11 papers · 1 filter
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…
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…