RECURSIVE CONSTRUCTION OF NOISELESS SUBSYSTEM FOR QUDITS

摘要

When the environmental noise acting on the system has certain symmetries, a subsystem of the total system can avoid errors. Encoding information into such a subsystem is advantageous since it does not require any error syndrome measurements, which may introduce further errors to the system. However, utilizing such a subsystem for large systems gets impractical with the increasing number of qudits. A recursive scheme offers a solution to this problem. Here, we review the recursive construct introduced in,~1 which can asymptotically protect 1/d of the qudits in system against collective errors.