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Concatenated Stabilizer Dynamical Decoupling

Gerardo Paz, University of Southern California

(Session 2 : Thursday from 8:30pm-9:00pm)

Abstract. We show how to integrate concatenated dynamical decoupling (CDD) techniques with quantum error correction (QEC) codes: the two main strategies to protect quantum information from the decoherence induced by unwanted interaction with the environment. It has been shown that CDD can be used as a lower level protection layer against decoherence and improves the effective error rate of a physical gate, provided one assumes certain locality conditions (local bath assumption) [Ng, Lidar, Preskill, arXiv:0911.3202]. The typical CDD protocol uses pulses from a group of non-commuting operators to decouple to arbitrary order, in the language of Magnus expansion, the state one wants to protect from the environment. In this work, in the same spirit as [Lidar, Phys. Rev. Lett. 100,160506 (2008)], we show how decouple a state encoded in some stabilizer QEC code to arbitrary order by applying pulses from the stabilizer group of the QEC code used. We demonstrate the technique for concatenated and non-concatenated QEC codes and show that, in contrast to the CDD case, (i) one can omit the local bath assumption, and (ii) has the freedom of introducing a fixed evolution for the protected quantum state. We show how to decouple a multiqubit state with a non-local system bath to arbitrary order (dictated by the distance of the QEC code).