Abstract
We study the dynamics of Majorana zero modes that are shuttled via local tuning of the electrochemical potential in a superconducting wire. By performing time-dependent simulations of microscopic lattice models, we show that diabatic corrections associated with the moving Majorana modes are quantitatively captured by a simple Landau-Zener description. We further simulate a Rabi-oscillation protocol in a specific qubit design with four Majorana zero modes in a single wire and quantify constraints on the timescales for performing qubit operations in this setup. Our simulations utilize a Majorana representation of the system, which greatly simplifies simulations of superconductors at the mean-field level.
Highlights
Quantum computation holds great promise to solve some of the most challenging computational problems
Topological quantum computation [4] promises a giant leap forward by encoding quantum information into degrees of freedom that are inherently robust against external perturbations
In this paper we studied the dynamical manipulation of Majorana-based qubits by tuning a small number of electric gates
Summary
Quantum computation holds great promise to solve some of the most challenging computational problems. One of the earliest proposals for performing quantum computation with Majorana zero modes (MZMs) relies on physically moving these MZMs by tuning a series of electric gates under the superconductor in such a way as to drive different regions of the wire into the topological or non-topological regime [13]. Some of these restrictions may become more stringent [23, 24] While theoretically appealing, this model of computation has been regarded as somewhat impractical due to the large voltages that might be required to tune the system in and out of the topological regime. We confirm the scaling relation for diabatic errors in these more realistic settings, and discuss the constraints on the qubit operation timescales and the accuracy limitations due to the finite size of the qubit
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