On some projective unitary qutrit gates
Claire I. Levaillant

TL;DR
This paper explores topological quantum gates for qutrits derived from braiding six anyons in a specific topological quantum field theory, revealing new group structures and ancilla states for qubits.
Contribution
It introduces a new interpretation of certain braid groups in topological quantum computation and constructs novel ancilla states for qubits.
Findings
Identifies the Freedman group as a specific D-group in a new basis.
Provides a physical interpretation for Blichfeldfeld generators.
Constructs new ancilla states for qubits.
Abstract
As part of a protocol, we braid in a certain way six anyons of topological charges in the Kauffman-Jones version of Chern-Simons theory at level . The gate we obtain is a braid for the usual qutrit but with respect to a different basis. With respect to that basis, the Freedman group of \cite{LEV} is identical to the -group . We give a physical interpretation for each Blichfeld generator of the group . Inspired by these new techniques for the qutrit, we are able to make new ancillas, namely and , for the qubit .
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Quantum Information and Cryptography
