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## Stabilizer Codes And Quantum Error Correction.

## 5 Qubit Code

## DiCarlo Contributions M.D.R.

## Contents |

Through the transmission in a **channel the relative** sign between | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } can become inverted. Implementing a strand of a scalable fault-tolerant quantum computing fabric. Since we always prepare the code qubits in the codeword state at the beginning of the quantum process, when no error is applied to Q1, state tomography of Q1 and Q3 B. news

Accel. Moving forward, continued improvement of gate and assignment fidelities will be required to reach fault-tolerance thresholds. Extra lines near 31 mΦ0 and 29 mΦ0 are due to higher-order interactions predicted by the Hamiltonian (|102 with |030 and |003 with |111), as is the larger first-order interaction at 25 mΦ0 (|102 Program and Integrated MS-Ph.D. https://en.wikipedia.org/wiki/Quantum_error_correction

Phys. Phys. 43, 4452–4505 (2002).ISIArticle13.Fowler, A. P. Each qubit is further coupled with an independent CPW resonator for both qubit control and readout.

Q2 **(Q4) is initialized** to . Science 345, 302–305 (2014).ISICASPubMedArticle7.Reed, M. Although previous work14,24,25,26 implemented parity checks on linear arrangements of qubits, our experiment goes beyond into the other planar dimension. Quantum Error Correction Book We implement our CNOT gates using a simplified version of the gate, ECRij, consisting of two cross-resonance pulses of different sign separated by a π rotation in the control qubit.

Phys. designed and supervised the project. Nature 432, 602–605 (2004).ISICASPubMedArticle5.Schindler, P. Chiaverini, D.

Figure 5 shows the RB decays for each of the four gates, yielding an error per two-qubit Clifford gate of 0.0604±0.0006, 0.0631±0.0007, 0.0569±0.0015 and 0.0353±0.0015 for ECR12, ECR23, ECR34 and ECR41, Quantum Code 7 Characterization of addressability by simultaneous randomized benchmarking. The coefficients here are reduced for processes with finite fidelity. The gate sequence for this state preparation can be compiled together with portions of the ZZ stabilizer encoding.

and R.J.S. The simplest of these are three-quantum-bit (three-qubit) codes, which map a one-qubit state to an entangled three-qubit state; they can correct any single phase-flip or bit-flip error on one of the Stabilizer Codes And Quantum Error Correction. Insets: the constituent state fidelities of the four basis states used to produce the process fidelity data in the case with error correction (right) and in the case with no correction 5-qubit Quantum Error Correction The system returned: (22) Invalid argument The remote host or network may be down.

D. http://caribtechsxm.com/quantum-error/quantum-error-correction-usc.php fabricated the devices. Moving forward, on improving the measurement **and gate fidelities in these systems,** further expanding the lattice will lead to important studies of different error-correcting codes and the encoding of logical qubits, Dark blue bars represent the ideal outcome for each ɛ and teal bars are measurements calibrated by the full X, Y and Z error rotation curves. Steane Code

- and J.M.G.
- Watson Research Center, Yorktown Heights, New York 10598, USAA.D.
- Phys.

Rohrs and K. Nature Phys. 5, 134–140 (2009) CAS ISI Article Monz, T. Comparing our theoretical model to published noise estimates from recent experiments on flux and transmon qubits, we find that logical state coherence could be improved by a factor of 40 or More about the author This entanglement is achieved in our architecture with one CNOT and one SWAP gate (a).

General codes[edit] In general, a quantum code for a quantum channel E {\displaystyle {\mathcal {E}}} is a subspace C ⊆ H {\displaystyle {\mathcal {C}}\subseteq {\mathcal {H}}} , where H {\displaystyle {\mathcal Bit Flip Memory Error h, Planck’s constant. The XX stabilizer is encoded onto the X-syndrome qubit Q4, which is initialized in the state.

ReedSearch for this author in:NPG journals• PubMed• Google ScholarL. Implementation of the three-qubit phase-flip error correction code with superconducting qubits. The colormaps show the single-shot histograms of the syndrome measurements on Q2 and Q4. Fault-tolerant Quantum Computation designed the three-qubit gate and conducted initial measurements.

As the magnitude of the Y error increases from 0 to π, the majority of the outcomes of the syndrome qubits changes from {M2,M4}={0,+} (black dots) to {M2,M4}={1,−} (blue dots), while partner of AGORA, HINARI, OARE, INASP, ORCID, CrossRef, COUNTER and COPE Skip to main contentNature.comNature CommunicationsArticlesArticleA Nature Research JournalMenuNature CommunicationsSearchE-alertSubmitLoginAltmetric: 211Views: 16,489Citations: 31More detailArticle | OpenDemonstration of a quantum error detection E. click site Rev.

We achieve independent single-shot readout for each qubit using a high-electron-mobility transistor (HEMT) amplifier following a JPA (provided by UC Berkeley) in each readout line. Nature 467, 570–573 (2010) CAS ISI PubMed Article Paik, H. The complete gate sequence in our error detection experiments is presented in e, where the dark boxes indicate refocus pulses during every two-qubit gate on the two qubits not involved on 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.

Superconducting quantum circuits at the surface code threshold for fault tolerance. et al. Smolin for engaging discussions. et al.

A. & Chuang, I. in Proc. 37th Symp. Rev. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/Article ToolsPDFDemonstration of a quantum error detection code using a square lattice of four superconducting qubitsDownload as PDFView interactive PDF in ReadCubeShare on