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 semipedagogical overview and computational toolbox designed to support further exploration of topological quantum computing platforms.

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• Majorana bound states
• Majorana fermions
• Topological quantum computing
• Topological superconductors