Steve Flammia (University of Sydney)
Sparse Quantum Codes with (Almost) Good Distance
QuICS Workshop on the Frontiers of Quantum Information and Computer Science (September 29, 2015)
Sparse error correcting codes, where every parity check involves only a small (constant) number of bits, have become ubiquitous because they can be generated easily and decoded efficiently, even when a constant fraction of bits are in error.
These properties do not carry over easily to the quantum case, however. In this talk, I will discuss a family of quantum sparse codes that can correct a nearly constant fraction of errors. The codes are sparse enough that each syndrome measurement involves just three qubits at a time. The construction is very general, and proceeds by transforming any other quantum code into a sparse one. The price we pay for this transformation is some extra qubits and that the new code is a more general subsystem code. If time permits, I will also discuss the connection between these new codes and the physics of self-correcting quantum memories.
Joint work with D. Bacon, A. Harrow, and J. Shi (arXiv:1411.3334).
