Quantum Stabilizer Codes Embedding Qubits Into Qudits

TL;DR

This paper introduces a novel quantum error-correcting code that embeds a qubit into a qudit using non-commutative geometry, demonstrating superior performance over standard stabilizer codes on Weyl channels.

Contribution

It presents a new stabilizer code embedding qubits into qudits, leveraging discrete phase space geometry for enhanced error correction capabilities.

Findings

The code effectively protects against amplitude and phase errors.

It outperforms five and seven qubit stabilizer codes on Weyl channels.

Entanglement fidelity analysis confirms its robustness.

Abstract

We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to protect the qubit against both amplitude and phase errors. The performance of such code is evaluated on Weyl channels by means of the entanglement fidelity as function of the error probability. A comparison with standard block codes, like five and seven qubit stabilizer codes, shows its superiority.