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Paper 1
Khovanov homology and quantum error-correcting codes
Rostislav Akhmechet, Milena Harned, Pranav Venkata Konda, Felix Shanglin Liu, Nikhil Mudumbi, Eric Yuang Shao, Zheheng Xiao
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.11252
- arXiv
- 2410.11252
Error-correcting codes for quantum computing are crucial to address the fundamental problem of communication in the presence of noise and imperfections. Audoux used Khovanov homology to define families of quantum error-correcting codes with desirable properties. We explore Khovanov homology and some of its many extensions, namely reduced, annular, and $\mathfrak{sl}_3$ homology, to generate new families of quantum codes and to establish several properties about codes that arise in this way, such as behavior of distance under Reidemeister moves or connected sums.
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Local-photon model of the momentum of light
Gabriel Waite, Daniel Hodgson, Ben Lang, Varghese Alapatt, Almut Beige
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.03633
- arXiv
- 2410.03633
Recently we introduced a local photon approach for modelling the quantised electromagnetic field in position space. Using this approach, we define the momentum of light in this paper as in quantum mechanics as the generator for spatial translation. Afterwards, we analyse the momentum dynamics of photonic wave packets which transition from air into a denser dielectric medium. Our analysis shines new light onto the Abraham-Minkowski controversy which highlights the intricacies involved in the characterisation of the momentum of the electromagnetic field. Although our results align with Minkowski's theory and with the definition of the canonical momentum of light in quantum electrodynamics, there are also some crucial differences.
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