A new type of local-check additive quantum code is presented. Qubits are associated with
edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces …

We study properties of stabilizer codes that permit a local description on a regular D-
dimensional lattice. Specifically, we assume that the stabilizer group of a code (the gauge …

Every good quantum error-correcting code discovered thus far, such as those known as
“stabilizer” or “additive” codes, has had the structure of an eigenspace of an Abelian group …

Quantum simulation of fermionic systems is a promising application of quantum computers,
but to program them, we need to map fermionic states and operators to qubit states and …

arXiv:quant-ph/0111080v1 14 Nov 2001 Page 1 arXiv:quant-ph/0111080v1 14 Nov 2001
Stabilizer codes can be realized as graph codes D. Schlingemann Institut für …

The existence is proved of a class of open quantum systems that admits a linear subspace
${\cal C} $ of the space of states such that the restriction of the dynamical semigroup to the …

Error operator bases for systems of any dimension are defined and natural generalizations
of the bit/sign flip error basis for qubits are given. These bases allow generalizing the …

Graph states are generalized from qubits to collections of n qudits of arbitrary dimension D,
and simple graphical methods are used to construct both additive and nonadditive, as well …

We present a quantum error correcting code with $\textit {dynamically generated logical
qubits} $. When viewed as a subsystem code, the code has no logical qubits. Nevertheless …

This report continues the discussion of unitary error bases and quantum codes begun in"
Non-binary Unitary Error Bases and Quantum Codes". Nice error bases are characterized in …