# Realization Of Quantum Error Correction

## Contents |

**D. **AT&T Bell Laboratories. ^ A.R.Calderbank E.M.Rains P.W.Shor and N.J.A.Sloane "Quantum Error Correction Via Codes Over GF(4)"IEEE.Transactions on Information Theory,Vol.44,No.4,July 1998 ^ D. J. PhysD G CoryNMR based quantum information processing…2000‹12›CitationsSort by:InfluenceRecencyShowing 1-10 of 22 extracted citations Quantum Computing with Trapped IonsH Häffner, C F Roos, R Blatt2008Highly Influenced8 ExcerptsOptimal architectures for long distance quantum this page

Rev. D. Program of IBS School-UST Institute for Basic Science Faculty Position for Research Director of the Animal BSL3 Facility at Duke-NUS DUKE-NUS Medical school More science jobs Post a job Realization of An encoded one-qubit state is protected against spin-flip errors by means of a three-qubit quantum error-correcting code.

## Quantum Error Correction Codes

Blok, M. DiCarlo, **S. **Sabuncu, A. Quantum error correction2, 3 protects information stored in two-level quantum systems (qubits) by rectifying errors with operations conditioned on the measurement outcomes.

Jacobs and J. Contact: Ferdinand Kuemmeth (kuemmeth@nbi.dk). Ready to apply? Schoelkopf, "Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits," Nature 482, 382-385 (2012), doi:10.1038/nature10786, arXiv:1109.4948 ^ M. Quantum Code 7 If U = **σ x {\displaystyle U=\sigma _{x}} ,** a bit flip error occurs.

Sun, L. Leuchs, N. Nature432.7017 (Dec 2, 2004): 602-5. Errors are induced at various rates.

Knill2, C. Bit Flip Memory Error In principle, the approach enables a quantum state to be maintained by means of repeated error correction, an important step towards scalable fault-tolerant quantum computation using trapped ions.Extracted Key PhrasesError Correction H. We verify error correction by comparing the corrected final state to the uncorrected state and to the initial state.

## Quantum Error Correction For Beginners

We perform a multi-qubit measurement that does not disturb the quantum information in the encoded state but retrieves information about the error. Leibfried1, T. Quantum Error Correction Codes Niset, G. Stabilizer Codes And Quantum Error Correction Schaetz, M.

The encoded state is decoded back to the primary ion one-qubit state, making error information available on the ancilla ions, which are separated from the primary ion and measured. http://vealcine.com/quantum-error/quantum-error-correction-usc.php Familiarity with quantum information will also be helpful. Blakestad1, J. What is more, the outcome of this operation (the syndrome) tells us not only which physical qubit was affected, but also, in which of several possible ways it was affected. 5 Qubit Code

J. Price, W. Chwalla, M. http://vealcine.com/quantum-error/quantum-error-correction-ppt.php Through the transmission in a channel the relative sign between | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } can become inverted.

Such implementations of quantum error correction are an important step towards scalable fault-tolerant quantum computation using trapped ions. Steane Code Quantum circuit of the bit flip code Let | ψ ⟩ = α 0 | 0 ⟩ + α 1 | 1 ⟩ {\displaystyle |\psi \rangle =\alpha _{0}|0\rangle +\alpha _{1}|1\rangle } Cory, M.

## The syndrome measurement "forces" the qubit to "decide" for a certain specific "Pauli error" to "have happened", and the syndrome tells us which, so that we can let the same Pauli

The reason is that the measurement of the syndrome has the projective effect of a quantum measurement. the Shor code, encodes 1 logical qubit in 9 physical qubits and can correct for arbitrary errors in a single qubit. We find 85\pm1% fidelity to the expected classical action of this gate and 78\pm1% fidelity to the ideal quantum process matrix. 5 Qubit Quantum Error Correction Cerf and U.

Bruno, V. So even if the error due to the noise was arbitrary, it can be expressed as a superposition of basis operations—the error basis (which is here given by the Pauli matrices NCBISkip to main contentSkip to navigationResourcesAll ResourcesChemicals & BioassaysBioSystemsPubChem BioAssayPubChem CompoundPubChem Structure SearchPubChem SubstanceAll Chemicals & Bioassays Resources...DNA & RNABLAST (Basic Local Alignment Search Tool)BLAST (Stand-alone)E-UtilitiesGenBankGenBank: BankItGenBank: SequinGenBank: tbl2asnGenome WorkbenchInfluenza VirusNucleotide see here The latter is counter-intuitive at first sight: Since noise is arbitrary, how can the effect of noise be one of only few distinct possibilities?

Girvin, R. If we assume that noisy errors are independent and occur with some probability p.It is most likely that the error is a single-bit error and the transmitted message is three ones. Lee To employ data analytics effectively and efficiently on manufacturing systems, engineers and data scientists need to collaborate closely to bring their domain... Information Theory2015Measurement-based Quantum Error CorrectionJanna Hinchliff20151 ExcerptPreparation of three-dimensional entanglement for distant atoms in coupled cavities via atomic spontaneous emission and cavity decayShi-Lei Su, Xiao-Qiang Shao, Hong-Fu Wang, Shou ZhangScientific reports2014Experimental

Cramer, N. Register now I want to subscribe to Nature Price: US$199 This includes a free subscription to Nature News together with Nature Journal. Fortschr. For example, in the case where the first qubit is flipped, the result would be | ψ r ′ ⟩ = α 0 | 100 ⟩ + α 1 | 011

Huang, A. Due to linearity, it follows that the Shor code can correct arbitrary 1-qubit errors. It is possible to correct for both types of errors using one code, and the Shor code does just that. If you do not have access to the article you require, you can purchase the article (see below) or access it through a site license.

Pittman, B. The 1st, 4th and 7th qubits are for the sign flip code, while the three group of qubits (1,2,3), (4,5,6), and (7,8,9) are designed for the bit flip code. Error-correction protocols have been implemented in nuclear magnetic resonance experiments4, 5, 6, but the inherent limitations of this technique7 prevent its application to quantum information processing. A primary ion qubit is prepared in an initial state, which is then encoded into an entangled state of three physical qubits (the primary and two ancilla qubits).

Huck, J. partner of AGORA, HINARI, OARE, INASP, ORCID, CrossRef, COUNTER and COPE Warning: The NCBI web site requires JavaScript to function. E. The first step of the three qubit bit flip code is to entangle the qubit with two other qubits using two CNOT gates with input | 0 ⟩ {\displaystyle |0\rangle }

Wineland Abstract Scalable quantum computation and communication require error control to protect quantum information against unavoidable noise. D. Britton1, W. Andersen, "Quantum optical coherence can survive photon losses using a continuous-variable quantum erasure-correcting code," Nature Photonics 4, 700 (2010), doi:10.1038/nphoton.2010.168 Bibliography[edit] Daniel Lidar and Todd Brun, ed. (2013). "Quantum Error Correction".