Quantum code for quantum error characterization

TL;DR

This paper introduces ambiguous stabilizer codes (ASCs), a new type of quantum code that aids in characterizing quantum dynamics by reducing probe state size, despite requiring more operations.

Contribution

The paper proposes ambiguous stabilizer codes (ASCs) as a novel tool for quantum error characterization, expanding the utility of stabilizer codes beyond traditional error correction.

Findings

ASCs can reduce the size of CQD probe states.

Using ASCs increases the number of operations needed.

ASCs enable error detection without full correction.

Abstract

A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within $\mathcal{C}$, can be used for detection of errors, but not for quantum error correction. Such a code with stabilizer structure, which we call an "ambiguous stabilizer code" (ASC), can nevertheless be useful for the characterization of quantum dynamics (CQD). The use of ASCs can help lower the size of CQD probe states used, but at the cost of increased number of operations.