Thresholds for topological codes in the presence of loss

Abstract

Many proposals for quantum information processing are subject to detectable loss errors. In this paper, we show that topological error correcting codes, which protect against computational errors, are also extremely robust against losses. We present analytical results showing the maximum tolerable loss rate is 50 %, which is determined by the square-lattice bond percolation threshold. This saturates the bound set by the no-cloning theorem. Our numerical results support this, and show a graceful trade-off between computational and loss errors.

4 pages, 3 figures. Accepted for publication in Phys. Rev. Lett., but comments still very welcome. TMS and SDB contributed equally to this work

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