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Decoding algorithms for subsystem codes

March 16 @ 2:00 pm - 3:00 pm

Title: Decoding algorithms for subsystem codes

Date: 16th March, 2018

Time: 2:00 P.M.

Venue : CSD 308

Speaker: Vinuta V. Gayatri (EE13S017)

Guide: Dr. Pradeep Kiran Sarvepalli

GTC Members:

Dr. Srikrishna Bhashyam (Chairperson)

Dr. Andrew Thangaraj (M)

Dr. Arul Lakshminarayanan (Ph)

Abstract

When a quantum computing system interacts with the surrounding environment, the quantum state it holds is modified. In order to ensure proper functioning of these systems quantum error correcting codes are used. Like classical codes which are characterized by parity checks, stabilizer codes are  completely characterized by a set of check operators called stabilizers. These stabilizers are measured while decoding to obtain the syndromes using which the error can be estimated. Topological subsystem codes(TSCs) are an interesting class of error correcting codes which can be defined using stabilizer formalism. The main advantage of using these codes is that the syndrome  measurement can be typically done by using two or three qubit local operators.

In our work, we present decoding algorithms for cubic subsystem codes,  hypergraph subsystem codes and generalized subsystem surface codes. We extend the algorithm proposed by Bravyi et al in 2010, to the cubic subsystem codes and to two classes of hypergraph TSCs. We show that these codes can be decoded using a two step decoding algorithm. In the first step all the bit flip errors are corrected locally using the syndromes obtained by measuring a subset of the stabilizer operators. In the second step, the phase flip errors are corrected by mapping the TSCs to color codes/surface codes, decoding them and lifting the error estimates back to the TSCs. An advantage of this decoding scheme is that it can make use of any well established algorithms for decoding surface codes or color codes. Our simulations of the decoder for the  subsystem code derived from a square octagon lattice resulted in a noise threshold of 1.75% which is comparable to results presented in the previous works on subsystem codes.

All are cordially invited

Details

Date:
March 16
Time:
2:00 pm - 3:00 pm
Event Category:

Venue

CSD-308
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