A brief introduction to operator quantum error correction

Operator quantum error correction

This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known techniques - i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method - as special cases, and relies on a generalized mathematical framework for noiseless subsystems that applies to arbitrary quantum operations. We also discuss a number of examples and introduce the notion of ``unitarily noiseless…

算子代数量子纠错中的稳定子形式体系

Stabilizer Formalism for Operator Algebra Quantum Error Correction

本文为算子代数量子纠错建立稳定子形式体系，推广 QEC 与 OQEC 的经典定理，并据此构造混合 Bacon-Shor 码、刻画可纠正 Pauli 错误及推导码距。

Recent progress on truncated Toeplitz operators

This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason's seminal paper in 2007.

混合 Clifford 码：基于算子代数量子纠错与投影表示理论

Hybrid Clifford Codes via Operator Algebra Quantum Error Correction and Projective Representation Theory

本文通过算子代数量子纠错框架和投影表示理论，将 Clifford 码推广到混合经典-量子信息与投影表示设置，提出了新的混合子空间和子系统 Clifford 码，并扩展了基本表示论量子纠错定理。