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## Surface Codes: Towards Practical Large-scale Quantum Computation

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

## A newer idea is Alexei Kitaev's topological quantum codes and the more general idea of a topological quantum computer.

## Contents |

**Rev. **T. Most of them work by repeatedly making measurements on the system to detect errors and then correct the errors before they can proliferate. Phys. (1980 - present) Flex. news

Math. (1993 - 1995) Sb. The qubits exist on the edges and vertices of the plaquettes and are acted upon by weight-3 X- and Z-triangle operators (which are modified to become weight-2 operators at the boundary). **Rev. **For all states in the code space, the product of the two phase factors is +1.

It thus makes sense to limit the set of quantum gates that a quantum computer is required to perform. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of fault-tolerant quantum computation, instructing us how to perform quantum gates on qubits H. Schoelkopf, "Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits," Nature 482, 382-385 (2012), doi:10.1038/nature10786, arXiv:1109.4948 ^ M.

- Phys.
- First, we allowed only for memory errors and assumed the error correction to be perfect.
- Then, error discretization is only approximate.
- Researchers develop the first-ever quantum device that detects and corrects its own errors March 4, 2015 When scientists develop a full quantum computer, the world of computing will undergo a revolution
- A 71, 052332 (2005), doi:10.1103/PhysRevA.71.052332 ^ J.
- A 52, R2493–R2496.
- SIAM J.
- They report their results in the journal ...

Phys. Quantum **information could thereby be lost. **Skip to main content Other PublicationsPhilosophical Transactions B Proceedings B Biology Letters Open Biology Philosophical Transactions A Proceedings A Royal Society Open Science Interface Interface Focus Notes and Records Biographical Memoirs If U = i σ y {\displaystyle U=i\sigma _{y}} then both a bit flip error and a sign flip error occur.

Cerf, Ulrik L. An Introduction To Quantum Error Correction And Fault-tolerant Quantum Computation A gate set is universal, if any unitary evolution on can be arbitrarily closely approximated by sequences of gates in . click to open popover Frequently Bought Together + Total price: $184.29 Add both to Cart Add both to List Buy the selected items togetherThis item:Quantum Error Correction by Daniel A. http://rsta.royalsocietypublishing.org/content/370/1975/4541 In the universal set of equation (2.4), the non-Clifford gate was eiπ/8Z.

Rev. However, the errors that, if sufficient in number, can cause failure of the gate come from a larger region called the ‘extended rectangle’. Frank Gaitan (2008). "Quantum Error Correction and Fault Tolerant Quantum Computing". 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.

Prog. Phys. (1968 - present) J. Surface Codes: Towards Practical Large-scale Quantum Computation Lett. 96, 050504. Quantum Error Correction For Beginners Your error would be in your precision.

Rev. http://caribtechsxm.com/quantum-error/quantum-error-correction-usc.php doi:10.1103/PhysRevA.71.022316 (doi:10.1103/PhysRevA.71.022316)OpenUrlCrossRef↵Chen X., Chung H., Cross A. Mater. (2000 - 2015) Semicond. Calderbank, Peter Shor and Andrew Steane. Fault Tolerant Quantum Computing

Trans. The earlier-mentioned discussion leaves open the possibility that there are angles αm=α0m, with , such that UZ(α) is an encoded gate. phys.org Nanotechnology All Nanotechnology Bio & Medicine Nanomaterials Nanophysics Physics All Physics Condensed Matter General Physics Optics & Photonics Plasma Physics Quantum Physics Soft Matter Superconductivity Earth All Earth Earth Sciences More about the author If you requested a response, we will make sure to get back to you shortly. × Please fill in the required fields in your feedback submission. × Home Physics Quantum Physics

This theorem seems to present an obstacle to formulating a theory of quantum error correction. M. Details List Price: $124.00 Save: $7.60 (6%) 24 New from $94.84 FREE Shipping.

L. This statement can be proved by using a special family of codes, the so-called concatenated codes. Phys. Please try again.

We then reverse an error by applying a corrective operation based on the syndrome. then build a quantum computer. Surely there is a set you may read without error. click site B: At.

By measuring the syndrome value, Sy(Ei) corresponds to a projection PSy(Ei) onto . Appl. The CNOT and conditional phase gates are also transversal, but the Hadamard gate is not! In addition, the passive method can partially suppress noise, so that there are fewer errors in the first place.

World (1988 - present) Phys.-Usp. (1993 - present) Physics in Technology (1973 - 1988) Physiol. Decoherence processes are associated with quantum gates, including the identity gate (memory) such that the following properties hold. — Independence. Clearing 'visual noise' to improve underwater vision and deep sea exploration October 24, 2016 Mankind has long been peering into the depths of the sea. As noted earlier, in the quantum case, learning the state generally changes it.

Second, we considered only storage of quantum information rather than universal quantum computation. Introduction to quantum dynamical decoupling Lorenza Viola 5. Britton, W. He is also currently working with an experimental team to try to build, test, and optimize the device in the next few years.

High order dynamical decoupling Zhen-Yu Wang and Ren-Bao Liu 15. Phys. 87, 307 – Published 7 April 2015 More×ArticleReferencesCiting Articles (27)ArticleReferencesCiting Articles (27)PDFHTMLExport CitationAbstractAuthorsArticle Text— Introduction— Concepts of Quantum Error Correction— 2D (Topological) Error Correction— Discussion— ACKNOWLEDGMENTSReferencesAbstractAuthorsArticle TextIntroductionConcepts of Quantum Error Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required. Apple Android Windows Phone Android To get the free But the error X3X4 remains.

He has worked on quantum control theory for the past 15 years and is well known for his contributions to quantum error correction, in particular the development of decoherence-free subspaces.Todd A. J. This question leads to the notion of a universal set of gates. Lidar Hardcover $116.40 In Stock.Ships from and sold by Amazon.com.FREE Shipping.

Langer, R. Institutional subscribers have access to the current volume, plus a 10-year back file (where available). By leveraging the good ideas of the natural world and the semiconductor ...