# Quantum Error Detection

## Contents |

**Rev. **If U = σ z {\displaystyle U=\sigma _{z}} , a sign flip error occurs. A SWAP gate operation is equivalent to three CNOT gates alternating direction (Fig. 8b). Sloane ([2], [3]); these are also called additive codes. have a peek at this web-site

[email protected] Summary A functioning quantum computer must be capable of maintaining coherent quantum superpositions of the 0 and 1 states of its quantum bits until an algorithm has completed. We also characterise the two-qubit gates via Clifford RB22. Every single-qubit pulse is accompanied by a scaled Gaussian derivative in the other quadrature to minimize the effect of leakage of information into higher qubit energy levels28. Histograms of the correlated single-shot syndrome qubit measurements are shown in the density plots on top for θ∼{−π,−π/2,0,π/2,π}, as indicated by the vertical dashed lines, with the syndrome states corresponding to

## Quantum Error Correction Codes

Contents 1 The bit flip code 2 The sign flip code 3 The Shor code 4 General codes 5 Models 6 Experimental realization 7 See also 8 References 9 Bibliography 10 Their error detection and error correction efforts are paving the way for larger quantum computing systems that could surpass classical computers in solving certain problems and do so reliably. Let E phase {\displaystyle E_{\text{phase}}} be a quantum channel that can cause at most one phase flip. et **al. **

Peter Shor first discovered this method of formulating a quantum error correcting code by storing the information of one qubit onto a highly entangled state of nine qubits. Langer, R. Rev. Quantum Code 7 Since we perform measurements of the syndrome qubits in the Z measurement basis, Q4 also undergoes a Hadamard transformation H right before measurement.

The results are consistent with a higher uncertainty in the phase-flip error detection, likely due to decoherence during the full sequence and the order of syndrome detection.Full size imageDiscussionWe have provided Quantum Error Correction For Beginners Girvin and R. Mathematics of quantum computation, 287–320, Comput. get redirected here Lett. 98, 190504 (2007).CASPubMedArticle11.Gottesman, D.

Each cross-resonance pulse has a Gaussian turn-on and off of width 3σ with σ=24 ns, included in τ. Bit Flip Memory Error Copying quantum information is not possible due to the no-cloning theorem. Franson, "Demonstration of quantum error correction using linear optics," Phys. 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

## Quantum Error Correction For Beginners

A., Gambetta, J. http://link.aps.org/doi/10.1103/PhysRevX.6.031006 Rev. Quantum Error Correction Codes Quantum computers are particularly susceptible to errors as quantum systems are highly sensitive to noise effects that can be exotic compared with the simple bit-flip errors of classical computation. Stabilizer Codes And Quantum Error Correction. Please enable JavaScript to use all the features on this page.

Michael, Matti Silveri, R. T. Check This Out Hence, for each of the 108 different measurement observables , has a single-shot variance that scales as . Reed, L. Nature 504, 419–422 (2013).ISICASPubMedArticle20.Johnson, J. Quantum Error Correction Book

Rev. Córcoles, Easwar Magesan& Srikanth J. Smolin for engaging discussions. Source H.

Dispersive readout signals for each qubit are amplified by distinct Josephson parametric amplifiers (JPAs) giving high single-shot readout fidelity20,21. Fault Tolerant Quantum Computation The sign flip code[edit] Quantum circuit of the phase flip code Flipped bits are the only kind of error in classical computer, but there is another possibility of an error with Hence, assuming depolarizing errors, we can obtain an approximate gate fidelity for the comprised circuit of ∼0.943=0.83 and state fidelities with similar values, which is consistent with our obtained fidelities in

## Nigg, M.

Each panel of Fig. 4 shows a teal bar plot reflecting the experimentally extracted population of each of the four possible syndrome qubit measurement outcomes for the set of errors {Yπ/3, Although previous work14,24,25,26 implemented parity checks on linear arrangements of qubits, our experiment goes beyond into the other planar dimension. M. Steane Code We then reverse an error by applying a corrective operation based on the syndrome.

The device studied in this work (false-colored optical micrograph in b) embodies two half-plaquettes of the SC as circled in a, and allows for independent and simultaneous detection of X and The dashed line shows the performance of the naive encoding L=0, |W↑/↓i⟩=|0/1⟩, whose rate of entanglement infidelity at small δt approaches κ/2 corresponding to the rate of a photon loss with designed the experiments. http://johnlautner.net/quantum-error/quantum-error-codes.html Rev.