# Quantum Error Correction Wiki

## Contents |

Wilde and Todd A. doi:10.1140/epjst/e2015-02346-0. ^ Lanting, T.; Przybysz, A. J.; Smirnov, A. Yu.; Spedalieri, F. M.; Amin, M. H.; Berkley, A. J.; Harris, R.; Altomare, F.; Boixo, S.; Bunyk, P.; Dickson, N.; Enderud, C.; Hilton, J. P.; Hoskinson, E.; Johnson, See templates for discussion to help reach a consensus.› v t e Quantum mechanics Background Introduction History timeline Classical mechanics Old quantum theory Glossary Fun Skip to main content Quantiki Toggle Sun, L. weblink

Despite using quantum effects the algorithm **run on the quantum computer does** not outperform Selby’s algorithm run on a classical computer.[84] In August 2016, scientists at the University of Maryland successfully 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. Note that the error syndrome does not tell us anything about the encoded state, only about the error that has occurred. Retrieved 2007-06-04. ^ Neumann, P.; et al. (June 6, 2008). "Multipartite Entanglement Among Single Spins in Diamond". https://en.wikipedia.org/wiki/Quantum_error_correction

## Stabilizer Codes And Quantum Error Correction.

Gottesman, "Stabilizer codes and quantum error correction," quant-ph/9705052, Caltech Ph.D. The fault-tolerant procedures concatenate as well, and after L levels of concatenation, the effective logical error rate is pt(p/pt)2L (for a base code correcting 1 error). D. **Rev. **

Cramming more components onto integrated circuits. If U = i σ y {\displaystyle U=i\sigma _{y}} then both a bit flip error and a sign flip error occur. Cory, M. Quantum Code Reel References[edit] H.

Singer, Stephanie Frank (2005). Breaking these would have significant ramifications for electronic privacy and security. Cambridge: Cambridge University Press. https://en.wikipedia.org/wiki/Quantum_convolutional_code Somaroo, "Experimental Quantum Error Correction," Phys.

Four Lectures on Quantum Computing given at Oxford University in July 2006 C. Bit Flip Memory Error R is a quantum operation and (R ∘ Ea)(∣ψ⟩) = ∣ψ⟩ for all Ea ∈ E, ∣ψ⟩ ∈ C. Thus, it is sufficient in general to check that the error-correction conditions hold for a basis of errors. For computing in either case, the system must be initialized, for example into the all-zeros string, | 000 ⟩ {\displaystyle |000\rangle } , corresponding to the vector (1,0,0,0,0,0,0,0).

## 5 Qubit Code

Bibcode:2004PhRvL..93m0503L. https://quantiki.org/wiki/quantum-error-correction-and-fault-tolerance-0 The theory of quantum error-correcting codes has been developed to counteract noise introduced in this way. Stabilizer Codes And Quantum Error Correction. The Australian. Quantum Code 7 Unsourced material may be challenged and removed. (June 2015) (Learn how and when to remove this template message) The Bloch sphere is a representation of a qubit, the fundamental building block

Tillich, “Quantum convolutional codes: fundamentals.” Available at http://arxiv.org/abs/quant-ph/0401134 J. have a peek at these guys The state of the computer at any time is a probability distribution over the 2 3 = 8 {\displaystyle 2^{3}=8} different three-bit strings 000, 001, 010, 011, 100, 101, 110, and All of them share some basic features: they involve creation and verification of specialized ancilla states, and use transversal gates which interact the data block with the ancilla state. Freedman, Michael H.; Meyer, David A.: Projective plane and planar quantum codes. 5 Qubit Quantum Error Correction

- A transversal operation is one in which the ith qubit in each block of a QECC interacts only with the ith qubit of other blocks of the code or of special
- The symplectic product ⊙ {\displaystyle \odot } of u {\displaystyle \mathbf {u} } and v {\displaystyle \mathbf {v} } is u ⊙ v ≡ ∑ i = 1 n z i
- Vandersypen, Lieven M.K.; Yannoni, Constantino S.; Chuang, Isaac L. (2000).
- This mapping gives a simplification of quantum error correction theory.
- Quantum Convolutional Coding with Shared Entanglement: General Structure.
- The USRA (Universities Space Research Association) will invite researchers to share time on it with the goal of studying quantum computing for machine learning.[77] In early 2014 it was reported, based
- However, the use of error correction brings with it the cost of a greatly increased number of required bits.

Stolze, Joachim; Suter, Dieter (2004). Consider the 2 n {\displaystyle 2n} -dimensional vector space ( Z 2 ) 2 n = { ( z , x ) : z , x ∈ ( Z 2 ) International Journal of Theoretical Physics. 21 (6): 467–488. check over here 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

Quantum Information Processing. 2 (6): 449–472. Steane Code MIT Technology Review. OCLC174527496.

## Then we interact the ancilla with the encoded data qubits using gates from our stock of transversal gates and perform a fault-tolerant measurement.

M.; Enderud, C.; Hilton, J. Quantum mechanically, we measure the three-qubit state, which is equivalent to collapsing the quantum state down to a classical distribution (with the coefficients in the classical state being the squared magnitudes if, say, one copy says, the bit is a 0, and two others claim it to be a 1, then probably all three were a 1 and the first bit got Quantum Code Burner 7.0 1 arXiv:quant-ph/0404083.

**arXiv:1304.4595. **Cambridge University Press. are designed with the help of Symmetric Functions organized from different quantum gates.[51][52] April 2011, a team of scientists from Australia and Japan made a breakthrough in quantum teleportation. http://vealcine.com/quantum-error/quantum-error-correction-ppt.php Johansson, G.

Steane, “Error correcting codes in quantum theory,” Phys. Cerf, Ulrik L. R. Copying quantum information is not possible due to the no-cloning theorem.

Bibcode:1980JSP....22..563B. Jacobs and J. SIAM Journal on Computing 26(5): 1510–1523 (1997). ^ Quantum Algorithm Zoo – Stephen Jordan's Homepage ^ Jon Schiller, Phd. "Quantum Computers". ^ Rich, Steven; Gellman, Barton (2014-02-01). "NSA seeks to build So, for example, there are only 6 stabilizer states on one qubit.

Nature. 410 (6830): 789–93. Quantum convolutional coding theory offers a different paradigm for coding quantum information. arXiv:1111.4147. Engadget. ^ "Learning to program the D-Wave One".

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. P∣ψ⟩ = ∣ψ⟩∀P ∈ S. A transversal operation has the virtue that an error occurring on the 3rd qubit in a block, say, can only ever propagate to the 3rd qubit of other blocks of the Both are suspected to not be NP-complete.

In particular the RSA, Diffie-Hellman, and Elliptic curve Diffie-Hellman algorithms could be broken. The outcome can therefore be at most n {\displaystyle n} classical bits of information. Science. 270 (5234): 255–261.