# Quantum Error Threshold

## Contents |

We then reverse **an error** by applying a corrective operation based on the syndrome. Franson, "Demonstration of quantum error correction using linear optics," Phys. Cerf, Ulrik L. The real value of the Threshold Theorem is, to me, that it places important demands on the kind of model on top of which a fault-tolerant architecture can be built. http://johnlautner.net/quantum-error/quantum-error-detection.html

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## An Introduction To Quantum Error Correction And Fault-tolerant Quantum Computation

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 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. J. Educ.

How do we match to a specific architecture and workload, to achieve a particular, desirable logical gate error rate? reply Yuval Sanders Thu, 2015-09-03 13:23 Permalink Thanks for the question! Whereas this is an important implication, it is of limited (but non-zero) value for engineers. Doherty Threshold The Z-error threshold is lower and, therefore, sets the overall threshold. (b) Depth-six circuits. (c) Depth-five circuits.Reuse & PermissionsFigure 5Logical error rate as a function of the physical error rate for

A 5-qubit code is the smallest possible code which protects a single logical qubit against single-qubit errors. Calderbank, Eric Rains, Peter Shor, and N. Generated Tue, 06 Dec 2016 04:19:07 GMT by s_wx1193 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.7/ Connection Nebendahl, D.

Chuang (2000). "Quantum Computation and Quantum Information". Daniel Gottesman Found. The sign flip code[edit] Quantum circuit of the phase flip code Flipped bits are the only kind of error in classical computer, but there is another possibility of an error with A quantum error correcting code protects quantum information against errors of a limited form.

## Quantum Error Correction For Beginners

Cambridge University Press. ^ W.Shor, Peter (1995). "Scheme for reducing decoherence in quantum computer memory". More formally, the theorem guarantees that a quantum circuit Q’ can be found for every quantum circuit Q such that Q and Q’ are ε-equivalent and the overhead of Q’ with An Introduction To Quantum Error Correction And Fault-tolerant Quantum Computation Rev. Reliable Quantum Computers Suppose further that a noisy error corrupts the three-bit state so that one bit is equal to zero but the other two are equal to one.

Cory, M. http://johnlautner.net/quantum-error/quantum-error-codes.html When Aharonov and Ben-Or refer to the total variation distance between f and f’, they seem to be referring to the maximum over x of the total variation distance between f(x) Aharonov and Ben-Or refer to total variation distance as a metric on the space of probability distributions or, more generally1, over the space of density matrices. Rev. Quantum Error Correction Lidar

My understanding is that Q and Q’ are computing the functions f and f’, respectively, on a register with a state represented by x. A 89, 022321 – Published 14 February 2014 More×ArticleReferencesCiting Articles (6)ArticleReferencesCiting Articles (6)PDFHTMLExport CitationAbstractAuthorsArticle Text— INTRODUCTION— THE SURFACE CODE— MEASURING AND INTERPRETING THE ERROR…— OVERVIEW OF NUMERICAL METHODS— NUMERICAL RESULTS— DISCUSSION— Stephens,*National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, [email protected] Text (Subscription Required) Click to ExpandReferences (Subscription Required) IssueVol. 89, Iss. 2 — February 2014Reuse & PermissionsAccess OptionsBuy Article »Get access Source Lett.

A non-degenerate code is one for which different elements of the set of correctable errors produce linearly independent results when applied to elements of the code. Dorit Aharonov Suppose we copy a bit three times. Schaetz, M.

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C. I divide this essential content into two categories: promises about the noise affecting a device and the guarantee that a given quantum circuit can be altered so as to be robust The nearness of the two functions can be measured in a variety of ways, but ε refers to a particular metric on the space of functions that Aharonov and Ben-Or call Quantum Eraser In most codes, the effect is either a bit flip, or a sign (of the phase) flip, or both (corresponding to the Pauli matrices X, Z, and Y).

Chiaverini, D. The syndrome measurement tells us as much as possible about the error that has happened, but nothing at all about the value that is stored in the logical qubit—as otherwise the I think it is work like yours that will establish the proper performance targets for real devices, not the abstract considerations of 'the' Threshold Theorem. have a peek here Schindler, J.

Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. A generalisation of this concept are the CSS codes, named for their inventors: A. The value of the physical error rate at the intersection is the threshold. (a) Depth-eight circuits where the threshold splits into an X-error threshold and a Z-error threshold due to the Barrett, R.

This essay discusses only the second point; the first is rather more complicated. Error bars indicate a ±2σ statistical error. [Compare with Fig. 4.]Reuse & Permissions×More LinksAPSCurrent IssueEarlier IssuesNews & AnnouncementsAbout this JournalJournal StaffAbout the JournalsJoin APSAuthorsGeneral InformationSubmit a ManuscriptPublication RightsOpen AccessPolicies & PracticesTips for Nielsen and Isaac L. Cerf and U.

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. Wineland, "Realization of quantum error correction," Nature 432, 602-605 (2004), doi:10.1038/nature03074 ^ P. Your cache administrator is webmaster. G.

A. As of late 2004, estimates for this threshold indicate that it could be as high as 1-3% [4], provided that there are sufficiently many qubits available. re-encode each logical qubit by the same code again, and so on, on logarithmically many levels—provided the error rate of individual quantum gates is below a certain threshold; as otherwise, the