Floquet Codes without Parent Subsystem Codes

Subsystem Codes

We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the quantum Gilbert-Varshamov bound. We derive linear programming bounds and other upper bounds. We answer the qu...

Topological subsystem codes

Encoding Subsystem Codes

In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the known results on encoding of stabilizer codes. Along the way we also show how Clifford codes can be encoded. We also show that gauge qubits can be exploited to...

Propagation Rules of Subsystem Codes

We demonstrate propagation rules of subsystem code constructions by extending, shortening and combining given subsystem codes. Given an [[n, k, r, d]]q subsystem code, we drive new subsystem codes with parameters [[n + 1, k, r,≥ d]]q, [[n − 1, k + 1, r,≥ d − 1]]q , [[n, k − 1, r + 1, d]]q . We present the short subsystem codes. The interested readers shall consult our companion papers for upper...

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...