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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 stabilizer code ： ウィキペディア英語版 stabilizer code The theory of quantum error correction plays a prominent role in the practical realization and engineering of quantum computing and quantum communication devices. The first quantum error-correcting codes are strikingly similar to classical block codes in their operation and performance. Quantum error-correcting codes restore a noisy, decohered quantum state to a pure quantum state. A stabilizer quantum error-correcting code appends ancilla qubits to qubits that we want to protect. A unitary encoding circuit rotates the global state into a subspace of a larger Hilbert space. This highly entangled, encoded state corrects for local noisy errors. A quantum error-correcting code makes quantum computation and quantum communication practical by providing a way for a sender and receiver to simulate a noiseless qubit channel given a noisy qubit channel that has a particular error model. The stabilizer theory of quantum error correction allows one to import some classical binary or quaternary codes for use as a quantum code. The only "catch" when importing is that the classical code must satisfy the dual-containing or self-orthogonality constraint. Researchers have found many examples of classical codes satisfying this constraint, but most classical codes do not. Nevertheless, it is still useful to import classical codes in this way (though, see how the entanglement-assisted stabilizer formalism overcomes this difficulty). == Mathematical background == The Stabilizer formalism exploits elements of the Pauli group $\backslash Pi$ in formulating quantum error-correcting codes. The set $\backslash Pi=\backslash left\backslash$ consists of the Pauli operators: :$$ I\equiv \begin 1 & 0\\ 0 & 1 \end ,\ X\equiv \begin 0 & 1\\ 1 & 0 \end ,\ Y\equiv \begin 0 & -i\\ i & 0 \end ,\ Z\equiv \begin 1 & 0\\ 0 & -1 \end . The above operators act on a single qubit---a state represented by a vector in a two-dimensional Hilbert space. Operators in $\backslash Pi$ have eigenvalues $\backslash pm1$ and either commute or anti-commute. The set $\backslash Pi^$ consists of $n$-fold tensor products of Pauli operators: :$$ \Pi^=\left\ e^A_\otimes\cdots\otimes A_:\forall j\in\left\ A_\in\Pi,\ \ \phi\in\left\ \end \right\} . Elements of $\backslash Pi^$ act on a quantum register of $n$ qubits. We occasionally omit tensor product symbols in what follows so that :$A\_\backslash cdots\; A\_\backslash equiv\; A\_\backslash otimes\backslash cdots\backslash otimes\; A\_.$ The $n$-fold Pauli group $\backslash Pi^$ plays an important role for both the encoding circuit and the error-correction procedure of a quantum stabilizer code over $n$ qubits. 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「stabilizer code」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.