Fault-Tolerant Computing with Single Qudit Encoding

TL;DR

This paper introduces a fault-tolerant quantum-error correction method using single multi-level qudits, demonstrating nearly exponential error suppression with linear resource growth, outperforming traditional multi-qubit codes.

Contribution

It presents a novel single-qudit encoding approach for fault-tolerant quantum error correction, reducing resource requirements and enhancing error suppression capabilities.

Findings

Nearly exponential error suppression achieved

Linear growth in qudit size suffices

Outperforms multi-qubit codes with thousands of units

Abstract

We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit to avoid resource escalation typical of multi-qubit codes. These codes can be customized to the specific physical errors on the qudit, effectively suppressing them. We demonstrate a Fault-Tolerant implementation on molecular spin qudits, showcasing nearly exponential error suppression with only linear qudit size growth. Notably, this outperforms qubit codes using thousands of units. We also outline the required properties for a generic physical system to Fault-Tolerantly implement these embedded codes.