Dephasing and leakage dynamics of noisy Majorana-based qubits: Topological versus Andreev

TL;DR

This paper proposes a protocol to verify topological protection in Majorana-based qubits, distinguishing them from trivial states, and analyzes how noise affects qubit coherence and leakage, revealing phase transition signatures.

Contribution

It introduces a Ramsey-type protocol for near-term Majorana qubits to validate topological protection and differentiate true Majoranas from Andreev bound states, including analysis of noise-induced leakage.

Findings

The protocol can distinguish Majorana from Andreev states via dephasing dependence.

Leakage analysis reveals the topological phase transition onset.

Measurement scheme is feasible with quantum dot coupling, requiring no braiding.

Abstract

Topological quantum computation encodes quantum information nonlocally by nucleating non-Abelian anyons separated by distances $L$, typically spanning the qubit device size. This nonlocality renders topological qubits exponentially immune to dephasing from all sources of classical noise with operator support local on the scale of $L$. We perform detailed analytical and numerical analyses of a time-domain Ramsey-type protocol for noisy Majorana-based qubits that is designed to validate this coveted topological protection in near-term devices such as the so-called `tetron' design. By assessing dependence of dephasing times on tunable parameters, e.g., magnetic field, our proposed protocol can clearly distinguish a bona fide Majorana qubit from one constructed from semilocal Andreev bound states, which can otherwise closely mimic the true topological scenario in local probes. In addition, we analyze leakage of the qubit out of its low-energy manifold due to classical-noise-induced generation of quasiparticle excitations; leakage limits the qubit lifetime when the bulk gap collapses, and hence our protocol further reveals the onset of a topological phase transition. This experiment requires measurement of two nearby Majorana modes for both initialization and readout---achievable, for example, by tunnel coupling to a nearby quantum dot---but no further Majorana manipulations, and thus constitutes an enticing pre-braiding experiment. Along the way, we address conceptual subtleties encountered when discussing dephasing and leakage in the context of Majorana qubits.