From the 1 of 9 linked papers with an AI index.
9 papers
Deep Holes in the Clifford Hierarchy
Ian Teixeira, David Meyer
We determine the covering radius of the topological closure of the single-qubit Clifford hierarchy in $\SU(2)\cong S^3$. This closure is a union of great circles --- the Cliff…
Nuclear-Spin Statistical Weights from Young Diagrams
Eric Kubischta, Ian Teixeira
Nuclear-spin statistical weights and selection rules in molecular spectroscopy are governed by the permutation symmetry of identical nuclei, although rigid and semi-rigid molecules…
Time-Reversal Selection Rules for Quantum Error Correction
Eric Kubischta, Ian Teixeira
We apply time-reversal symmetry to quantum codes and show that it imposes parity selection rules on the physical error algebra. A time-reversal-invariant logical qubit on an odd nu…
Classical and Quantum MacWilliams Transforms as Spin Kinematics
Eric Kubischta, Ian Teixeira
The paper shows that MacWilliams transforms for both classical and quantum error‑correcting codes can be derived as spin‑kinematic operations, specifically as Wigner‑D rotations be…
Minimal Permutation-Invariant Qudit Codes from Edge-Colorings of Complete Graphs
Eric Kubischta, Ian Teixeira
We study permutation-invariant quantum codes in the symmetric subspace of qudits of local dimension . For every integer , we constru…
Orthogonal Polynomials and the MacWilliams Transform for Permutation-Invariant Qudit Codes
Ian Teixeira
We derive an explicit formula for the intrinsic MacWilliams transform for permutation-invariant qudit codes. Such codes naturally live in symmetric power representations, where the…