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We propose and analyze a physical system capable of performing topological quantum computation with Majorana zero modes (MZM) in a one-dimensional topological superconductor (1DTS). One of the leading methods to realize quantum gates in 1DTS is to use T-junctions, which allows one to maneuver MZMs such as to achieve braiding. In this paper, we propose a scheme that is in a purely one-dimensional geometry and does not require T-junctions, instead replacing it with an auxiliary qubit. We show that this allows one to perform one and two logical qubit $ Z $ rotations. We first design a topologically protected logical $Z$-gate based entirely on local interactions within the 1DTS. Using an auxiliary qubit coupled to the topological superconductors, we extend the $Z$-gate to single and multiqubit arbitrary rotations with partial topological protection. Finally, to perform universal quantum computing, we introduce a scheme for performing arbitrary unitary rotations, albeit without topological protection. We develop a formalism based on unitary braids which creates transitions between different topological phases of the 1DTS system. The unitary formalism can be simply converted to an equivalent adiabatic scheme, which we numerically simulate and show that high fidelity operations should be possible with reasonable parameters.
The oscillation of Majorana modes with near zero energy plays a very important role for ascertaining Majorana fermions. The edge states, which also have almost-zero-energy in one-dimensional Su-Schrieffer-Heeger chain (SSHc), have been extensively st
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We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor, in order to understand their use as a building block for topological quantum computers. We analyze the second-order topological corner modes that ari
As part of the intense effort towards identifying platforms in which Majorana bound states can be realized and manipulated to perform qubit operations, we propose a topological Josephson junction architecture that achieves these capabilities and whic