Loss Tolerance with a Concatenated Graph State

TL;DR

This paper introduces a novel loss-tolerant quantum computation scheme combining measurement-based methods and concatenated codes, achieving high loss thresholds with lower overhead and fully analytic threshold determination.

Contribution

It presents a new loss-tolerance scheme using concatenated graph states that improves thresholds and reduces overhead compared to existing methods.

Findings

Performs well at 23% loss rate with leakage detection.

Achieves over 50% loss tolerance when qubits are tagged.

Analytically derived the loss threshold.

Abstract

A new way of addressing loss errors is introduced which combines ideas from measurement-based quantum computation and concatenated quantum codes, allowing for universal quantum computation. It is shown that for the case where leakage is detected upon measurement, the scheme performs well under 23% loss rate. For loss rates below 10%, this approach performs better than the best scheme known up to date [Phys. Rev.Lett., 97(12):120501]. If lost qubits are tagged prior to measurement, it can tolerate up to 50% loss. The overhead per logical qubit is shown to be significantly lower than other schemes. The obtention of the threshold is entirely analytic.