Keeping One Step Ahead of Errors

Statistical mechanical models are the key to understanding the performance of error correction in topological quantum computers.

Quantum systems are very delicate, both because they tend to be very small, and thus vulnerable to even tiny disturbances, and because any process that gains information about the state of a quantum system alters it. Nevertheless, quantum coherence can, in principle, be maintained indefinitely using error-correcting codes that shield quantum information from the ravages of a harsh environment. Protected quantum information in turn enables large-scale quantum technologies, such as quantum computers, which can take advantage of quantum interference to solve some computational problems much faster than any conceivable classical computer. One promising approach is to use topological error-correcting codes, which store quantum information safely by associating it with some topological property of the system, such as a path stretching all the way around it. Now, in a paper appearing in Physical Review X, Hector Bombin at the Perimeter Institute in Waterloo, Canada and an international group of scientists from Switzerland, Japan and the US have collaborated to study two families of topological codes and determine how much protection they provide against the most symmetric type of errors [1]. They do this by making a connection between the error-correcting codes and certain purely classical systems. The low-error regime, where the quantum code functions, corresponds to the low-temperature ordered phase in the classical system.