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

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 $\ddot{I}{„}_X=14.5\pm 0.3\hat{\mathrm{I}}¼\mathrm{s}$ and $\ddot{I}{„}_Z=12.4\pm 0.4\mathrm{ms}$ 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 ${\mathrm{err}}_a^X=16\%$ and ${\mathrm{err}}_a^Z=0.5\%$ for $X$ and $Z$ measurement-based operations, respectively.

Extended discussion of switching dynamics and multiple time scales in App. A. Added App. C on alternative scenarios. Corrected Figs. 2(i) & A4. Explained the method for extracting multiple time scales from long time traces in App. A