Anyon condensation and the color code

Kesselring, Markus S.; Fuente, Julio C. Magdalena de la; Thomsen, Felix Sebastian Leo; Eisert, Jens; Bartlett, Stephen D.; Brown, B. R.

doi:10.48550/arxiv.2212.00042

Cited by 7 publications

(11 citation statements)

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“…The bulk-to-boundary fusion multiplicities can also be used to study computational protocols including boundaries and domain walls [18,36,47]. This includes lattice surgery [20,48] schemes in Abelian topological codes and allows for systematic study of the computational possibilities of a given code via anyon condensation [18]. Moreover, domain walls between non-Abelian phases und Abelian ones can be used to generalize the scheme presented in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…The boundary of the regular neighborhood of this vertex is a pair of pants -or three-punctured sphere. Just as before we can define a vector space (in terms of its basis) by tessellating this manifold with trivalent vertices from the input fusion category (see (18)). Let's call this space F .…”

Section: Fusion and Braiding In The Bulkmentioning

confidence: 99%

“…For example, the logical operators of a topological code on a manifold with boundary are associated to ribbon operators [17] of anyons which connect different boundary segments through the bulk. Moreover, any lattice-surgery-based computation scheme ultimately relies on deforming non-transparent domain walls between code patches into (partly-)transparent ones in a systematic way [18][19][20]. Understanding how the anyon ribbon operators precisely behave close to these domain walls is therefore essential in the design of novel computational protocols in topological codes.…”

mentioning

confidence: 99%

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Bulk-to-boundary anyon fusion from microscopic models

Fuente¹,

Eisert²,

Bauer³

2023

Preprint

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Topological quantum error correction based on the manipulation of the anyonic defects constitutes one of the most promising frameworks towards realizing fault-tolerant quantum devices. Hence, it is crucial to understand how these defects interact with external defects such as boundaries or domain walls. Motivated by this line of thought, in this work, we study the fusion events between anyons in the bulk and at the boundary in fixed-point models of 2+1-dimensional nonchiral topological order defined by arbitrary fusion categories. Our construction uses generalized tube algebra techniques to construct a bi-representation of bulk and boundary defects. We explicitly derive a formula to calculate the fusion multiplicities of a bulk-to-boundary fusion event for twisted quantum double models and calculate some exemplary fusion events for Abelian models and the (twisted) quantum double model of S 3 , the simplest non-Abelian group-theoretical model. Moreover, we use the folding trick to study the anyonic behavior at non-trivial domain walls between twisted S 3 and twisted Z 2 as well as Z 3 models. A recurring theme in our construction is an isomorphism relating twisted cohomology groups to untwisted ones. The results of this work can directly be applied to study logical operators in two-dimensional topological error correcting codes with boundaries described by a twisted gauge theory of a finite group.

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Section: Discussionmentioning

confidence: 99%

Section: Fusion and Braiding In The Bulkmentioning

confidence: 99%

mentioning

confidence: 99%

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Bulk-to-boundary anyon fusion from microscopic models

Fuente¹,

Eisert²,

Bauer³

2023

Preprint

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“…. This is a relatively recent development also referred to as pairmeasurement codes [7][8][9][10][11][12]. As in CBQC, the base model assumes a fixed set of physical qubits which evolve in time with the aid of projective parity measurements on qubit pairs.…”

Section: Floquet-based Quantum Computation (Flobqc)mentioning

confidence: 99%

“…This is equivalent to the Floquet code presented in Ref. [12]. The Z checks (c) and X checks (d) consist of six ZZ and XX measurement outcomes, respectively.…”

Section: Expressing Fault-tolerance As Zx Instrument Networkmentioning

confidence: 99%

Logical Blocks for Fault-Tolerant Topological Quantum Computation

et al. 2023

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There are several models of quantum computation which exhibit shared fundamental fault-tolerance properties. This article makes commonalities explicit by presenting these different models in a unifying framework based on the ZX calculus. We focus on models of topological fault tolerance -specifically surface codesincluding circuit-based, measurement-based and fusion-based quantum computation, as well as the recently introduced model of Floquet codes. We find that all of these models can be viewed as different flavors of the same underlying stabilizer fault-tolerance structure, and sustain this through a set of local equivalence transformations which allow mapping between flavors. We anticipate that this unifying perspective will pave the way to transferring progress among the different views of stabilizer fault-tolerance and help researchers familiar with one model easily understand others.

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