# Quantum Error Correcting Codes Associated With Graphs

Measurement-based quantum computation with the toric code states. The idlers from both sources are filtered with tuneable bandpass filters of ~4 nm bandwidth to remove Raman emission and other background, while 40 nm wide bandpass filters are used for the signals’ Ann. Cluster-based architecture for fault-tolerant quantum computation. http://johnlautner.net/quantum-error/quantum-error-codes.html

We have used an all-optical setup to encode quantum information into photons representing the code. Rev. Rev. Here, the operators Mi correspond to a complete basis for the Hilbert space allowing any physical channel to be described.

If an error has occurred then it will be detected and the ancilla can be encoded again to allow the continuation of a given protocol. Fault tolerant **quantum computation** with very high thresholds for loss errors. Resilient quantum computation: error models and thresholds. **Proc. **

The density matrix for this logical state is shown in Fig. 2b and the fidelity with respect to the ideal case is F=0.77±0.01For the |+› probe state, we find that it Nature 434, 39–44 (2005).ISICASPubMedArticle53.Knill, E. Opt. Preprint at http://arxiv.org/abs/quant-ph/0602096 (2006).45.Schlingemann, D. & Werner, R.

Polarization analysis consists of a QWP, HWP, then a PBS, with both outputs of the PBS collected into multimode fibres coupled to silicon avalanche photodiodes65. A. Phys. http://cds.cern.ch/record/481947/files/0012111.pdf A.

If an error is detected via the stabilizers, then the state is discarded and one starts a given quantum protocol again by re-encoding. J. Phys. Soc.

Opt. Inf. Quant. Express 17, 4670–4676 (2009).ISICASPubMedArticle63.Browne, D.

et al. Check This Out Y., **Lee, D.-H. & Choi, S.-K. **Physical Review A™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. A 56, 2567–2573 (1997).CASArticle50.Grassl, M., Beth, T. & Pellizari, T.

New J. A scheme for efficient quantum computation with linear optics. In this case, the encoding transforms a single-qubit input state ρ for the ancilla into the output density matrix ε(ρ) in the graph code’s logical qubit basis and can be formally Source Loss tolerance in one-way quantum computation via counterfactual error correction.

Phys. This is a basic quantum information transfer primitive in MBQC and propagates the qubit into the code while at the same time applying a Hadamard operation, so that the qubit is Our experimental demonstration and characterization of a four-qubit graph code’s performance contributes to the first steps in the direction of full-scale fault-tolerant quantum information processing.MethodsExperimental setupThe fibre source used was a

## Phys.

M., Haselgrove, H. Lett. 100, 210501 (2008).CASPubMedArticle24.Vallone, G., Pomarico, E., De Martini, F. & Mataloni, P. First, the best codes currently known for classical channels are based on sparse graphs. Please try the request again.

F. All rights reserved.partner of AGORA, HINARI, OARE, INASP, ORCID, CrossRef and COUNTER Sign on SAO/NASA ADS Physics Abstract Service Find Similar Abstracts (with default settings below) · Electronic Refereed Journal As examples, we construct a large class of maximum distance separable codes, i.e. have a peek here Express 20, 6915–6926 (2012).PubMedArticle28.Bell, B.

In order to see how the graph code tolerates loss, consider the case in which qubit 4 is lost, as shown in Fig. 3a. Phys. Bibtex entry for this abstractPreferred format for this abstract (see Preferences) Find Similar Abstracts: Use: Authors Title Keywords (in text query field) Abstract Text Return: Query Results Return items starting The logical density matrix is shown in Fig. 2b and the fidelity with respect to the ideal case is F=0.78±0.01.

D. & Stace, T. B 27, A181–A184 (2010).ISICASArticle19.Walther, P. L., Wadsworth, W. We start our characterization of the graph code’s performance by analysing the quality of the logical encodings for general input states.

New J. Previous experiments have realized error-correcting codes of compact size, such as the 3-qubit code in an ion-trap setup55. WadsworthAuthorsSearch for B. This means the signal-idler pair are generated almost without spectral correlations in a pure quantum state, and do not require tight spectral filtering to show quantum interference.To generate entangled pairs from

The |±y,.L› states are the only encodings not expected to show GME under ideal conditions; instead they are biseparable and composed of two maximally entangled pairs and . The combination of the identity and Y operation gives rise to the squeezing effect seen in the Bloch sphere, which maintains the position of the Y eigenstates, but sends the X Phys.