New Three and Four-Dimensional Toric and Burst-Error-Correcting Quantum Codes

TL;DR

This paper introduces new three and four-dimensional toric quantum codes with enhanced burst-error correction capabilities using quantum interleaving, improving information rates and robustness for quantum memory and channels with memory.

Contribution

It presents novel 3D and 4D toric quantum codes combined with quantum interleaving, creating effective burst-error-correcting codes with better information rates than existing codes.

Findings

New 3D and 4D toric quantum codes developed.

Quantum interleaving enhances burst-error correction.

Codes show improved information rates.

Abstract

Ongoing research and experiments have enabled quantum memory to realize the storage of qubits. On the other hand, interleaving techniques are used to deal with burst of errors. Effective interleaving techniques for combating burst of errors by using classical error-correcting codes have been proposed in several articles found in the literature, however, to the best of our knowledge, little is known regarding interleaving techniques for combating clusters of errors in topological quantum error-correcting codes. Motivated by that, in this work, we present new three and four-dimensional toric quantum codes which are featured by lattice codes and apply a quantum interleaving method to such new three and four-dimensional toric quantum codes. By applying such a method to these new codes we provide new three and four-dimensional quantum burst-error-correcting codes. As a consequence, new three and four-dimensional toric and burst-error-correcting quantum codes are obtained which have better information rates than those three and four-dimensional toric quantum codes from the literature. In addition to these proposed three and four-dimensional quantum burst-error-correcting codes improve such information rates, they can be used for burst-error-correction in errors which are located, quantum data stored and quantum channels with memory.