Now showing 1 - 3 of 3
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    Quantum computation with charge-and-color-permuting twists in qudit color codes
    (01-02-2022)
    Gowda, Manoj G.
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    Twists are defects in the lattice which can be utilized to perform computations on encoded data. Twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes, and qubit subsystem color codes. They are known to exhibit projective non-Abelian statistics, which is exploited to perform encoded gates. In this paper, we initiate the study of twists in qudit color codes over the odd prime alphabet. Specifically, we present a systematic construction of twists in qudit color codes that permute both charge and color of the excitations. We also present a mapping between generalized Pauli operators and strings in the lattice. Making use of the construction, we give protocols to implement generalized Clifford gates using charge-and-color-permuting twists.
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    Quantum computation with generalized dislocation codes
    (29-10-2020)
    Gowda, Manoj G.
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    In this paper, we study quantum computing with twists. Twists are yet another form of defects in a lattice. They arise from dislocations in the lattice and can be used to encode and process quantum information. Surface codes with twists are also called dislocation codes. Hastings and Geller showed that dislocation codes could provide gains in space-time complexity of quantum computation. In this paper, we undertake a detailed study of generalized dislocation codes. We develop the theory of qubit dislocation codes over arbitrary four-valent and bicolorable lattices. We give a construction to introduce twists in such lattices and also study the structure of logical operators. We then study dislocation codes over odd prime dimensions in square lattices. Using the theory developed, we present protocols for implementing a universal gate set in qubit dislocation codes. We also show how to implement the generalized Clifford group in qudit dislocation codes in odd prime dimensions.
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    Publication
    Color codes with twists: Construction and universal-gate-set implementation
    (01-07-2021)
    Gowda, Manoj G.
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    Twists are defects in a lattice that can be used to perform encoded computations. Three basic types of twists can be introduced in color codes: twists that permute color, charge of anyons, and domino twists that permute the charge label of an anyon with a color label. In this paper, we study a subset these twists from a coding theoretic viewpoint. Specifically, we discuss systematic construction of charge permuting and color permuting twists in color codes. We show that by braiding alone, Clifford gates can be realized in color codes with charge permuting twists. We also discuss implementing single-qubit Clifford gates by a Pauli frame update and CNOT gate by braiding holes around twists in color codes with color permuting twists. Finally, we also discuss implementing a non-Clifford gate by state injection, thus completing the realization of a universal gate set.