Distinct Lifetimes for $X$ and $Z$ Loop Measurements in a Majorana Tetron Device

TL;DR

This paper reports on a Majorana-based tetron device with distinct parity lifetimes for $X$ and $Z$ measurements, highlighting different decoherence mechanisms and measurement fidelities in a superconductor-semiconductor heterostructure.

Contribution

It introduces a novel tetron qubit device with separate $X$ and $Z$ loop measurements and characterizes their different parity lifetimes and error rates.

Findings

Parity lifetime for $X$ loop is approximately 14.5 microseconds.

Parity lifetime for $Z$ loop is approximately 12.4 milliseconds.

Measurement errors are 16% for $X$ and 0.5% for $Z$ operations.

Abstract

We present a hardware realization and measurements of a tetron qubit device in a superconductor-semiconductor heterostructure. The device architecture contains two parallel superconducting nanowires, which support four Majorana zero modes (MZMs) when tuned into the topological phase, and a trivial superconducting backbone. Two distinct readout interferometers are formed by connecting the superconducting structure to a series of quantum dots. We perform single-shot interferometric measurements of the fermion parity for the two loops, designed to implement Pauli-$X$ and $Z$ measurements of the tetron. Performing repeated single-shot measurements yields two widely separated time scales $\tau_X = 14.5\pm 0.3 \, \mathrm{\mu s}$ and $\tau_Z = 12.4\pm 0.4\, \mathrm{ms}$ for parity switches observed in the $X$ and $Z$ measurement loops, which we attribute to intra-wire parity switches and external quasiparticle poisoning, respectively. We estimate assignment errors of $\mathrm{err}^X_a=16\%$ and $\mathrm{err}^Z_a=0.5\%$ for $X$ and $Z$ measurement-based operations, respectively.