Enhanced fault-tolerant quantum computing in $d$-level systems

TL;DR

This paper introduces new error-correcting codes for $d$-level qudit systems that enable fault-tolerant quantum computing with improved performance as the system dimension increases.

Contribution

It presents novel codes with a transverse non-Clifford gate for prime $d$-level systems, enhancing fault-tolerance and error detection capabilities.

Findings

Codes detect up to approximately $d/3$ errors

Performance improves with increasing $d$

Enhances magic state distillation efficiency

Abstract

Error correcting codes protect quantum information and form the basis of fault tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transverse non-Clifford gate. Codes with the desired property are presented for $d$-level, qudit, systems with prime $d$. The codes use $n=d-1$ qudits and can detect upto $\sim d/3$ errors. We quantify the performance of these codes for one approach to quantum computation, known as magic state distillation. Unlike prior work, we find performance is always enhanced by increasing $d$.