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Paper 1
Asymptotically good CSS-T codes and a new construction of triorthogonal codes
Elena Berardini, Reza Dastbasteh, Josu Etxezarreta Martinez, Shreyas Jain, Olatz Sanz Larrarte
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2412.08586
- arXiv
- 2412.08586
We propose a new systematic construction of CSS-T codes from any given CSS code using a map $φ$. When $φ$ is the identity map $I$, we retrieve the construction of [1] and use it to prove the existence of asymptotically good binary CSS-T codes, resolving a previously open problem in the literature, and of asymptotically good quantum LDPC CSS-T codes. We analyze the structure of the logical operators corresponding to certain non-Clifford gates supported by the quantum codes obtained from this construction ($φ= I$), concluding that they always result in the logical identity. An immediate application of these codes in dealing with coherent noise is discussed. We then develop a new doubling transformation for obtaining triorthogonal codes, which generalizes the doubling construction presented in [2]. Our approach permits using self-orthogonal codes, instead of only doubly-even codes, as building blocks for triorthogonal codes. This broadens the range of codes available for magic state distillation.
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Proceedings 9th Workshop on Quantum Physics and Logic
Ross Duncan, Prakash Panangaden
- Year
- 2014
- Journal
- arXiv preprint
- DOI
- arXiv:1407.8427
- arXiv
- 1407.8427
This volume contains the proceedings of the ninth workshop on Quantum Physics and Logic (QPL2012) which took place in Brussels from the 10th to the 12th of October 2012. QPL2012 brought together researchers working on mathematical foundations of quantum physics, quantum computing, and spatio-temporal causal structures. The particular focus was on the use of logical tools, ordered algebraic and category-theoretic structures, formal languages, semantical techniques, and other computer science methods for the study of physical behaviour in general.
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