# Quantum Error Correction Via Codes Over

The system returned: **(22) Invalid argument The** remote host or network may be down. It represents quantum codes with binary vectors and binary operations rather than with Pauli operators and matrix operations respectively. The operators g 1 , … , g n − k {\displaystyle g_{1},\ldots ,g_{n-k}} function in the same way as a parity check matrix does for a classical linear block code. Information Theory1999Quantum Channel Capacity of Very Noisy Channels Typeset Using Revt E X 1David P Divincenzo, Peter W Shor, John A Smolin1998Quantum Weight EnumeratorsEric M. Source

Quantum error-correcting codes restore a noisy, decohered quantum state to a pure quantum state. RainsIEEE Trans. Calderbank and P. As in entanglement assistance, our scheme can import any binary or quaternary linear codes. https://arxiv.org/abs/quant-ph/9608006

Researchers have found many examples of classical codes satisfying this constraint, but most classical codes do not. SloaneIEEE Trans. However, the known entanglement-assisted scheme requires noiseless qubits that help correct quantum errors on noisy qubits, which can be too severe an assumption. J.

M Rains (2), P. **A. **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 Its stabilizer S {\displaystyle {\mathcal {S}}} is an abelian subgroup of the n {\displaystyle n} -fold Pauli group Π n {\displaystyle \Pi ^{n}} : S ⊂ Π n {\displaystyle {\mathcal {S}}\subset

J. Warning: The NCBI web site requires JavaScript to function. W. His current research interests include optical networks, error control coding, constrained coding, coded modulation, turbo equalization, OFDM applications, and quantum error correction.

Gives an intuitive understanding by not assuming knowledge of quantum mechanics, thereby avoiding heavy mathematics. Unique Features Unique in covering both quantum information processing and quantum error correction - everything in one book that an engineer needs to understand and implement quantum-level circuits. A. SIGN IN SIGN UP Quantum error correction via codes over GF(4) Authors: A.

In communications and information processing, encoding is the process by which information from a source is converted into symbols to be communicated. Replaced Sept. 24, 1996, to correct a number of minor errors. R. This highly entangled, encoded state corrects for local noisy errors.

SteaneIEEE Trans. this contact form Information Theory1999Quantum Reed-Muller codesAndrew M. M. So we compactly summarize the stabilizer error-correcting conditions: a stabilizer code can correct any errors E 1 , E 2 {\displaystyle E_{1},E_{2}} in E {\displaystyle {\mathcal {E}}} if E 1 †

Comments: Latex, 46 pages. Let us define a map N : ( Z 2 ) 2 n → Π n {\displaystyle \mathbf {N} :\left(\mathbb {Z} _{2}\right)^{2n}\rightarrow \Pi ^{n}} as follows: N ( u ) ≡ Encheva, Simon LitsynIEEE Trans. have a peek here Dr.

A symplectic subspace corresponds to a direct sum of Pauli algebras (i.e., encoded qubits), while an isotropic subspace corresponds to a set of stabilizers. Suppose [ A ] {\displaystyle \left[A\right]} is a set of equivalence classes of an operator A {\displaystyle A} that have the same phase: [ A ] = { β A Find out why...Add to ClipboardAdd to CollectionsOrder articlesAdd to My BibliographyGenerate a file for use with external citation management software.Create File See comment in PubMed Commons belowPhys Rev Lett. 2013 Apr

## Calderbank AT&T Labs.-Res., Florham Park, NJ E.

Contents 1 Mathematical background 2 Definition 3 Stabilizer error-correction conditions 4 Relation between Pauli group and binary vectors 5 Example of a stabilizer code 6 References Mathematical background[edit] The Stabilizer formalism No cleanup reason has been specified. The ACM Guide to Computing Literature All Tags Export Formats Save to Binder Sign inBack to the previous page.ShareQuantum Error Correction Via Codes Over GF(4)A. Therefore the codespace is the simultaneous +1-eigenspace of the above operators.

To appear in IEEE Transactions on Information Theory. The extension of the above definitions and mapping N {\displaystyle N} to multiple qubits is straightforward. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit any classical linear codes over the binary or quaternary finite field. Check This Out M.

morefromWikipedia Qubit In quantum computing, a qubit or quantum bit is a unit of quantum information¿the quantum analogue of the classical bit. If the auxiliary qubits are noiseless, our codes become entanglement-assisted codes, and saturate the quantum Singleton bound when the underlying classical codes are maximum distance separable.PMID: 23679693 DOI: 10.1103/PhysRevLett.110.170501 [PubMed] ShareLinkOut Your cache administrator is webmaster. Preview this book » What people are saying-Write a reviewWe haven't found any reviews in the usual places.Selected pagesTitle PageTable of ContentsIndexReferencesContents1 Introduction1 2 Quantum Error Correcting Codes57 3 Quantum Stabilizer

Prior to this appointment in August 2006, he was with University of Arizona, Tucson, USA (as a Research Assistant Professor); University of the West of England, Bristol, UK; University of Bristol,