Universal Gates via Fusion and Measurement Operations on SU$(2{)}_4$ Anyons

Abstract

We examine a class of operations for topological quantum computation based on fusing and measuring topological charges for systems with SU$(2{)}_4$ or $k=4$ Jones-Kauffman anyons. We show that such operations augment the braiding operations, which, by themselves, are not computationally universal. This augmentation results in a computationally universal gate set through the generation of an exact, topologically protected irrational phase gate and an approximate, topologically protected controlled-$Z$ gate.

18 pages; v2: new title, minor corrections and clarifications made

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Measurement-Only Topological Quantum Computation
• Genons, twist defects, and projective non-Abelian braiding statistics
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Interferometry of non-Abelian Anyons
• Measurement-Only Topological Quantum Computation via Anyonic Interferometry
• Introduction to Quantum Computation
• Measurement-Only Topological Quantum Computation via Tunable Interactions
• Efficient synthesis of probabilistic quantum circuits with fallback
• Decoherence of Anyonic Charge in Interferometry Measurements
• Topological quantum computation within the anyonic system the Kauffman-Jones version of SU(2) Chern-Simons theory at level 4

Cited by in corpus (12)

• Qutrit Toric Code and Parafermions in Trapped Ions
• Baryogenesis, magnetogenesis and the strength of anomalous interactions
• Large-scale gauge spectra and pseudoscalar couplings
• A framework for exact synthesis
• Measuring Topological Order
• How SU(2)${}_4$ Anyons are Z${}_3$ Parafermions
• On measuring the topological charge of anyons
• Ternary Logic Design in Topological Quantum Computing
• Topological quantum compilation of metaplectic anyons based on the genetic optimized algorithms
• Topological Quantum Computation on Supersymmetric Spin Chains
• The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm
• Universal Gates from Braiding and Fusing Anyons on Quantum Hardware