Publication: Self-correcting quantum computers
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2013-05-29
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IOP Publishing
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Abstract
Is the notion of a quantum computer (QC) resilient to thermal noise unphysical? We address this question from a constructive perspective and show that local quantum Hamiltonian models provide self-correcting QCs. To this end, we first give a sufficient condition on the connectedness of excitations for a stabilizer code model to be a self-correcting quantum memory. We then study the two main examples of topological stabilizer codes in arbitrary dimensions and establish their self-correcting capabilities. Also, we address the transversality properties of topological color codes, showing that six-dimensional color codes provide a self-correcting model that allows the transversal and local implementation of a universal set of operations in seven spatial dimensions. Finally, we give a procedure for initializing such quantum memories at finite temperature.
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© IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We are grateful to Robert Alicki for asking questions that led to this paper and for numerous discussions. MH thanks Jonathan Oppenheim for discussions. HB and MAM-D acknowledge financial support from a PFI grant of EJ-GV, DGS grants under contract, FIS2006-04885 and the ESF INSTANS 2005-10. RWC and MH are supported by EC IP SCALA and by the Polish Ministry of Science and Higher Education through grant no. NN20223193. RWC also acknowledges support from the Foundation of Polish Science (FNP). The support from the Polish research network LFPPI is also acknowledged. Part of this work was done in the National Quantum Information Centre of Gdansk. Part of this work was initiated during the Madrid 2008 conference on the Mathematical Foundations of Quantum Control and Quantum Information Theory (Fundación Areces).