Flag Fault-Tolerant Error Correction with Qudits

Abstract

In this thesis, I explore fault-tolerant quantum error correction using qudits. I show that a specific flag-fault-tolerant procedure for the five-qubit code may be extended to work on the five qudit code for any prime dimension. Using insights from this proof, I go on to show how to extend a procedure for doing flag-fault-tolerant quantum error correction on any stabilizer code to any qudit stabilizer code. These low overhead codes will be useful in development of quantum error correction on devices in the NISQ era.