Quantum sets and clifford algebras

A. K. Kwaśniewski, W. Bajguz, I. Jaroszewski

Wuming Li

Pedro Amao, Hernán Castillo

Jonas Eidesen, David W. Kribs, Andrew Nemec

Clifford codes are a natural generalization of quantum stabilizer codes based primarily on representation theory. This class of codes has previously been extended to the setting of quantum subsystem codes. We formulate a two-fold generalization of Clifford codes, for both the hybrid classical and quantum information and projective representation theory settings. This leads to new classes of hybrid subspace and subsystem Clifford codes. We extend the fundamental representation theoretic quantum error correction theorem to include these codes, based on the operator algebra quantum error correction framework. We also discuss several examples throughout the presentation, of both stabilizer and non-stabilizer type.

Alexander Yu. Vlasov

In this paper is shown an application of Clifford algebras to the construction of computationally universal sets of quantum gates for n-qubit systems. It is based on the well-known application of Lie algebras together with the especially simple commutation law for Clifford algebras, which states that all basic elements either commute or anticommute.

Guihua Zeng, Yuan Li, Ying Guo +1 more

The key problem for constructing a stabilizer quantum code is how to create a set of generators for the stabilizer of the stabilizer quantum code, i.e. check matrix. In this paper, we suggest an approach based on the Clifford algebra to create the check matrix for the stabilizer quantum codes. In the proposed approach, the recursive relation of the matrix transform over the Clifford algebra is employed to generate the check matrix. With the proposed approach, a quantum code with any length can be constructed easily. Especially some new codes, which are impossible via previous approaches, are constructed.