# Quantum Error Control Codes

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All qubit control lines are heavily attenuated at different thermal stages and home-made Eccosorb microwave filters are added at the coldest refrigerator plate. Phys. B. et al. http://johnlautner.net/quantum-error/quantum-error-codes.html

L. Errors of ɛ=Yθ, with θ∈[−π,π] are detected by both syndromes, as Y errors can be decomposed into a combination of bit- and phase-flip errors. The latter is counter-intuitive at first sight: Since noise is arbitrary, how can the effect of noise be one of only few distinct possibilities? The SC is an example of a stabilizer code11, which is a code whose state is uniquely defined by the measurement of a set of observables called stabilizers.

## Quantum Error Correction Codes

and S.J.S. Chow1Nature Communications 6, Articlenumber:6979 (2015)doi:10.1038/ncomms7979Download CitationApplied **physicsQubitsSuperconducting properties and materialsReceived:16 January 2015Accepted:18** March 2015Published online:29 April 2015AbstractThe ability to detect and deal with errors when manipulating quantum systems is a fundamental et al. Quantum convolutional codes are particularly
well-suited for communication applications.

Suppose we copy a bit three times. developed the gate breakdown for the code implementation. Chwalla, M. Quantum Error Correction Book Since these qubits are not nearest **neighbours and there is no provision** for interaction between them—a key feature of the SC—we first entangle Q1 and Q2 and then perform a swap

The simplest way is to store the information multiple times, and—if these copies are later found to disagree—just take a majority vote; e.g. Each of the possible four outcomes of correlated single-shot measurements of the syndrome qubits is mapped onto one of the four maximally entangled Bell states of the code qubits. Ozeri and D. https://www.researchgate.net/publication/26903543_Quantum_error_control_codes Lett. 81, 2152–2155 (1998).ISICASArticle2.Zhang, J., Laflamme, R. & Suter, D.

We present a method of construction of the mutually orthogonal supersquares. Quantum Code 7 Andersen, Quantum optical coherence can survive photon losses using a continuous-variable quantum erasure-correcting code , Nature Photonics 4 10 (2010)(this document online) External links[edit] Prospects Error-check breakthrough in quantum computing[permanent dead Demonstration of a quantum error detection code using a square lattice of four superconducting qubits. et al.

## Quantum Error Correction For Beginners

See all ›14 CitationsSee all ›107 ReferencesShare Facebook Twitter Google+ LinkedIn Reddit Request full-textQuantum error control codesArticle with 31 ReadsSource: OAI1st Sala Abdelhamid Awad Aly AhmedAbstractIt is conjectured that quantum computers are able et al. Quantum Error Correction Codes To diagnose bit flips in any of the three possible qubits, syndrome diagnosis is needed, which includes four projection operators: P 0 = | 000 ⟩ ⟨ 000 | + | Steane Code Integrating kernels are obtained for each measurement channel, which extract the full time-dependent readout information27.

The complete circuit as shown in Fig. 1c will detect an arbitrary single-qubit error ɛ to the code qubits via the projective measurements of the syndrome qubits. Check This Out Surface codes: towards practical large-scale quantum computation. Inset shows ZX oscillations22 of the target qubit state population as a function of the cross-resonance drive length when the control qubit is in the ground (blue) or in the excited We use the ECRij as our CNOT genesis. Stabilizer Codes And Quantum Error Correction.

Gambetta& **Jerry M.** Copying quantum information is not possible due to the no-cloning theorem. and M.S. Source Each readout signal is reflected off a JPA, pumped at frequency ωPi, before being sent to a HEMT amplifier at 4 K.

Commun. 5, 500 (2014).CASArticle15.Paik, H. 5 Qubit Code Schoelkopf, "Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits," Nature 482, 382-385 (2012), doi:10.1038/nature10786, arXiv:1109.4948 ^ M. If U = σ x {\displaystyle U=\sigma _{x}} , a bit flip error occurs.

## We either use external Marki I/Q mixers with a Holzworth microwave generator or an Agilent vector signal generator (E8257D) as depicted in Fig. 6.

The device is protected from environmental radiation by an Amuneal cryoperm shield with an inner coat of Emerson & Cuming CR-124 Eccosorb. Nebendahl, D. Moving forward, continued improvement of gate and assignment fidelities will be required to reach fault-tolerance thresholds. Bit Flip Memory Error Niset, G.

Quantum circuit of the Shor code Let E {\displaystyle E} be a quantum channel that can arbitrarily corrupt a single qubit. Implementing a strand of a scalable fault-tolerant quantum computing fabric. Monz, V. have a peek here The research topic of MOLS has recently attracted attention in the young field of quantum information theory: the mean king's problem [8], quantum error correction codes [1], mutually unbiased bases [7],

Modulating shapes for readout are produced by Arbitrary Pulse Sequencers from Raytheon BBN Technologies. This process is repeated 19,200 times to gather sufficient statistics. These and other relevant system experimental parameters including qubit frequencies, anharmonicities, energy relaxation and coherence times are further discussed in the Methods.Figure 1: Surface code implementation and error detection quantum circuit.(a) Lett. 107, 160501 (2011).CASPubMedArticle4.Chiaverini, J.

A. Math. 1 (2001), no. 3, 325–332. Next, for the case of a bit-flip error to Q1, or ɛ=Xπ, the resulting syndrome histograms are shown in the colour map in Fig. 2b, where a majority of results are D.

AhlswedeA. Full-text · Article · Nov 2011 Salah A.alyAndreasklappeneckerRead full-textAsymmetric Quantum Cyclic Codes"The interested readers may look at the previous work in constructions of asymmetric quantum error control codes (AQEC) [3,567. Initialization by measurement of a superconducting quantum bit circuit. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply.

This allows us to establish the degree of addressability error23 present in our system. et al.