Time scales for charge-transfer based operations on Majorana systems

TL;DR

This paper analyzes the time scales and fidelity limits of charge-transfer operations on Majorana systems, providing a full dynamical description and identifying regimes for high-fidelity quantum operations.

Contribution

It introduces a comprehensive method for modeling the full time-evolution of charge transfer in Majorana systems and establishes bounds on operation times using full counting statistics.

Findings

Existence of a high-fidelity operation regime with realistic parameters

Bounds on operation time scales depend on superconducting phase difference and quasiparticle tunneling

Proposed protocol to measure dephasing and dynamical phase effects

Abstract

In this article we analyze the efficiency of operations based on transferring charge from a quantum dot (QD) to two coupled topological superconductors, which can be used for performing nonabelian operations on Majorana bound states (MBSs). We develop a method which allows us to describe the full time-evolution of the system as the QD energy is manipulated. Using a full counting statistics analysis, we set bounds to the operation time scales. The lower bound depends on the superconducting phase difference due to a partial decoupling of the different MBSs parity sectors, while the upper bound is set by the tunneling of quasiparticles to the MBSs. Using realistic parameters, we find the existence of a regime where the operation can be carried out with a fidelity close to unity. Finally, we propose the use of a two operations protocol to quantify the effect of the dephasing and accumulated dynamical phases, demonstrating their absence for certain superconducting phase differences.