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Published March 19, 2007 | public
Journal Article Open

Physical Limits of Heat-Bath Algorithmic Cooling


Simultaneous near-certain preparation of qubits (quantum bits) in their ground states is a key hurdle in quantum computing proposals as varied as liquid-state NMR and ion traps. "Closed-system" cooling mechanisms are of limited applicability due to the need for a continual supply of ancillas for fault tolerance and to the high initial temperatures of some systems. "Open-system" mechanisms are therefore required. We describe a new, efficient initialization procedure for such open systems. With this procedure, an $n$-qubit device that is originally maximally mixed, but is in contact with a heat bath of bias $\varepsilon \gg 2^{-n}$, can be almost perfectly initialized. This performance is optimal due to a newly discovered threshold effect: For bias $\varepsilon \ll 2^{-n}$ no cooling procedure can, even in principle (running indefinitely without any decoherence), significantly initialize even a single qubit.

Additional Information

©2007 Society for Industrial and Applied Mathematics (Received March 9, 2005; accepted October 6, 2006; published March 19, 2007) Thanks go to R. Laflamme and J. Fernandez for helpful discussions, and to an anonymous referee for a careful reading of the manuscript. The work of this author [L.J.S.] was supported in part by the NSF (PHY-0456720 and CCF-0524828), the ARO (W911NF-05-1-0294), the Mathematical Sciences Research Institute, and the Okawa Foundation. The work of these authors [T.M. and Y.W.] was supported in part by the Israel Ministry of Defense and by the Institute for Future Defense Research at the Technion.


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