Anyon condensation and the color code
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
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| _version_ | 1866911794997493760 |
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| author | Kesselring, Markus S. de la Fuente, Julio C. Magdalena Thomsen, Felix Eisert, Jens Bartlett, Stephen D. Brown, Benjamin J. |
| author_facet | Kesselring, Markus S. de la Fuente, Julio C. Magdalena Thomsen, Felix Eisert, Jens Bartlett, Stephen D. Brown, Benjamin J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00042 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Anyon condensation and the color code Kesselring, Markus S. de la Fuente, Julio C. Magdalena Thomsen, Felix Eisert, Jens Bartlett, Stephen D. Brown, Benjamin J. Quantum Physics Strongly Correlated Electrons 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. |
| title | Anyon condensation and the color code |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2212.00042 |