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arXiv · 2212.00042

Anyon condensation and the color code

Markus S. Kesselring·Julio C. Magdalena de la Fuente·Felix Thomsen·Jens Eisert·Stephen D. Bartlett·Benjamin J. Brown
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Abstract

The manipulation of topologically-ordered phases of matter to encode and process quantum information forms the cornerstone of many approaches to fault-tolerant quantum computing. Here we demonstrate that fault-tolerant logical operations in these approaches can be interpreted as instances of anyon condensation. We present a constructive theory for anyon condensation and, in tandem, illustrate our theory explicitly using the color-code model. We show that different condensation processes are associated with a general class of domain walls, which can exist in both space- and time-like directions. This class includes semi-transparent domain walls that condense certain subsets of anyons. We use our theory to classify topological objects and design novel fault-tolerant logic gates for the color code. As a final example, we also argue that dynamical `Floquet codes' can be viewed as a series of condensation operations. We propose a general construction for realising planar dynamically driven codes based on condensation operations on the color code. We use our construction to introduce a new Calderbank-Shor Steane-type Floquet code that we call the Floquet color code.

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Markus S. Kesselring, Julio C. Magdalena de la Fuente, Felix Thomsen, Jens Eisert, Stephen D. Bartlett, Benjamin J. Brown. 2022-11-30. Anyon condensation and the color code. https://doi.org/10.1103/prxquantum.5.010342

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