26 citations · 47 across the 16 of their papers we have counts for
9 papers · 1 filter
From Steane to A7: Quantum Codes from Invariant States
Ian Teixeira
We construct a two-parameter family of single-error-correcting seven-ququart codes with transversal symmetry, realizing the finite component of a two-qubit super-gold…
-frames, negacyclic glue, and extremal strongly -modular lattices
Ian Teixeira
The classical -frame construction of the Coxeter--Todd lattice uses the hexacode as its glue. Here we replace the inert Eisenstein reduction at by the ramified Gaussian ch…
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
Spin is the hidden engine behind the zoo of MacWilliams transforms in weight enumerator theories - not only for qubits and qudits, but even for classical codes. From nothing more t…
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…
MacWilliams Identities for Intrinsic Quantum Codes
Eric Kubischta, Ian Teixeira
This paper develops a MacWilliams-type enumerator theory and semidefinite programming bounds for intrinsic quantum codes. An intrinsic code is a subspace of…