Majorana braiding simulations with projective measurements

TL;DR

This paper reviews the theoretical foundations and introduces a numerical simulation method for Majorana-based topological quantum computing, emphasizing projective measurements and device architecture modeling.

Contribution

It presents an efficient numerical method using the time-dependent Pfaffian formalism for simulating Majorana systems with measurements and disorder, supporting quantum computing research.

Findings

Developed a simulation tool for Majorana braiding and measurements.

Extended the computational capabilities beyond braiding alone.

Provided a semi-pedagogical overview and a practical simulation toolbox.

Abstract

We summarize the key ingredients required for universal topological quantum computation using Majorana zero modes in networks of topological superconductor nanowires. Particular emphasis is placed on the use of both sparse and dense logical qubit encodings, and on the transitions between them via projective parity measurements. Combined with hybridization, these operations extend the computational capabilities beyond braiding alone and enable universal gate sets. In addition to outlining the theoretical foundations-including the algebra of Majorana operators, along with the stabilizer formalism-we introduce an efficient numerical method for simulating the time-dependent dynamics of such systems. This method, based on the time dependent Pfaffian formalism, allows for the classical simulation of realistic device architectures that incorporate braiding, projective measurements, and disorder. The result is a semi-pedagogical overview and computational toolbox designed to support further exploration of topological quantum computing platforms.