for the paper "Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective".

Dimitrios Alanis, Panagiotis Botsinis, Zunaira Babar, Hung Viet Nguyen, Daryus Chandra,  Soon Xin Ng, Lajos Hanzo.

IEEE Access (accepted). 

Results may reproduced using GLE graphics.

Abstract: Wireless Multihop Networks (WMHNs) have to strike a trade-off among diverse and often conflicting Quality-of-Service (QoS) requirements. The resultant solutions may be included by the Pareto Front under the concept of Pareto Optimality. However, the problem of finding all the Pareto-optimal routes in WMHNs is classified as NP-hard, since the number of legitimate routes increases exponentially, as the nodes proliferate. Quantum Computing offers an attractive framework of rendering the Pareto-optimal routing problem tractable. In this context, a pair of quantum-assisted algorithms have been proposed, namely the Non-Dominated Quantum Optimization (NDQO) and the Non-Dominated Quantum Iterative Optimization (NDQIO). However, their complexity is proportional to $\sqrt{N}$, where $N$ corresponds to the total number of legitimate routes, thus still failing to find the solutions in ``polynomial time''. As a remedy, we devise a dynamic programming framework and propose the so-called Evolutionary Quantum Pareto Optimization (EQPO) algorithm. We analytically characterize the complexity imposed by the EQPO algorithm and demonstrate that it succeeds in solving the Pareto-optimal routing problem in polynomial time. Finally, we demonstrate by simulations that the EQPO algorithm achieves a complexity reduction, which is at least an order of magnitude, when compared to its predecessors, albeit at the cost of a modest heuristic accuracy reduction.

Acknowledgements: The financial support of the European Research Council under the Advanced Fellow Grant, that of the Royal Society’s Wolfson Research Merit Award and that of the Engineering and Physical Sciences Research Council under Grant EP/L018659/1 is gratefully acknowledged. The use of the IRIDIS High Performance Computing Facility at the University of Southampton is also acknowledged.

* Fig 1 of the paper is located at ./Fig-1/Fig1.eps and may be reproduced from ./Fig-1/Fig-1.gle. The respective dataset is located at ./Fig-1/datasets directory.
* Fig 4a of the paper is located at ./Fig-4/Fig-4a.eps and may be reproduced from ./Fig-4/Fig-4a.gle. The respective dataset is located at ./Fig-4/datasets/ directory.
* Fig 4b of the paper is located at ./Fig-4/Fig-4b.eps and may be reproduced from ./Fig-4/Fig-4b.gle. The respective dataset is located at ./Fig-4/datasets/ directory.
* Fig 5a of the paper is located at ./Fig-5/Fig-5a.eps and may be reproduced from ./Fig-5/Fig-5a.gle. The respective dataset is located at ./Fig-4/datasets/parallel/ directory.
* Fig 5b of the paper is located at ./Fig-5/Fig-5b.eps and may be reproduced from ./Fig-5/Fig-5b.gle. The respective dataset is located at ./Fig-4/datasets/sequential/ directory.
* Fig 5c of the paper is located at ./Fig-5/Fig-5c.eps and may be reproduced from ./Fig-5/Fig-5c.gle. The respective dataset is located at ./Fig-4/datasets/parallel/ directory.
* Fig 5d of the paper is located at ./Fig-5/Fig-5d.eps and may be reproduced from ./Fig-5/Fig-5d.gle. The respective dataset is located at ./Fig-4/datasets/sequential/ directory.
