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# Quantum Error Correction Wiki

## Contents

Of these, only the assumption of independent errors is at all necessary, and that can be considerably relaxed to allow short-range correlations and certain kinds of non-Markovian environments. We perform a multi-qubit measurement that does not disturb the quantum information in the encoded state but retrieves information about the error. The state of the computer at any time is a probability distribution over the 2 3 = 8 {\displaystyle 2^{3}=8} different three-bit strings 000, 001, 010, 011, 100, 101, 110, and Quantum circuit of the bit flip code Let | ψ ⟩ = α 0 | 0 ⟩ + α 1 | 1 ⟩ {\displaystyle |\psi \rangle =\alpha _{0}|0\rangle +\alpha _{1}|1\rangle } news

doi:10.1090/S0273-0979-02-00964-3. Cambridge University Press. The European Physical Journal Special Topics. 224 (111): 111. He finally decodes the encoded qubits with a decoding circuit. my response

## Stabilizer Codes And Quantum Error Correction.

Some stabilizer codes have interesting symmetries under the action of certain Clifford group elements, and these symmetries result in transversal gate operations. re-encode each logical qubit by the same code again, and so on, on logarithmically many levels—provided the error rate of individual quantum gates is below a certain threshold; as otherwise, the Then the bit flip code from above can recover | ψ ⟩ {\displaystyle |\psi \rangle } by transforming into the Hadamard basis before and after transmission through E phase {\displaystyle E_{\text{phase}}}

New Scientist. ^ Das, A.; Chakrabarti, B. References H. The state of a three-qubit quantum computer is similarly described by an eight-dimensional vector (a,b,c,d,e,f,g,h), called a ket. Quantum Code Reel The encoding circuit for a quantum convolutional code has a much lower complexity than an encoding circuit needed for a large block code.

Hiroshi, Imai; Masahito, Hayashi (2006). 5 Qubit Code Nature. 473 (7346): 194–198. The quantum Singleton bound (or Knill-Laflamme bound) states that any ((n, K, d)) QECC must satisfy n − logK ≥ 2d − 2 We can set a lower bound on the existence of QECCs using the quantum Gilbert-Varshamov bound, https://en.wikipedia.org/wiki/Quantum_convolutional_code Barrett, R.

G. Bit Flip Memory Error Huck, J. Available at http://arxiv.org/abs/0903.3894 v t e Quantum information science General Quantum computer Qubit Quantum information Quantum machine Quantum programming Timeline of quantum computing Quantum communication Quantum capacity Classical capacity Entanglement-assisted classical W.; Amin, M.

## 5 Qubit Code

Mod. Then N ( u ) = X {\displaystyle N\left(u\right)=X} . Stabilizer Codes And Quantum Error Correction. In classical randomized computation, the system evolves according to the application of stochastic matrices, which preserve that the probabilities add up to one (i.e., preserve the L1 norm). Quantum Code 7 Nielsen, M.

Jost, E. http://caribtechsxm.com/quantum-error/quantum-error-correction.php Liquid state NMR Quantum Computing. Nature. 409 (6816): 46–52. Quantum Computing Devices: Principles, Designs, and Analysis helps fulfill this need by providing a comprehensive collection of the most promising devices for the future. Προεπισκόπηση αυτού του βιβλίου » Τι λένε 5 Qubit Quantum Error Correction

1. It is possible that a double-bit error occurs and the transmitted message is equal to three zeros, but this outcome is less likely than the above outcome.
2. Let us define the n {\displaystyle n} -qubit delay operator D {\displaystyle D} acting on any Pauli sequence A ∈ Π Z + {\displaystyle \mathbf {A} \in \Pi ^{\mathbb {Z} ^{+}}}
3. Monz, V.
4. Retrieved 2013-03-04. ^ Feynman, R.
5. H.
6. Since these two operations are completely separate, it can also correct Y errors as both a bit flip and a phase error.
7. Theory, vol. 53, pp. 865–880, 2007.
8. Wichert, Andreas (2014).

the Shor code, encodes 1 logical qubit in 9 physical qubits and can correct for one bit flip and one phase flip error. Ser., Chapman & Hall/CRC, Boca Raton, FL, 2002. Keyes, R. More about the author By adding extra qubits and carefully encoding the quantum state we wish to protect, a quantum system can be insulated to great extent against errors.

Stabilizer Codes In order to better manipulate and discover quantum error-correcting codes, it is helpful to have a more detailed mathematical structure to work with. Steane Code Please try the request again. Bibcode:2005OptSp..99..233N.

## Electronics Magazine.

The most widely-used structure gives a class of codes known as stabilizer codes. New York: Gordon & Breach. ^ Gershon, Eric (2013-01-14). "New qubit control bodes well for future of quantum computing". Retrieved 8 August 2016. ^ https://www.unibas.ch/en/News-Events/News/Uni-Research/A-new-Type-of-Quantum-Bit.html ^ Nielsen, p. 42 ^ Nielsen, p. 41 ^ a b Bernstein, Ethan; Vazirani, Umesh (1997). "Quantum Complexity Theory". Quantum Code Burner 7.0 1 Berlin: Springer.

Each measurement gives us one bit of the error syndrome, which we then decipher classically to determine the actual error. Suppose a single-qubit error occurs on the encoded quantum register. J. (2001). "A scheme for efficient quantum computation with linear optics". http://caribtechsxm.com/quantum-error/quantum-error-correction-usc.php Consider a problem that has these four properties: The only way to solve it is to guess answers repeatedly and check them, The number of possible answers to check is the

Decoherence times for candidate systems, in particular the transverse relaxation time T2 (for NMR and MRI technology, also called the dephasing time), typically range between nanoseconds and seconds at low temperature.[12] Many algorithms will only give the correct answer with a certain probability.