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Paper 1
An analytic study of the independent coherent errors in the surface code
Yuanchen Zhao, Dong E. Liu
- Year
- 2021
- Journal
- arXiv preprint
- DOI
- arXiv:2112.00473
- arXiv
- 2112.00473
The realistic coherent errors could induce very different behaviors compared with their stochastic counterparts in the quantum error correction (QEC) and fault tolerant quantum computation. Their impacts are believed to be very subtle, more detrimental and hard to analyze compared to those ideal stochastic errors. In this paper, we study the independent coherent error due to the imperfect unitary rotation on each physical qubit of the toric code. We find that the surface code under coherent error satisfies generalized Knill-Laflamme (K-L) criterion and falls into the category of approximate QEC. The extra term in the generalized K-L criterion corresponds to the coherent part of the error channel at logical level, and then show that the generalized K-L criterion approaches the normal K-L criterion when the code distance becomes large. In addition, we also find that if the code with a fixed distance d is $ε$-correctable, the value of $ε$ describing the accuracy of the approximate QEC cannot be smaller than a lower bound. We then study the success probability of QEC under such coherent errors, and confirm that the exact success probability under coherent error is smaller than the results using Pauli twirling approximation at physical level.
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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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