Self-Correcting Quantum Computers
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.
Cite
@article{arxiv.0907.5228,
title = {Self-Correcting Quantum Computers},
author = {H. Bombin and R. W. Chhajlany and M. Horodecki and M. A. Martin-Delgado},
journal= {arXiv preprint arXiv:0907.5228},
year = {2013}
}
Comments
RevTeX, 24 pages, version revised to increase readability: added sketch of proof of stability criterion, rewritten section on implementation of quantum computation, revised introduction and conclusions