Thresholds for topological codes in the presence of loss

TL;DR

This paper demonstrates that topological quantum error-correcting codes are highly robust against loss errors, tolerating up to 50% loss rate, which aligns with the percolation threshold and the no-cloning limit.

Contribution

It provides analytical and numerical evidence that topological codes can withstand up to 50% loss, establishing a fundamental limit based on percolation theory.

Findings

Maximum tolerable loss rate is 50%

Loss tolerance aligns with the square-lattice bond percolation threshold

Trade-off exists between computational and loss errors

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.