# Quantum Error Correction For Idiots

## Contents |

Quantum Computing and **Error Cor-eds,** pp.284-298 (IOS Press, Amsterdam, 2001), quant-ph/0304016, 2001. [Ste02] A.M. Decoherence-FreeSubspaces and Subsystems. Another approach isto not enforce the correction requirement. A SchemeNature (London), 409:46, 2001. [KLP05] D. check over here

Consequentlythe probability of measuring the correct result at the endof a speciﬁc algorithm increases when the system is en-coded.This example shows the basic principles of error cor-rection. Generated Sun, 23 Oct 2016 14:04:24 GMT by s_ac4 (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 In more recent years QEC pro-tocols have been developed for various systems, such ascontinuous variables (LS98; Bra98; vL08; ATK+08), ion-traps and other systems containing motional degrees offreedom (LW03b; ST98), adiabatic computation A theory of Fault-Tolerant quantumcomputation.

## Quantum Error Correction Codes

If adecoherence model is employed, initialization is modeledexactly the same way as imperfect measurement. If the result is |0i, the input state is projected to(neglecting normalization),|ψiF= |ψiI+ U |ψiI. (46)Since U is Hermitian, U |ψiF= |ψiF, hence |ψiFis a +1eigenstate of U. Rev. The algorithm basically lets us encode a qubit with extra ancillary qubits, which allows any subsequent errors to be corrected.

Please note that this site is currently undergoing Beta testing. Tables III and IV shows thestabilizer structure of two other well known codes, the9-qubit code (Sho95) which we have examined and the5-qubit code (LMPZ96) which represents the smallestpossible quantum code that Knight. Surface Code News, 33(2):186, 2005. [BLWZ05] M.S.

Lett., 89:127901, 2002. [WZ82] W.K. Stabilizer Codes And Quantum Error Correction Rev. Von Neumann. arxiv:0811.3616, 2008. [VT99] D.

Post navigation ← Rss Feed Error 0x800c0006 Radasm Make Error(s) Occured → Search Striker WordPress Theme Powered By WordPress ERROR The requested URL could not be retrieved The following error was Bit Flip Error Thestructure of this ion is clearly not a 2-level quantum system.Hence leakage into non-qubit states is an important factor toconsider.eﬀects the system. The papers are organized...https://books.google.com/books/about/Reversible_Computation.html?id=QlcqBAAAQBAJ&utm_source=gb-gplus-shareReversible ComputationMy libraryHelpAdvanced Book SearchGet print bookNo eBook availableSpringer ShopAmazon.comBarnes&Noble.comBooks-A-MillionIndieBoundFind in a libraryAll sellers»Get Textbooks on Google PlayRent and save from the world's largest eBookstore. If a particular system isfound to be improperly conﬁned to the qubit subspace itwould simply be discarded.

## Stabilizer Codes And Quantum Error Correction

State Preparation 13B. Quantum system (Qubit particle) De‐coherence time (sec) Electrons in gold atoms \(10^{-8}\) Trapped iridium atoms \(10^{-1}\) Electron spin \(10^{-3}\) Electron quantum dot \(10^{-3}\) Nuclear spin \(10^4\) Table 1: Source Lecture on Quantum Error Correction Codes Codes forthe quantum erasure channel. 5 Qubit Code Consider an Nqubit unitary operation, UN, which is valid on encodeddata.

In the context ofmass manufacturing of qubit systems, leakage would bequantiﬁed immediately after the fabrication of a device,using intrinsic characterization protocols such as thosediscussed in Ref. (DSO+07). http://vealcine.com/quantum-error/quantum-error-correction-usc.php The resulting statewill contain a superposition of a clean state and cor-rupted states, the point is that the ﬁdelity of the cor-rupted states, at the logical level, is greater than the Finally in section XIV we review speciﬁccodes for qubit loss and examine two of the more mod-ern techniques for error correction. This is achieved by changing the quantum particle type; changing the physical size of the quantum computer (quantum system); or by changing the environment the quantum computer operates in to be Steane Code

- Phys.
- Comp., 8:330, 2008. [Sho95] P.W.
- Phys., 68:733,1996. [Fey82] R.P.
- Steane.
- It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large scale quantum
- Quan-tum gate operations are represented by unitary opera-tions acting on the Hilbert space of a qubit array.
- Phys.
- Zanardi and M.

Calderbank, E.M. Digitization of Quantum Errors 15A. Lloyd. http://vealcine.com/quantum-error/quantum-error-correction-ppt.php As I discovered from a lecture of C.

Rev. Hadamard Gate A Theory of QuantumError-Correcting Codes. Environmental decoherence 15∗electronic address: [email protected]

## Rev.

Consider an arbi-trary single qubit state that has been encoded,α |0i + β |1i → α |0iL+ β |1iL= |ψiL. (51)Now assume that an error occurs on one (or multiple)qubits which A., 59:4178, 1999. [VWW05] J. This will thenlead to a description of full fault-tolerant quantum errorcorrection.V. Quantum Code Pashkin, Y.

Section VII then introduces the stabilizerformalism (Got97), demonstrating how QEC circuits aresynthesized once the structure of the code is known. PhD Thesis (Caltech). Phys. have a peek at these guys Gottesman.

Rev. arXiv:0904.2557, 2009. [Gro97] L.K. However, in general the 9-qubitcode is only a single error correcting code as it cannothandle multiple errors if they occur in certain locations.The 9-qubit code is in fact a member of The actual eﬀect of this type oferror can manifest in several diﬀerent ways.

Farhi, and P.W. Rev. Mod. Or use your Academic/Social account: Congratulations!

Mod. Loss, Leakage, Measurement and Initialization:Variations of the aboveOther sources of error such as qubit initialization, mea-surement errors, qubit loss and qubit leakage are modeledin a very similar manner. Since a error free stateis already a +1 eigenstate of all the stabilizers, any er-ror which anti-commutes with a stabilizer will ﬂip theeigenstate and consequently the parity measurement willreturn a result Quantum codes on a2:43, 2001. [BKD04] G.

Schirmer, D.K.L. Consequently, the density matrixevolution is given by,∂tρ = −i~[H, ρ] + ΓZ(ZρZ − ρ) +Γ2(XρX + Y ρY −2ρ).(56)If it is assumed that the qubit is not undergoing anycoherent evolution (H Therefore, you must use error correction models that can detect and correct errors without determining any information about the qubit states. The basic idea in post-selected schemes is to en-code the computer with error detecting circuits and if er-rors are detected, the relevant subroutine of the quantum 11algorithm is reset and run

Rev. Munro, and K. Subsystem Codes 26B. Instead of the 7-qubit code, we willuse the stabilizer set shown in Table IV to calculate the|0iLstate for the 5-qubit code.