Article

Abstract

• Recent work has shown that a self-correcting quantum memory can exist in three spatial dimensions, provided that it is protected by a 1-form symmetry. Requiring that the dynamics of a system obey this type of symmetry is equivalent to enforcing a macroscopic number of symmetry terms throughout the bulk. In this paper, we show how to replace the explicit 1-form symmetry with an emergent 1-form symmetry in the bulk and an explicit 1-form symmetry on the boundary. To do so, we use the extended excitations of a three-dimensional (3D) toric code to confine anyons in a two-dimensional (2D) toric code on the boundary. The boundary anyons are bound to the bulk excitations by the explicit 1-form symmetry. Although the symmetry still has to be explicitly enforced on the boundary, this could conceivably be a more attainable constraint due to the accessibility of the boundary qubits. Furthermore, this only requires $O\left(L^2\right)$ terms for a system of linear size $L$, instead of $O\left(L^3\right)$ terms.

Creator

• Stahl, Charles

Date Issued

• 2023

Additional Information

• Publication of this article was funded by the University of Colorado Boulder Libraries Open Access Fund.

Academic Affiliation

• Physics

Journal Title

• PRX Quantum

Journal Issue/Number

• 3

Journal Volume

• 4

Last Modified

• 2023-09-29

Resource Type

• Article

Rights Statement

• In Copyright

DOI

•  https://doi.org/10.1103/PRXQuantum.4.030341

ISSN

• 2691-3399

Language

• English [eng]

License

• Creative Commons BY Attribution 4.0 International

Relationships

In Collection:

• University Libraries Open Access Fund Supported Publications

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