# Measurement and control of a Coulomb-blockaded parafermion box

## TL;DR

This paper presents methods to measure and control parafermionic zero modes in a Coulomb-blockaded setup, enabling direct observation and manipulation of their quantum states for potential quantum computing applications.

## Contribution

It introduces a Coulomb-based parafermion box with protocols for detection, manipulation, and control of parafermionic states, advancing experimental access to these quasiparticles.

## Key findings

- Demonstrates a Coulomb blockade setup for parafermions
- Provides protocols for detecting and manipulating parafermionic states
- Enables direct measurement of zero-mode Hilbert space dimension

## Abstract

Parafermionic zero modes are fractional topologically protected quasiparticles expected to arise in various platforms. We show that Coulomb charging effects define a parafermion box with unique access options via fractional edge states and/or quantum antidots. Basic protocols for the detection, manipulation, and control of parafermionic quantum states are formulated. With those tools, one may directly observe the dimension of the zero-mode Hilbert space, prove the degeneracy of this space, and perform on-demand digital operations satisfying a parafermionic algebra.