Optimal error correction in topological subsystem codes

Topological subsystem codes

Quantum Error-Correction Codes on Abelian Groups

We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.

Optimal codes for single-error correction, double-adjacent-error detection

In certain memory systems the most common error is a single error and the next most common error is two errors in positions which are stored physically adjacent in the memory. In this correspondence we present optimal codes for recovering from such errors. We correct single errors and detect double adjacent errors. For detecting adjacent errors we consider codes which are byte-organized. In the...

Topological subsystem codes from graphs and hypergraphs

Topological subsystem codes were proposed by Bombin based on 3-face-colorable cubic graphs. Suchara, Bravyi, and Terhal generalized this construction and proposed a method to construct topological subsystem codes using 3-valent hypergraphs that satisfy certain constraints. Finding such hypergraphs and computing their parameters, however, is a nontrivial task. We propose families of topological ...

Quantum Error Correcting Subsystem Codes From Two Classical Linear Codes

The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most general method for encoding quantum information is to encode it into a subsystem, there exists a novel form of quantum error correction beyond the tradition...