Cheshire qudits from fractional quantum spin Hall states in twisted MoTe$_2$

TL;DR

This paper proposes a method to create topological quantum memory elements called Cheshire qudits from fractional quantum spin Hall states in twisted MoTe$_2$, utilizing hole punching and superconductivity to encode and manipulate quantum information.

Contribution

It introduces Cheshire qudits as a novel topological quantum memory platform based on fractional quantum spin Hall states and provides a systematic classification of gapped boundaries and defects.

Findings

Cheshire qudits encode quantum information using fractional topological charges.

Control of edge tunneling enables readout of Cheshire qudits.

Experimental signatures are proposed to distinguish different FQSH orders.

Abstract

Twisted MoTe$_2$ homobilayers exhibit transport signatures consistent with a fractional quantum spin Hall (FQSH) state. We describe a route to construct topological quantum memory elements, dubbed Cheshire qudits, formed from punching holes in such a FQSH state and using proximity-induced superconductivity to gap out the resulting helical edge states. Cheshire qudits encode quantum information in states that differ by a fractional topological "Cheshire" charge that is hidden from local detection within a condensate anyons. Control of inter-edge tunneling by gates enables both supercurrent-based readout of a Cheshire qudit, and capacitive measurement of the thermal entropy associated with its topological ground-space degeneracy. Additionally, we systematically classify different types of gapped boundaries, Cheshire qudits, and parafermionic twist defects for various Abelian and non-Abelian candidate FQSH orders that are consistent with the transport data, and describe experimental signatures to distinguish these orders.