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Published March 2017 | Published + Submitted
Journal Article Open

Topological order and memory time in marginally-self-correcting quantum memory

Abstract

We examine two proposals for marginally-self-correcting quantum memory: the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their Gibbs ensembles can be prepared via a short-depth quantum circuit from classical ensembles. Our proof technique naturally gives rise to the notion of free energy associated with excitations. Further, we develop a framework for an ergodic decomposition of Davies generators in CSS codes which enables formal reduction to simpler classical memory problems. We then show that memory time in the welded code is doubly exponential in inverse temperature via the Peierls argument. These results introduce further connections between thermal topological order and self-correction from the viewpoint of free energy and quantum circuit depth.

Additional Information

© 2017 American Physical Society. (Received 22 April 2016; published 22 March 2017) We would like to thank J. Preskill and K. Temme for discussions and O. Motrunich for providing computational resources for numerics. This work was supported through Summer Undergraduate Research Fellowship (SURF) and NSF Grant No. PHY-1125565 at the California Institute of Technology. Research at Perimeter Institute was supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.

Attached Files

Published - PhysRevA.95.032324.pdf

Submitted - 1603.07805v1.pdf

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August 19, 2023
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October 19, 2023