Universal gates via fusion and measurement operations on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>SU</mml:mi><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>anyons

Levaillant, Claire I.; Bauer, Bela; Freedman, Michael; Wang, Zhenghan; Bonderson, Parsa

doi:10.1103/physreva.92.012301

Cited by 29 publications

(21 citation statements)

References 49 publications

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“…This particular twist liquid may be of practical interest in the context of quantum computing. Although the SU (2) 4 state does not contain a Fibonacci anyon 59,137 , it may still support universal quantum computing 138,139 if interferometric measurements 140 are incorporated with braiding operations.…”

Section: Connections Between the Z3-parafermionsmentioning

confidence: 99%

Theory of twist liquids: Gauging an anyonic symmetry

2015

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Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric-magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids, which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the Z2-symmetric toric code, SO(2N )1 and SU (3)1 state as well as the S3-symmetric SO(8)1 state and a non-Abelian chiral state we call the "4-Potts" state.

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Section: Connections Between the Z3-parafermionsmentioning

confidence: 99%

Theory of twist liquids: Gauging an anyonic symmetry

2015

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“…where D = a √ d 2 a is such that for modular theories the S-matrix is unitary. For modular theories, a collective charge projector can be defined [50] by Π 1...n a = a 1 a 2 . .…”

Section: Basic Data Of the Algebraic Theory Of Anyonsmentioning

confidence: 99%

Fault-Tolerant Quantum Error Correction for non-Abelian Anyons

Dauphinais

Poulin

2017

Commun. Math. Phys.

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While topological quantum computation is intrinsically fault-tolerant at zero temperature, it loses its topological protection at any finite temperature. We present a scheme to protect the information stored in a system supporting non-cyclic anyons against thermal and measurement errors. The correction procedure builds on the work of Gács [1] and Harrington [2] and operates as a local cellular automaton. In contrast to previously studied schemes, our scheme is valid for both abelian and non-abelian anyons and accounts for measurement errors. We analytically prove the existence of a fault-tolerant threshold for a certain class of non-Abelian anyon models, and numerically simulate the procedure for the specific example of Ising anyons. The result of our simulations are consistent with a threshold between 10 −4 and 10 −3 .

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“…This anyon model is closely related to models of parafermionic zero modes at defects in gapped fractional quantum Hall states [22][23][24] . It has recently been shown that the P = 3 case of metaplectic anyons is universal for quantum computation when braiding is supplemented by measurement 25,26 ; this is likely to be true for P > 3 as well.…”

Section: Transitions To Metaplectic Quantum Hall Statesmentioning

confidence: 95%

Chern-Simons-Higgs transitions out of topological superconducting phases

Clarke

Nayak

2015

Phys. Rev. B

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In this study, we examine effective field theories of superconducting phases with topological order, making connection to proposed realizations of exotic topological phases (including those hosting Ising and Fibonacci anyons) in superconductor-quantum Hall heterostructures. Our effective field theories for the non-Abelian superconducting states are non-Abelian Chern-Simons theories in which the condensation of vortex-quasiparticle composites lead to the associated Abelian quantum Hall states. This Chern-Simons-Higgs condensation process is dual to the emergence of superconducting non-Abelian topological phases in coupled chain constructions. In such transitions, the chiral central charge of the system generally changes, so they fall outside the description of bosonic condensation transitions put forth by Bais and Slingerland 1 (though the two approaches agree when the described transitions coincide). Our condensation process may be generalized to Chern-Simons theories based on arbitrary Lie groups, always describing a transition from a Lie Algebra to its Cartan subalgebra. We include several instructive examples of such transitions.

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Universal gates via fusion and measurement operations onSU(2)4anyons

Cited by 29 publications

References 49 publications

Theory of twist liquids: Gauging an anyonic symmetry

Theory of twist liquids: Gauging an anyonic symmetry

Fault-Tolerant Quantum Error Correction for non-Abelian Anyons

Chern-Simons-Higgs transitions out of topological superconducting phases

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