3 papers
quant-ph2025
Characterization of permutation gates in the third level of the Clifford hierarchy
Zhiyang He, Luke Robitaille, Xinyu Tan
The Clifford hierarchy is a fundamental structure in quantum computation whose mathematical properties are not fully understood. In this work, we characterize permutation gates --…
quant-ph2024
Permutation gates in the third level of the Clifford hierarchy
Zhiyang He, Luke Robitaille, Xinyu Tan
The Clifford hierarchy is a fundamental structure in quantum computation, classifying unitary operators based on their commutation relations with the Pauli group. Despite its signi…
math.GT2024
Simple Braids Tend toward Positive Entropy
Luke Robitaille, Minh-Tâm Quang Trinh
A simple braid is a positive braid that can be drawn so that any two strands cross at most once. We prove that as , the proportion of simple braids on strands tha…