# Quantum Error Correcting Codes Associated With Graphs

However, the squeezing is now mainly **in the** X direction due to the additional presence of a Pauli Z operation, as can be seen more clearly in the χ matrix shown The measurements are X1X2X3X4X5 and Z1Y2Y3Y4Z5 (see Methods), which result in a witness value ofwhere the error has been calculated using a Monte Carlo method with Poissonian noise on the count et al. Photonics 5, 117–123 (2011).Article33.Aliferis, P. & Leung, D. weblink

Information about registration may be found here. Experimental quantum coding against qubit loss error. The next steps will be to design and realize QECC schemes using larger graph states45,46,47 with enhanced error-correction capabilities70, and introduce concatenation methods against loss errors68,69,70. Phys.

Your cache administrator is webmaster. US & Canada: +1 800 678 4333 Worldwide: +1 732 981 0060 Contact & Support About IEEE Xplore Contact Us Help Terms of Use Nondiscrimination Policy Sitemap Privacy & Opting Out Quantum error-correcting codes associated with graphs. This is an important distinction, as the quantum information to be encoded is untouched during the generation of the code resource.

Rev. Rev. Register now for a free account in order to: Sign in to various IEEE sites with a single account Manage your membership Get member discounts Personalize your experience Manage your profile For the case that the state |0›3 is measured, the remaining four qubits should be left in the logical code state |+L›, which corresponds to a ‘box’ cluster state,Using the relevant

Here, the vertices correspond to qubits initialized in the state |+› and edges correspond to controlled-phase gates, CZ=diag(1,1,1,−1), applied to the qubits. Conditioned on a fourfold coincidence detection, this will leave a GHZ state on three of the photons, . Rev. http://link.aps.org/doi/10.1103/PhysRevA.65.012308 We choose the Pauli basis, Mi=(I, X, Y, Z), for the operators so that the elements of the χ matrix define the channel completely.

G. Rev. The system returned: (22) Invalid argument The remote host or network may be down. We showed that the graph state code can be used to correct and detect errors in a photonic setting with the results in close agreement with the theory and limited only

Rev. http://ieeexplore.ieee.org/iel5/18/29493/01337106.pdf While the four-qubit code has been realized before in several works, most notably in ref. 56, these studies have been restricted to quantum error-correction with the four-qubit code using the original Measurements in the Pauli Z basis can be achieved by blocking one or the other interferometer path, in which case the BS reduces the measurement rate by 50%. Phys.

USA 105, 11050–11054 (2008).CASPubMedArticle57.Barz, S. have a peek at these guys Phys. If an error is detected via the stabilizers, then the state is discarded and one starts a given quantum protocol again by re-encoding. Wadsworth6& J.

- Phys.
- Here, for any GHZ or linear cluster state, it is possible to detect genuine multipartite entanglement (GME) using correlations taken from just two local measurement bases.
- Active one-way quantum computation with 2-photon 4-qubit cluster states.
- E. & Rudolph, T.
- He has worked in the field of quantum information science for nearly 20 years, and has made many influential contributions to quantum error correction, where he is especially known for his
- Subscribe Enter Search Term First Name / Given Name Family Name / Last Name / Surname Publication Title Volume Issue Start Page Search Basic Search Author Search Publication Search Advanced Search
- Here, [[n,k,d]] is the standard notation for QECCs, where n denotes the number of physical qubits, k is the number of logical qubits encoded and d is the distance, which indicates

M. Phys. One can see in Fig. 3e the recovered Bloch sphere is similar to that of the path qubit loss. check over here A 454, 365–384 (1998).Article10.Raussendorf, R. & Briegel, H.

Quantum computations: algorithms and error correction. Lett. 105, 250503 (2010).CASPubMedArticle41.Fujii, K. & Yamamoto, K. Rarity1Nature Communications 5, Articlenumber:3658 (2014)doi:10.1038/ncomms4658Download CitationQuantum informationQuantum opticsReceived:22 September 2013Accepted:14 March 2014Published online:22 April 2014AbstractScalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence

## Lidar, Todd A.

The polarization qubits are measured after the path qubits using a quarter-wave plate (QWP), HWP and PBS chain, followed by a detection of the photon using single-photon avalanche photodiodes. Rev. Comp. 2, 307–323 (2002).47.Schlingemann, D. Lett. 98, 140501 (2007).CASPubMedArticle22.Chen, K.

The APS Physics logo and Physics logo are trademarks of the American Physical Society. A 55, 900–911 (1997).ISICASArticle6.Preskill, J. The signal photons from both sources are fused using a PBS, which transmits horizontally polarized photons and reflects vertically polarized photons, as described in ref. 59. http://vealcine.com/quantum-error/quantum-error-correcting-codes-from-the-compression-formalism.php WernerInstitut für Mathematische Physik, TU Braunschweig, Mendelssohnstrasse 3, 38106 Braunschweig, GermanyReferences (Subscription Required) IssueVol. 65, Iss. 1 — January 2002Reuse & PermissionsAccess OptionsBuy Article »Get access through a U.S.

J. This is a locally rotated version of the witness given in ref. 66 for a five-qubit linear cluster state and takes into account the local complementation operations described in Fig. 1b The graph we realize is setup independent, thus it could be employed in other physical settings. Inf.

This allows a simple verification of the one-error correcting property of codes of length 5 in any dimension. Herrera-Martí2, M. Phys. IEEE Trans.

Inf. J. G.