# Quantum Error Correction

## Contents |

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 } In fact, most interactions with the environment will act just like a measurement and will collapse the state. Blatt, "Experimental Repetitive Quantum Error Correction," Science 332, 1059-1061 (2011), doi:10.1126/science.1203329 ^ M. Classical error correction employs redundancy. http://johnlautner.net/quantum-error/quantum-error-correction-ppt.html

S. If the three bit flip group (1,2,3), (4,5,6), and (7,8,9) are considered as three inputs, then the Shor code circuit can be reduced as a sign flip code. If U = σ x {\displaystyle U=\sigma _{x}} , a bit flip error occurs. Nevertheless, in quantum computing there is another method, namely the three qubit bit flip code.

## Quantum Error Correction For Beginners

Chwalla, M. This process is known as decoherence. A quantum error correcting code protects quantum information against errors of a limited form. Lidar is a Professor of Electrical Engineering, Chemistry and Physics at the University of Southern California, and directs the USC Center for Quantum Information Science and Technology.

Quantum error correction also employs syndrome measurements. J. However, quantum error correction and fault-tolerant computation is now a much larger field and many new codes, techniques, and methodologies have been developed to implement error correction for large scale quantum Steane Code Simons Institute 1,024 **views 44:24 Theoretical Physicist Finds Computer** Code in String Theory - Duration: 12:05.

Sign inYour AccountSign inYour AccountTry PrimeListsCart0 Your Amazon.comToday's DealsGift Cards & RegistrySellHelp Books Advanced Search New Releases Best Sellers The New York Times® Best Sellers Children's Books Textbooks Textbook Rentals Sell Stabilizer Codes And Quantum Error Correction. J. 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. https://arxiv.org/abs/0905.2794 Munro (Submitted on 18 May 2009 (v1), last revised 21 Jun 2013 (this version, v4)) Abstract: Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical

the Shor code, encodes 1 logical qubit in 9 physical qubits and can correct for arbitrary errors in a single qubit. Quantum Code 7 Phys. 76 (2013) 076001 DOI: 10.1088/0034-4885/76/7/076001 Citeas: arXiv:0905.2794 [quant-ph] (or arXiv:0905.2794v4 [quant-ph] for this version) Submission history From: Simon Devitt Dr [view email] [v1] Mon, 18 May 2009 03:26:04 GMT Ozeri and D. Jacobs **and J. **

## Stabilizer Codes And Quantum Error Correction.

Quantum error correction is essential if one is to achieve fault-tolerant quantum computation that can deal not only with noise on stored quantum information, but also with faulty quantum gates, faulty http://news.mit.edu/2015/quantum-error-correction-0526 Lassen, M. Quantum Error Correction For Beginners Reed, L. Quantum Error Correction Book Math. 1 (2001), no. 3, 325–332.

It may be possible to implement the researchers’ scheme without actually duplicating banks of qubits. this contact form Math. C. If an error is modeled by a unitary transform U, which will act on a qubit | ψ ⟩ {\displaystyle |\psi \rangle } , then U {\displaystyle U} can be described Fault-tolerant Quantum Computation

Technion 221 views 42:05 Data Structures for Quasistrict Higher Categories - Duration: 47:35. Close Yeah, keep it Undo Close This video is unavailable. Here R {\displaystyle {\mathcal {R}}} is known as the correction operation. have a peek here A simple error-correcting code could, for instance, instantiate a single qubit of data as three physical qubits.

Simons Institute 422 views 57:22 The Next Quantum Leap: Here, There, and Everywhere - Duration: 1:02:32. Bit Flip Memory Error The simplest way is to store the information multiple times, and—if these copies are later found to disagree—just take a majority vote; e.g. The simplest classical error-correcting code is the repetition code.

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If U = σ z {\displaystyle U=\sigma _{z}} , a sign flip error occurs. Back to top Get to Know UsCareersAbout AmazonInvestor RelationsAmazon DevicesMake Money with UsSell on AmazonSell Your Services on AmazonSell on Amazon BusinessSell Your Apps on AmazonBecome an AffiliateAdvertise Your ProductsSelf-Publish with Working... 5 Qubit Code Using this code, we can correct an arbitrary single-qubit quantum error.

But, Harrow says, “Almost all of the sparse schemes started out with not very many logical qubits, and then people figured out how to get a lot more. Generated Tue, 06 Dec 2016 04:00:28 GMT by s_wx1079 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection The key to quantum algorithm design is manipulating the quantum state of the qubits so that when the superposition collapses, the result is (with high probability) the solution to a problem. Check This Out D.

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It is similar to the three bits repetition code in a classical computer. Trade in Learn More Have one to sell? Suppose that the state of qubit 8 at time 5 has implications for the states of both qubit 8 and qubit 11 at time 6. Your cache administrator is webmaster.

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