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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 convolutional code ： ウィキペディア英語版 Quantum convolutional code Quantum block codes are useful in quantum computing and in quantum communications. The encoding circuit for a large block code typically has a high complexity although those for modern codes do have lower complexity. Quantum convolutional coding theory offers a different paradigm for coding quantum information. The convolutional structure is useful for a quantum communication scenario where a sender possesses a stream of qubits to send to a receiver. The encoding circuit for a quantum convolutional code has a much lower complexity than an encoding circuit needed for a large block code. It also has a repetitive pattern so that the same physical devices or the same routines can manipulate the stream of quantum information. Quantum convolutional stabilizer codes borrow heavily from the structure of their classical counterparts. Quantum convolutional codes are similar because some of the qubits feed back into a repeated encoding unitary and give the code a memory structure like that of a classical convolutional code. The quantum codes feature online encoding and decoding of qubits. This feature gives quantum convolutional codes both their low encoding and decoding complexity and their ability to correct a larger set of errors than a block code with similar parameters. ==Definition== A quantum convolutional stabilizer code acts on a Hilbert space $\backslash mathcal,$ which is a countably infinite tensor product of two-dimensional qubit Hilbert spaces indexed over integers ≥ 0 $\backslash left\backslash \backslash right\backslash \}\; \_\}$: :$$ \mathcal= } \ \mathcal_. A sequence $\backslash mathbf$ of Pauli matrices $\backslash left\backslash \; \_\}$ , where :$$ \mathbf= } \ A_, can act on states in $\backslash mathcal$. Let $\backslash Pi^\}$ denote the set of all Pauli sequences. The support supp$\backslash left(\; \backslash mathbf\backslash right)$ of a Pauli sequence $\backslash mathbf$ is the set of indices of the entries in $\backslash mathbf$ that are not equal to the identity. The weight of a sequence $\backslash mathbf$ is the size $\backslash left\backslash vert\; \backslash text\backslash left(\; \backslash mathbf\backslash right)$ \right\vert of its support. The delay del$\backslash left(\; \backslash mathbf\backslash right)$ of a sequence $\backslash mathbf$ is the smallest index for an entry not equal to the identity. The degree deg$\backslash left(\; \backslash mathbf\backslash right)$ of a sequence $\backslash mathbf$ is the largest index for an entry not equal to the identity. E.g., the following Pauli sequence :$$ \begin () I & X & I & Y & Z & I & I & \cdots \end , has support $\backslash left\backslash$, weight three, delay one, and degree four. A sequence has finite support if its weight is finite. Let $F(\backslash Pi^\})$ denote the set of Pauli sequences with finite support. The following definition for a quantum convolutional code utilizes the set $F(\backslash Pi^\})$ in its description. A rate $k/n$-convolutional stabilizer code with $0\backslash leq$ k\leq n is a commuting set $\backslash mathcal$ of all $n$-qubit shifts of a basic generator set $\backslash mathcal\_$. The basic generator set $\backslash mathcal\_$ has $n-k$ Pauli sequences of finite support: :$$ \mathcal_=\left\\in F(\Pi^}):1\leq i\leq n-k\right\} . The constraint length $\backslash nu$ of the code is the maximum degree of the generators in $\backslash mathcal\_$. A frame of the code consists of $n$ qubits. A quantum convolutional code admits an equivalent definition in terms of the delay transform or $D$-transform. The $D$-transform captures shifts of the basic generator set $\backslash mathcal\_$. Let us define the $n$-qubit delay operator $D$ acting on any Pauli sequence $\backslash mathbf\backslash in\backslash Pi^\}$ as follows: :$$ D\left( \mathbf\right) =I^\otimes\mathbf We can write $j$ repeated applications of $D$ as a power of $D$: :$$ D^\left( \mathbf\right) =I^\otimes\mathbf Let $D^\backslash left(\; \backslash mathcal\_\backslash right)$ be the set of shifts of elements of $\backslash mathcal\_$ by $j$. Then the full stabilizer $\backslash mathcal$ for the convolutional stabilizer code is :$$ \mathcal= }} D^\left( \mathcal_\right) . 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 convolutional 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.