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# Quantum Error Correction With Imperfect Gates

Phys. (N.Y.) 43, 4452 (2002).X.-G. Blatt, "Experimental Repetitive Quantum Error Correction," Science 332, 1059-1061 (2011), doi:10.1126/science.1203329 ^ M. Rev. 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 news

Then the Pauli operators of weight t or less form a basis for the set of all errors acting on t or fewer qubits, so a QECC which corrects these Pauli Page %P Close Plain text Look Inside Chapter Metrics Provided by Bookmetrix Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Shor, “Good quantum error-correcting codes exist”, LANL e-print quant-ph/9512032, http://​xxx.​lanl.​gov (to appear in Phys. Res.

An operation consisting only of single-qubit gates is automatically transversal. A number of different techniques have been developed. Zurek, Resilient Quantum Computation: Error Models and Thresholds, Proc. Thus, it is sufficient in general to check that the error-correction conditions hold for a basis of errors.

In that case, let us consider tensor products of the Pauli matrices $I=\begin{pmatrix}1&0\\0&1\end{pmatrix}, X=\begin{pmatrix}0&1\\1&0\end{pmatrix}, Y=\begin{pmatrix}0&-i\\i&0\end{pmatrix}, Z=\begin{pmatrix}1&0\\0&-1\end{pmatrix}$ Define the Pauli group Pn as the group consisting of tensor products of I, X, Rev. Dorit Aharonov,et al. Share this on Skip to main content Quantiki Toggle navigation Browse News Forums Video Abstracts Journal Articles RSS Feeds Journal Articles News Positions Video Abstracts Events Past events Groups Positions Wiki

Caves (3) Editor Affiliations 1. Rev. Rev. The solution is to use transversal gates whenever possible.

Ben-Or, Fault-Tolerant Quantum Computation with Constant Error, in Proceedings of the 29th Annual ACM Symposium on Theory of Computing (ACM, 1997), p. 188.D. In general, a gate coupling pairs of qubits allows errors to spread in both directions across the coupling. High-fidelity universal quantum gates through group-symmetrized rapid passage Ran Li, Frank Gaitan Published in 2010. Bombin, Topological Codes, in Quantum Error Correction, edited by D. A.

It is similar to the three bits repetition code in a classical computer. https://journals.aps.org/prx/references/10.1103/PhysRevX.5.031043 Kitaev, “Quantum computing: algorithms and error correction”, Russian Mathematical Surveys, to appear. Amazingly, as noted in the introduction, all elements from the set S ∪Z 2 —a universal set—are " easy " to perform at the logical level for 3D color codes, but R.

Then we complete the operation with a further transversal gate which depends on the outcome of the measurement. http://caribtechsxm.com/quantum-error/quantum-error-correction.php In-depth coverage of the design and implementation of quantum information processing and quantum error correction circuits. Ryan-Anderson, Quantum Computing by Color-Code Lattice Surgery, arXiv:1407.5103.A. J. Laflamme, and W. H.

W. Fault-Tolerance Given a QECC, we can attempt to supplement it with protocols for performing fault-tolerant operations. Yu. http://caribtechsxm.com/quantum-error/quantum-error-correction-usc.php If we only wish to detect errors, a distance d code can detect errors on up to d − 1 qubits.

Dyn. 17, 1 (2010).B. J. 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 Horodecki, P.

## The theory of fault-tolerant quantum computation tells us how to perform operations on states encoded in a quantum error-correcting code without compromising the code's ability to protect against errors.

Instead of the unencoded ∣ + ⟩ state, we must use a more complex ancilla state ∣00…0⟩ + ∣11…1⟩ known as a 'cat' state. Cumulative Annual Citation Context (22) ...We remark that for m = 4, the graph Gr(4) is a combinatorial torus and the quantum code Qr(4) is a version of Kitaev’s toric code Steklov Mathematical Institute 3. Nickerson, and D. E.

A Phys. Phys. The reason is that the measurement of the syndrome has the projective effect of a quantum measurement. click site The set is also almost " easy " for Kitaev's 2D surface codes [24], except generating S and S † requires some constant startup costs that can be amortized [46].

Loss, J. K. Lett. 110, 170503 (2013).S.