Tutte seminar - Graeme Smith

Codeword Stabilized Quantum Codes

Abstract:

I will describe an approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. Our quantum codes are described by a single graph state, together with a classical binary code. The graph state may be thought of as mapping quantum errors to an exotic classical error model, which we must then arrange to correct with our classical code. Stabilizer codes arise naturally as those quantum codes with a linear classical code. I will show how to use this framework to generate new codes with superior parameters to any previously known, as well construct encoding circuits for all codes within this family.