Implementation of single-qubit gates via parametric modulation in the Majorana transmon

TL;DR

This paper proposes a voltage gate-based control method for Majorana transmons using sinusoidal modulation, achieving high-fidelity single-qubit gates with robustness against charge noise.

Contribution

It introduces a novel modulation protocol for Majorana transmons that enables tunable single-qubit gates with minimal control errors and analyzes noise effects.

Findings

Achieved qubit control errors below 2×10^{-4}.

Demonstrated long dephasing times (~milliseconds) at sweet spots.

Showed resilience of the $X$-gate fidelity against charge noise.

Abstract

We present a voltage gate-based method for controlling the Majorana transmon, using a sinusoidal modulation of the induced offset charge $n_g$. Working in the transmon regime and in the instantaneous eigenstates basis, we find the time evolution under this protocol that realises tunable $X$-$Z$ rotations. We optimise the parameters of the system for different single-qubit gates in both the laboratory frame and the qubit rotating frame, obtaining qubit control errors $1-\mathcal{F}$ smaller than $\sim2\times 10^{-4}$. In addition to this, we conduct an analysis of the effects of the charge noise, assuming wide-band $1/f$ additive noise in $n_g$, both for the free and the driven evolutions. For the free evolution, the relaxation and dephasing rates are calculated perturbatively, obtaining long dephasing times of the order of milliseconds at the system's sweet-spots. For the driven case, the average fidelity for the $X$-gate is obtained via a numerical simulation, demonstrating remarkable resilience.