Fault-Tolerant Quantum Computation with Higher-Dimensional Systems

Abstract

Instead of a quantum computer where the fundamental units are 2-dimensional qubits, we can consider a quantum computer made up of d-dimensional systems. There is a straightforward generalization of the class of stabilizer codes to d-dimensional systems, and I will discuss the theory of fault-tolerant computation using such codes. I prove that universal fault-tolerant computation is possible with any higher-dimensional stabilizer code for prime d.