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Pradeep Sarvepalli
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Pradeep Sarvepalli
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Pradeep Sarvepalli
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Sarvepalli, P.
Sarvepalli, Pradeep Kiran
Sarvepalli, Pradeep
Sarvepalli, Pradeep K.
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2 results
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- PublicationDecoding Topological Subsystem Color Codes Over the Erasure Channel Using Gauge Fixing(01-07-2023)
;Solanki, Hiteshvi ManishTopological subsystem color codes (TSCCs) are an important class of topological subsystem codes that allow for syndrome measurement with only 2-body measurements. It is expected that such low complexity measurements can help in fault tolerance. While TSCCs have been studied over depolarizing noise model, their performance over the erasure channel has not been studied as much. Recently, we proposed erasure decoders for TSCCs and reported a threshold of 9.7%. In this paper, we continue our study of TSCCS over the erasure channel. We propose two erasure decoders for topological subsystem color codes. These decoders employ a mapping of the TSCCs to topological color codes (TCCs). In addition, these decoders use the technique of gauge fixing, where some of the gauge operators of the subsystem code are promoted to stabilizers. We perform gauge fixing using 4-body and 8-body gauge operators. With partial gauge fixing, we obtained a threshold of 17.7% on a TSCC derived from the square octagon lattice. Using an order maximal gauge fixing decoder we were able to improve the threshold to 44%. The performance of the order maximal gauge fixing decoder can be further improved to close to 50% in conjunction with an optimal erasure decoder for topolological color codes. We also study the correctability of erasures on the subsystem codes. - PublicationDecoding Toric Codes on Three Dimensional Simplical Complexes(01-02-2021)
;Aloshious, Arun B.Three dimensional (3D) toric codes are a class of stabilizer codes with local checks and come under the umbrella of topological codes. While decoding algorithms have been proposed for the 3D toric code on a cubic lattice, there have been very few studies on the decoding of 3D toric codes over arbitrary lattices. Color codes in 3D can be mapped to toric codes. However, the resulting toric codes are not defined on cubic lattice. They are arbitrary lattices with triangular faces. Decoding toric codes over an arbitrary lattice will help in studying the performance of color codes. Furthermore, gauge color codes can also be decoded via 3D toric codes. Motivated by this, we propose an efficient algorithm to decode 3D toric codes on arbitrary lattices (with and without boundaries).