## Abstract

One of the main challenges facing linear optical quantum computing (LOQC) is loss. Each implementation of LOQC suffers some significant degree of loss, be it from reflective bulk optics, interfaces in fibre networks, or scattering and free-carrier absorption in integrated devices. For fault tolerant measurement-based quantum computation one typically requires a large, highly entangled qubit lattice on which quantum error correction is performed. While such schemes can account for certain loss levels [1–3], these thresholds are still too low for practical use. To overcome this loss-tolerant protocols must be developed.

In this report we shall therefore investigate a modern loss-tolerance scheme proposed by Varnava, Browne and Rudolph, known as counterfactual error correction. For such we shall specifically consider photonic implementations. To provide a complete understanding of the scheme, the prerequisite theory will also be revised. The report is hence structured as follows: Section 2 provides a brief introduction to measurement-based quantum computing (MBQC) and the cluster state picture; Section 3 shall introduce the stabiliser formalism and its use for efficiently describing cluster states; Section 4 describes modern approaches to constructing cluster states; Section 5 then details the loss tolerant scheme in question; Lastly Section 6 concludes by offering some areas for further research towards practical implementation of the scheme.

In this report we shall therefore investigate a modern loss-tolerance scheme proposed by Varnava, Browne and Rudolph, known as counterfactual error correction. For such we shall specifically consider photonic implementations. To provide a complete understanding of the scheme, the prerequisite theory will also be revised. The report is hence structured as follows: Section 2 provides a brief introduction to measurement-based quantum computing (MBQC) and the cluster state picture; Section 3 shall introduce the stabiliser formalism and its use for efficiently describing cluster states; Section 4 describes modern approaches to constructing cluster states; Section 5 then details the loss tolerant scheme in question; Lastly Section 6 concludes by offering some areas for further research towards practical implementation of the scheme.

Original language | English |
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Type | QECDT Individual Project Report |

Media of output | Personal Dissemination |

Number of pages | 15 |

Publication status | Unpublished - 16 Sep 2015 |

## Structured keywords

- QETLabs

## Keywords

- Quantum Computation