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## Quantum Error Correction For Beginners

## Quantum Error Correction Lidar

## Cornell University Library We gratefully acknowledge support fromthe Simons Foundation and member institutions arXiv.org > quant-ph > arXiv:1607.00627 Search or Article-id (Help | Advanced search) All papers Titles Authors Abstracts

Quantum self-correction **in the 3D cubic code** model. Phys. For cases where a correctable cluster of gauge defects returns stabilizer defects, we assign their positions such that they lie at the mean position of all the gauge defects within the D. news

Owing to the symmetry of the gauge group, it suffices here to consider only bit-flip, that is, Pauli-X errors. That way, measurements made on the final state of the qubits are guaranteed to reveal relationships between qubits without revealing their values. Knill, and R. A 66, 052313 (2002) CrossRefADS3. find this

Magic-state **distillation with the** four-qubit code. Comp. 13, 0195–0209 (2013).28.Li, Y. A.

The system returned: (22) Invalid argument The remote host or network may be down. A site license includes a minimum of four years of archived content; institutions can add additional archived content to their license at any time. Restrictions on transveral encoded quantum gate sets. As such, the resource cost of realizing scalable quantum computation is sensitive to the method a fault-tolerant computational scheme uses to realize non-Clifford gates.

Devetak, Entanglement-assisted quantum quasicyclic low-density parity-check codes. Quantum Error Correction Lidar A 89, **032316 (2014).CASArticle50.Hutter, A.** & Loss, D. Most known codes achieve confinement by performing syndrome measurements many times. The blue and red regions indicate a range of T1 times (x axis) for which encoding a qubit in |1L〉 in surface-17 reduces or increases, respectively, the logical error rate compared

Fault-tolerant quantum computing with color codes. The convergent trend provides evidence that we achieve steady-state confinement in the high-N limit, as is required of a practical error-correction scheme.To verify further the threshold error rates we have determined, J., Anderson, J. Phys.

N. MacKay, G. Quantum Error Correction For Beginners Calderbank, and P.W. Quantum Code Chiaverini1 Email:[email protected] read this story in full you will need to login or make a payment (see right).

Phys. http://caribtechsxm.com/quantum-error/quantum-error-correction-code.php As an example, the gauge syndrome in Fig. 3a depicts the gauge defects and measurement error string shown in Fig. 2c where the measurement errors have occurred on the faces that Pairs of uv gauge defects are caused by strings of incorrect uv face outcomes and therefore form correctable configurations, as shown in Fig. 3a. To simulate errors that occur during the readout process, we apply the noise operator E(p) to the encoded state before decoding.

Rev. Blakestad1, J. Phys. 47, 062106 (2006) CrossRefADSMathSciNet4. http://caribtechsxm.com/quantum-error/quantum-error-code-2401.php The yellow surface is the simulated logical error rate given T1 for a qubit encoded in the |1L〉 state in surface-17.

So they could correct eight errors in a 64-qubit quantum computer, for instance, but not 10. Four identity gates are used, based on the other location type in the given time step: preparation (P), single-qubit gate (H), two-qubit gate (C), and measurement (M).Reuse & PermissionsFigure 8Illustration of It is problematic then that the small quantum systems that we might use to realize such technologies decohere rapidly due to unavoidable interactions with the environment.

- Topological quantum memory.
- Phys.
- In the gauge color code we do not measure stabilizer operators directly, but instead infer their values by measuring face operators, which is possible due to the fact that .In addition
- The figure shows the logarithm of the gradients found in Fig. 6, log g(d), plotted as a function of the logarithm of the code distance, log d, for the case where

Efficient high-fidelity quantum computation using matter qubits and linear optics. The stabilizer at the cell with thick red edges contains a stabilizer defect. Chiaverini1, D. Details on the fitting calculation are given in Methods.

We consider face f, colored uv, that is adjacent to cell c. NickersonDepartment of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UKDan E. Decoding color codes by projection onto surface codes. click site High threshold error correction for the surface code.

The discovery of such a point suggests that the error correlations caused by our correction protocol do not extend beyond a constant, finite and decodable length, thus showing that we can M.A. We can now determine α and β using, respectively, the d=1 intersection and the gradient of a linear fit shown in Fig. 7.Figure 6: Logical failure rates for the gauge color J.

We therefore calculate logical failure rateswhere . Active error correction for Abelian and non-Abelian anyons. Rev. Britton1, W.

ICC’93, Geneva, Switzerland, May 1993, pp. 1064–1070 (1993) 2. New J. Knill2, C. Rev.

Devitt, Rodney Van Meter (Submitted on 3 Jul 2016) Abstract: The yield of physical qubits fabricated in the laboratory is much lower than that of classical transistors in production semiconductor fabrication. Rains, P.W. Gottesman, Stabilizer codes and quantum error correction. Topological subsystem codes.

Sloane, Quantum error correction via codes over GF(4). G., Mariantoni, M., Martinis, J. A 86, 032324 (2012).CASArticle26.Bravyi, S. & Haah, J. R. & Hutter, A.

Error-correcting codes in quantum theory. Phys. Magic-state distillation with low overhead.