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arXiv · 0907.5228

Self-Correcting Quantum Computers

H. Bombin·R. W. Chhajlany·M. Horodecki·M. A. Martin-Delgado
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Abstract

Is the notion of a quantum computer resilient to thermal noise unphysical? We address this question from a constructive perspective and show that local quantum Hamiltonian models provide self-correcting quantum computers. To this end, we first give a sufficient condition on the connect- edness 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 6D 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 to initialize such quantum memories at finite temperature.

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H. Bombin, R. W. Chhajlany, M. Horodecki, M. A. Martin-Delgado. 2009-07-29. Self-Correcting Quantum Computers. https://arxiv.org/abs/0907.5228

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