Quantum Error Correction Thresholds for the Universal Fibonacci Turaev-Viro Code

Schotte, Alexis; Zhu, Guanyu; Burgelman, Lander; Verstraete, Frank

doi:10.1103/physrevx.12.021012

Cited by 14 publications

(4 citation statements)

References 54 publications

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“…In these cases, one has to concatenate coherent errors and dephasing channels that mimic the syndrome measurement in order to make better contact to quantum error correction based on that syndrome measurement. It is also interesting to further consider non-Abelian quantum codes [65][66][67].…”

Section: Discussionmentioning

confidence: 99%

Diagnostics of mixed-state topological order and breakdown of quantum memory

Fan¹,

Bao²,

Altman³

et al. 2023

Preprint

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Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed states describing corrupted memories. Here we provide an intrinsic characterization of the breakdown of topological quantum memory, which both gives a bound on the performance of decoding algorithms and provides examples of topologically distinct mixed states. We employ three information-theoretical quantities that can be regarded as generalizations of the diagnostics of ground-state topological order, and serve as a definition for topological order in error-corrupted mixed states. We consider the topological contribution to entanglement negativity and two other metrics based on quantum relative entropy and coherent information. In the concrete example of the 2D Toric code with local bit-flip and phase errors, we map three quantities to observables in 2D classical spin models and analytically show they all undergo a transition at the same error threshold. This threshold is an upper bound on that achieved in any decoding algorithm and is indeed saturated by that in the optimal decoding algorithm for the Toric code.

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Section: Discussionmentioning

confidence: 99%

Diagnostics of mixed-state topological order and breakdown of quantum memory

Fan¹,

Bao²,

Altman³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Lastly, to fully understand the computational capabilities of non-Abelian quantum error correction [43,44] we want to investigate domain walls between non-Abelian phases to see how external defects can extend non-Abelian codes. This is again partially motivated by the quest to find schemes for quantum computing without the need for magic state distillation.…”

Section: Discussionmentioning

confidence: 99%

“…One approach to achieve a topologically protected universal gate set is to go beyond stabilizer-based topological QEC and use non-Abelian phases. However, even though first analysis show that -in principlenon-Abelian QEC is possible [43,44], it does not appear to be the best approach to simply store a qubit and perform simple operations, like Clifford gates. In Ref.…”

Section: Non-abelian Islands In Abelian Phasesmentioning

confidence: 99%

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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“…The string-net condensed state exhibits topological order, which is classified by the UMTC. In short, to simulate SU(3) Yang-Mills theory, which is necessary for high-energy physics, we should keep k, so that the state is in the confined phase (an extrapolation to the k → ∞ limit is also needed), while the state should be in the topological phase to use topological quantum computation or quantum error correcting code [47,48].…”

Section: Minimization Of Hmentioning

confidence: 99%

q deformed formulation of Hamiltonian SU(3) Yang-Mills theory

Hayata,

Hidaka

2023

J. High Energ. Phys.

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We study SU(3) Yang-Mills theory in (2 + 1) dimensions based on networks of Wilson lines. With the help of the q deformation, networks respect the (discretized) SU(3) gauge symmetry as a quantum group, i.e., SU(3)k, and may enable implementations of SU(3) Yang-Mills theory in quantum and classical algorithms by referring to those of the stringnet model. As a demonstration, we perform a mean-field computation of the groundstate of SU(3)k Yang-Mills theory, which is in good agreement with the conventional Monte Carlo simulation by taking sufficiently large k. The variational ansatz of the mean-field computation can be represented by the tensor networks called infinite projected entangled pair states. The success of the mean-field computation indicates that the essential features of Yang-Mills theory are well described by tensor networks, so that they may be useful in numerical simulations of Yang-Mills theory.

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Quantum Error Correction Thresholds for the Universal Fibonacci Turaev-Viro Code

Cited by 14 publications

References 54 publications

Diagnostics of mixed-state topological order and breakdown of quantum memory

Diagnostics of mixed-state topological order and breakdown of quantum memory

Bulk-to-boundary anyon fusion from microscopic models

q deformed formulation of Hamiltonian SU(3) Yang-Mills theory

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