Non-binary Entanglement-assisted Stabilizer Quantum Codes

TL;DR

This paper introduces a method to construct non-binary entanglement-assisted stabilizer quantum codes using pre-shared entanglement, expanding the range of classical codes applicable for quantum error correction.

Contribution

It presents a new construction approach for non-binary entanglement-assisted stabilizer codes that relaxes the dual-containing constraint, enabling the use of a broader class of classical codes.

Findings

Codes do not require dual-containing constraint

Algorithm for circuit construction provided

Applicable to non-binary LDPC codes

Abstract

In this paper, we show how to construct non-binary entanglement-assisted stabilizer quantum codes by using pre-shared entanglement between the sender and receiver. We also give an algorithm to determine the circuit for non-binary entanglement-assisted stabilizer quantum codes and some illustrated examples. The codes we constructed do not require the dual-containing constraint, and many non-binary classical codes, like non-binary LDPC codes, which do not satisfy the condition, can be used to construct non-binary entanglement-assisted stabilizer quantum codes.