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Paper 1
Balanced Product Quantum Codes
Nikolas P. Breuckmann, Jens N. Eberhardt
- Year
- 2020
- Journal
- arXiv preprint
- DOI
- arXiv:2012.09271
- arXiv
- 2012.09271
This work provides the first explicit and non-random family of $[[N,K,D]]$ LDPC quantum codes which encode $K \in Θ(N^\frac{4}{5})$ logical qubits with distance $D \in Ω(N^\frac{3}{5})$. The family is constructed by amalgamating classical codes and Ramanujan graphs via an operation called balanced product. Recently, Hastings-Haah-O'Donnell and Panteleev-Kalachev were the first to show that there exist families of LDPC quantum codes which break the $\operatorname{polylog}(N)\sqrt{N}$ distance barrier. However, their constructions are based on probabilistic arguments which only guarantee the code parameters with high probability whereas our bounds hold unconditionally. Further, balanced products allow for non-abelian twisting of the check matrices, leading to a construction of LDPC quantum codes that can be shown to have $K\in Θ(N)$ and that we conjecture to have linear distance $D\in Θ(N)$.
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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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