# Measurement-only quantum computation with Majorana corner modes

## TL;DR

This paper proposes a measurement-only quantum computation scheme using Majorana corner modes in second-order topological superconductors, enabling fault-tolerant quantum gates via conductance interference.

## Contribution

It introduces a novel approach to realize measurement-only quantum computation with Majorana corner modes in 2D systems, expanding the potential for scalable topological quantum computing.

## Key findings

- Constructs two logical qubits and an ancilla qubit from eight Majorana corner modes.
- Demonstrates topologically protected gate operations via Majorana parity measurements.
- Proposes conductance interference as a method for measurement implementation.

## Abstract

Majorana modes, typically arising at the edges of one-dimensional topological superconductors, are considered to be a promising candidate for encoding nonlocal qubits in fault-tolerant quantum computation. Here we propose to exploit the two-dimensional geometry of Majorana corner modes in second-order topological superconductors to realize measurement-only quantum computation. In particular, a periodically modulated topological superconducting system may host eight Majorana corner modes, through which two logical qubits as well as one ancilla qubit can be constructed and topologically protected gate operations can be implemented by a series of Majorana parity measurements. The measurements are achieved via Mach-Zehnder type interference in the conductance of a semiconductor based topological superconductor. Our proposal represents a scenario in which single- and two-qubit gate operations can be carried out in a minimal setup that may provide a natural building block for Majorana-based qubit architectures.