# Quantum Error Correction With Imperfect Gates

## Contents |

Nielsen **and Isaac L. **The phenomenon of degeneracy has no analogue for classical error correcting codes, and makes the study of quantum codes substantially more difficult than the study of classical error correction. However, the theorem specifies the distance of the code by considering S ⊥ \ S. It uses entanglement and syndrome measurements and is comparable in performance with the repetition code. Source

Reed, L. Furthermore, these calculations make a number of assumptions about the physical properties of the computer. We develop a complex instruction set computing (\textsc{cisc}) architecture whose instruction set includes stabilizer operations and preparation of magic states from which $Z(\pi/2^k)$ gates can be teleported, for $2 \leq k The syndrome measurement "forces" the qubit to "decide" for a certain specific "Pauli error" to "have happened", and the syndrome tells us which, so that we can let the same Pauli http://link.springer.com/chapter/10.1007%2F978-1-4615-5923-8_19

## Quantum Error Correction Codes

Dr. The disadvantage is that it is not transversal, and thus not fault-tolerant. H.

The system returned: (22) Invalid argument The remote host or network may be down. M. W. Bit Flip Memory Error Chwalla, M.

The basic design principle of a fault-tolerant protocol is that an error in a single location --- either a faulty gate or noise on a quiescent qubit --- should not be Quantum Error Correction For Beginners About this Chapter Title Quantum Error Correction with Imperfect Gates Book Title Quantum Communication, Computing, and Measurement Book Part Part II Pages pp 181-188 Copyright 1997 DOI 10.1007/978-1-4615-5923-8_19 Print ISBN 978-1-4613-7716-0 more stack exchange communities company blog Stack Exchange Inbox Reputation and Badges sign up log in tour help Tour Start here for a quick overview of the site Help Center Detailed https://en.wikipedia.org/wiki/Quantum_error_correction This theorem seems to present an obstacle to formulating a theory of quantum error correction.

A procedure due to Knill (for any stabilizer code) teleports the data qubit through an ancilla consisting of two blocks of the QECC containing an encoded Bell state $\left|\overline{00}\right\rangle + \left|\overline{11}\right\rangle$. Quantum Error Correction Book Barrett, R. Calderbank and P. The set of stabilizer codes is exactly the set of codes which can be created by a Clifford group encoder circuit using ∣0⟩ ancilla states.

## Quantum Error Correction For Beginners

However for larger N an exponentially growing number of states are possible. http://physics.stackexchange.com/questions/56160/scaling-of-quantum-error-correction/56205 When these details are considered, we estimate that color codes achieve a threshold of 0.082(3)%, which is higher than the threshold of $1.3 \times 10^{-5}$ achieved by concatenated coding schemes restricted Quantum Error Correction Codes Roy. Stabilizer Codes And Quantum Error Correction. Another useful representation is to map the single-qubit Pauli operators I, X, Y, Z to the finite field GF(4), which sets up a connection between stabilizer codes and a subset of

P. this contact form The encoded $\left|\overline{0}\right\rangle$ for this code consists of the superposition of all even-weight classical codewords and the encoded $\left|\overline{1}\right\rangle$ is the superposition of all odd-weight classical codewords. partner of AGORA, HINARI, OARE, INASP, ORCID, CrossRef, COUNTER and COPE ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.8/ 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 Quantum Code 7

Franson, "Demonstration of quantum error correction using linear optics," Phys. Monz, V. Jumptomaincontent Jumptonavigation nature.com homepage PublicationsA-ZindexBrowsebysubject My accountSubmit manuscript RegisterSubscribe LoginCart Search Advancedsearch AccessTo read this story in full you will need to login or make a payment (see right).nature.com > Journal http://johnlautner.net/quantum-error/quantum-error-correction-ppt.html A procedure due to Steane uses (forCSS codes) one ancilla in a logical $\left|\overline{0}\right\rangle$ state of the same code and one ancilla in a logical $\left|\overline{0}\right\rangle + \left|\overline{1}\right\rangle$ state.

J. Steane Code Also, note that a single phase error in the cat state will cause the final measurement outcome to be wrong (even and odd switch places), so we should repeat the measurement Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view Skip to main content Quantiki Toggle navigation Browse News Forums Video Abstracts Journal Articles RSS Feeds Journal Articles News

## Frequently, we are interested in codes that correct any error affecting t or fewer physical qubits.

Britton1, W. Classical error correcting codes use a syndrome measurement to diagnose which error corrupts an encoded state. Therefore, given the ability to perform fault-tolerant Clifford group operations, fault-tolerant measurements, and to prepare the encoded ∣ψπ/8⟩ state, we have universal fault-tolerant quantum computation. Quantum Code Burner 7.0 1 Rains, P.

The encoded state is decoded back to the primary ion one-qubit state, making error information available on the ancilla ions, which are separated from the primary ion and measured. Taylor & Francis. If U = σ x {\displaystyle U=\sigma _{x}} , a bit flip error occurs. Check This Out Your cache administrator is webmaster.