26 citations · 47 across the 16 of their papers we have counts for
17 papers
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…
Intrinsic Quantum Codes
Eric Kubischta, Ian Teixeira
We introduce an intrinsic formulation of quantum error correction based on representation theory, in which error-protection structure is encoded directly in a unitary group represe…
Classification of the Subgroups of the Two-Qubit Clifford Group
Eric Kubischta, Ian Teixeira
We perform a complete classification of all 56 subgroups of the two-qubit Clifford group containing the two-qubit Pauli group. We provide generators for these groups using gates fa…
Flexible Fault Tolerant Gate Gadgets
Eric Kubischta, Ian Teixeira
We design flexible fault tolerant gate gadgets that allow the data and the ancilla to be encoded using different codes. By picking a stabilizer code for the ancilla we are able to…
Quantum Codes and Irreducible Products of Characters
Eric Kubischta, Ian Teixeira
In a recent paper, we defined twisted unitary -groups and showed that they automatically induced error-detecting quantum codes. We also showed that twisted unitary -groups co…
Quantum Codes from Twisted Unitary -groups
Eric Kubischta, Ian Teixeira
We introduce twisted unitary -groups, a generalization of unitary -groups under a twisting by an irreducible representation. We then apply representation theoretic methods to…
Permutation-Invariant Quantum Codes with Transversal Generalized Phase Gates
Eric Kubischta, Ian Teixeira
With respect to the transversal gate group (an invariant of quantum codes), we demonstrate that non-additive codes can outperform stabilizer codes. We do this by constructing spin…
Quantum Weight Enumerators for Real Codes with and Exactly Transversal
Eric Kubischta, Ian Teixeira, J. Maxwell Silvester
In this note we show that the weight enumerators of a real quantum error correcting code with and exactly transversal must satisfy certain identities. One consequence o…
A Family of Quantum Codes with Exotic Transversal Gates
Eric Kubischta, Ian Teixeira
Recently an algorithm has been constructed that shows the binary icosahedral group $\2I$ together with a -like gate forms the most efficient single-qubit universal gate set. To…