# Quantum Error Correction Review

## Contents |

Judging by the mere elegance of **a new** approach for handling imperfections in quantum registers, the answer must be 'yes'.Top of page MORE ARTICLES LIKE THIS These links to content published or More Buying Choices 24 New from $94.84 14 Used from $51.77 38used&newfrom$51.77 See All Buying Options Quantum computation and information is one of the most exciting developments in science and Rev. More recently, scientists ... weblink

Ser.: Earth Environ. A number n of qubits stacked together form a quantum register, the logical structure on which quantum operations are performed in a quantum circuit. Definition 3.2 (Set of correctable errors) **A set of Pauli errors** is correctable for a given code with stabilizer if, for all either Sy(E1)≠Sy(E2), or E2=E1g for some . The 1st, 4th and 7th qubits are for the sign flip code, while the three group of qubits (1,2,3), (4,5,6), and (7,8,9) are designed for the bit flip code.

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

This is the most likely case. Ser.: Mater. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

The storage time for quantum information is thus prolonged with these codes, but it remains finite. Spurious interactions inevitably entangle the **quantum register with the** degrees of freedom in the environment that we can neither measure nor control. Denote by PSy the projector onto , and . Quantum convolutional codes Mark Wilde 10.

PhD thesis Pasadena, CA:California Institute of Technology.↵Knill E., Laflamme R., Zurek W. An Introduction To Quantum Error Correction And Fault-tolerant Quantum Computation In this section, we argue that quantum error correction cannot work, based on arguments presented by Landauer [13] and Unruh [14]. Because both errors are correctable by assumption, in either case, we return to the true encoded state after error correction. http://rsta.royalsocietypublishing.org/content/370/1975/4541 Using the truncated expression equation (3.14) for U, the only remaining compatible error is I.

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 computers. Phys. Comput. 6, 97–165.OpenUrlWeb of Science↵Aharonov D., Kitaev A., Preskill J. 2006 Fault-tolerant quantum computation with long-range correlated noise. Quantum error correction also employs syndrome measurements.

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

Mathematics of quantum computation, 287–320, Comput. Quantum information could thereby be lost. Surface Codes: Towards Practical Large-scale Quantum Computation Make sure you include the unit and box numbers (if assigned). Quantum Error Correction For Beginners Thus, error correction is used to reset a rotation angle that was slightly off.

What is more, the outcome of this operation (the syndrome) tells us not only which physical qubit was affected, but also, in which of several possible ways it was affected. have a peek at these guys The Pauli operator Z1, as noted earlier, acts as and thus has trivial error syndrome. Opt. (1977 - 1998) J. Rev. Fault Tolerant Quantum Computing

- Therefore, if the error at the bare level is below a critical value, then the residual error rapidly decreases with increasing coding level.
- But majority voting is not suitable for generalization to the quantum case because in the process, the encoded state is learned.
- Energy, Part C Plasma Phys. (1959 - 1966) J.
- Note, however, that for the quantum-mechanical CNOT gate, this is a basis-dependent statement.

D. Opt. This work is based on notes for the summer school ‘Frontiers of Quantum Information Science’ held at Tsinghua University, Bejing, China, in July 2011. http://vealcine.com/quantum-error/quantum-error-correction-usc.php Concatenated, encoded gates for fault-tolerant quantum computation. (a) The fault-tolerant gate, comprising a transversal gate and an error correction (EC), is repeated at every coding level. (b) The rectangle consists of

By continuing to use this site you agree to our use of cookies. Amazon Try Prime Books All Departments Amazon Video Amazon Warehouse Deals Appliances Apps & Games Arts, Crafts Then, . If you would like to buy this article, but not online, please contact [email protected]

## You were only trying to define a single state.

Figure 5a shows the recursive structure for a fault-tolerant-encoded gate at coding level l. Calderbank, Peter Shor and Andrew Steane. The book is not limited to a single approach, but reviews many different methods to control quantum errors, including topological codes, dynamical decoupling and decoherence-free subspaces. Parity-check matrices exist for a very large class of classical codes, not just for repetition codes.

Beams Phys. Both events are likely, however, and the quantum repetition code offers no protection against a local partially depolarizing error. Technol. (1999 - present) Plasma Sources Sci. this content Phys. (1982 - present) Comput.

Barrett, R. Scalable quantum computers require a far-reaching theory of fault-tolerant quantum computation. In §3, a class of quantum codes, the stabilizer codes [4], are developed from classical codes. For example, in the case where the first qubit is flipped, the result would be | ψ r ′ ⟩ = α 0 | 100 ⟩ + α 1 | 011

Your cache administrator is webmaster. Consider the example of an error Z1. For Δτ≠0, we have implemented an erroneous unitary, and have no way of detecting it. R.

Res. B: At. Optimization-based quantum error correction Andrew Fletcher Part IV. Features chapters by leading experts in the field of quantum science to give readers insight into different methods Covers experimental and practical issues as well as theory A comprehensive review of