Landauer Dissipation Bounds in Topological Quantum Computing

Abstract

We derive an exact analytical expression for the Landauer energy dissipation bound of non-Abelian anyonic quantum gates within topological surface codes under finite temperatures (T > 0) and system-bath correlation backflow. The derivation incorporates multi-anyon fusion channels, topological spin factors, quantum dimensions, and modular tensor category parameters into the exact partition function of the anyonic defect cluster. By integrating open quantum system master equations featuring non-Markovian memory kernels and system-bath correlation backflow tensors, we establish the generalized Landauer energy dissipation bound and prove the entropy scaling law mapping microscopic sub-system geometric entanglement entropy to macroscopic thermodynamic entropy production.