@article{discovery10188839, note = {This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.}, publisher = {VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF}, volume = {8}, month = {February}, year = {2024}, title = {Continuous-time quantum walks for MAX-CUT are hot}, journal = {Quantum}, keywords = {Science \& Technology, Physical Sciences, Quantum Science \& Technology, Physics, Multidisciplinary, Physics, MANY-BODY LOCALIZATION, STATISTICAL-MECHANICS, PYTHON FRAMEWORK, THERMALIZATION, DYNAMICS, QUTIP, CHAOS}, issn = {2521-327X}, url = {https://doi.org/10.22331/q-2024-02-13-1254}, author = {Banks, Robert J and Haque, Ehsan and Nazef, Farah and Fethallah, Fatima and Ruqaya, Fatima and Ahsan, Hamza and Vora, Het and Tahir, Hibah and Ahmed, Ibrahim and Hewins, Isaac and Shah, Ishaq and Baranwal, Krish and Arora, Mannan and Asad, Mateen and Khan, Mubasshirah and Hasan, Nabian and Azad, Nuh and Fedaiee, Salgai and Majeed, Shakeel and Bhuyan, Shayam and Tarannum, Tasfia and Ali, Yahya and Browne, Dan E and Warburton, PA}, abstract = {By exploiting the link between time-independent Hamiltonians and thermalisation, heuristic predictions on the performance of continuous-time quantum walks for MAX-CUT are made. The resulting predictions depend on the number of triangles in the underlying MAX-CUT graph. We extend these results to the time-dependent setting with multi-stage quantum walks and Floquet systems. The approach followed here provides a novel way of understanding the role of unitary dynamics in tackling combinatorial optimisation problems with continuous-time quantum algorithms.} }