Sparse Quantum Codes With (Almost) Good Distance

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 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.

Speaker Bio: Steven Flammia is a Senior Lecturer and ARC Future Fellow at The University of Sydney, and a faculty member in the Quantum Physics Group. His research interests center around quantum information theory and applications of the theory to a broad range of topics, including condensed matter theory, topologically ordered phases, tensor networks, error correction, quantum optics, precision metrology, and classical statistical inference and machine learning, specifically compressed sensing. He received his Bachelor's degrees in physics and mathematics from Penn State in 2002 and his Ph.D. in physics from the University of New Mexico in 2007.

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