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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Quantum error correction ： ウィキペディア英語版 Quantum error correction Quantum error correction is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is essential if one is to achieve fault-tolerant quantum computation that can deal not only with noise on stored quantum information, but also with faulty quantum gates, faulty quantum preparation, and faulty measurements. Classical error correction employs redundancy. 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. Suppose we copy a bit three times. Suppose further that a noisy error corrupts the three-bit state so that one bit is equal to zero but the other two are equal to one. If we assume that noisy errors are independent and occur with some probability p. It is most likely that the error is a single-bit error and the transmitted message is three ones. 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. Copying quantum information is not possible due to the no-cloning theorem. This theorem seems to present an obstacle to formulating a theory of quantum error correction. But it is possible to ''spread'' the information of one qubit onto a highly entangled state of several (''physical'') qubits. 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. A quantum error correcting code protects quantum information against errors of a limited form. Classical error correcting codes use a ''syndrome measurement'' to diagnose which error corrupts an encoded state. We then reverse an error by applying a corrective operation based on the syndrome. Quantum error correction also employs syndrome measurements. We perform a multi-qubit measurement that does not disturb the quantum information in the encoded state but retrieves information about the error. A syndrome measurement can determine whether a qubit has been corrupted, and if so, which one. What is more, the outcome of this operation (the ''syndrome'') tells us not only which physical qubit was affected, but also, in which of several possible ways it was affected. 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? In most codes, the effect is either a bit flip, or a sign (of the phase) flip, or both (corresponding to the Pauli matrices ''X'', ''Z'', and ''Y''). The reason is that the measurement of the syndrome has the projective effect of a quantum measurement. So even if the error due to the noise was arbitrary, it can be expressed as a superposition of basis operations—the ''error basis'' (which is here given by the Pauli matrices and the identity). 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 operator act again on the corrupted qubit to revert the effect of the error. The syndrome measurement tells us as much as possible about the error that has happened, but ''nothing'' at all about the ''value'' that is stored in the logical qubit—as otherwise the measurement would destroy any quantum superposition of this logical qubit with other qubits in the quantum computer. ==The bit flip code== The repetition code works in a classical channel, because classical bits are easy to measure and to repeat. However, in a quantum channel, it is no longer possible, due to the no-cloning theorem, which forbids the creation of identical copies of an arbitrary unknown quantum state. So a single qubit can not be repeated three times as in the previous example, as any measurement of the qubit will change its wave function. Nevertheless, in a quantum computer, there is another method, which is called the three qubits bit flip code. It uses entanglement and syndrome measurements, and can perform the similar results to the repetition code. Let $|\backslash psi\backslash rangle\; =\; \backslash alpha\_0|0\backslash rangle\; +\; \backslash alpha\_1|1\backslash rangle$ be an arbitrary qubit. The first step of the three qubit bit flip code is to entangle the qubit with two other qubits using two CNOT gates with input $|0\backslash rangle$.〔 〕 The result will be $|\backslash psi\text{'}\backslash rangle=\; \backslash alpha\_0\; |000\backslash rangle\; +\; \backslash alpha\_1|111\backslash rangle.$ This is just a tensor product of three qubits, and different from cloning a state. Now these qubits will be sent through a channel $E\_\{\backslash text\{bit\}\}$ where we assume that at most one bit flip may occur. For example, in the case where the first qubit is flipped, the result would be $|\backslash psi\text{'}\_r\backslash rangle=\backslash alpha\_0|100\backslash rangle\; +\; \backslash alpha\_1|011\backslash rangle$. To diagnose bit flips in any of the three possible qubits, syndrome diagnosis is needed, which includes four projection operators: $P\_0=|000\backslash rangle\backslash langle000|+|111\backslash rangle\backslash langle111|$ $P\_1=|100\backslash rangle\backslash langle100|+|011\backslash rangle\backslash langle011|$ $P\_2=|010\backslash rangle\backslash langle010|+|101\backslash rangle\backslash langle101|$ $P\_3=|001\backslash rangle\backslash langle001|+|110\backslash rangle\backslash langle110|$ It can be obtained: $\backslash langle\backslash psi\text{'}\_r|P\_0|\backslash psi\text{'}\_r\backslash rangle\; =\; 0$ $\backslash langle\backslash psi\text{'}\_r|P\_1|\backslash psi\text{'}\_r\backslash rangle\; =\; 1$ $\backslash langle\backslash psi\text{'}\_r|P\_2|\backslash psi\text{'}\_r\backslash rangle\; =\; 0$ $\backslash langle\backslash psi\text{'}\_r|P\_3|\backslash psi\text{'}\_r\backslash rangle\; =\; 0$ So it will be known that the error syndrome corresponds to $P\_1$. This three qubits bit flip code can correct one error if at most one bit-flip-error occurred in the channel. It is similar to the three bits repetition code in a classical computer. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Quantum error correction」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.