Dephasing of Majorana-based qubits

TL;DR

This paper investigates the dephasing mechanisms in Majorana-based qubits, identifying charge noise as a key factor and estimating coherence times based on MZM separation and temperature effects.

Contribution

It provides a detailed analysis of residual dephasing in Majorana qubits due to charge noise, including quantitative estimates of coherence times and their dependence on MZM separation.

Findings

Charge noise is the dominant dephasing source.

Coherence time is hundreds of nanoseconds at certain MZM separations.

Coherence time increases exponentially with MZM separation and is temperature-limited at large distances.

Abstract

We analyze charging-energy-protected Majorana-based qubits, focusing on the residual dephasing that is present when the distance between Majorana zero modes (MZMs) is insufficient for full topological protection. We argue that the leading source of dephasing is $1/f$ charge noise. This noise affects the qubit as a result of the hybridization energy and charge distribution associated with weakly-overlapping MZMs, which we calculate using a charge-conserving formalism. We estimate the coherence time to be hundreds of nanoseconds for Majorana-based qubits whose MZM separation is $L\sim 5\xi$ (with $\xi$ being the coherence length). The coherence time grows exponentially with MZM separation and eventually becomes temperature-limited for $L/\xi \sim 30$.