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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 matrix product state ： ウィキペディア英語版 matrix product state Matrix product state (MPS) is a pure quantum state of many particles, written in the following form: : $$ |\Psi\rangle = \sum_(A_2^ \cdots A_N^ ) |s_1 s_2 \ldots s_N\rangle, where $A\_i^$ are complex, square matrices of order $\backslash chi$ (this dimension is called local dimension). Indices $s\_i$ go over states in the computational basis. For qubits, it is $s\_i\backslash in\; \backslash$. For qudits (d-level systems), it is $s\_i\backslash in\; \backslash$. It is particularly useful for dealing with ground states of one-dimensional quantum spin models (e.g. Heisenberg model (quantum)). The parameter $\backslash chi$ is related to entanglement between particles. In particular, if the state is a product state (i.e. not entangled at all), it can be described as a matrix product state with$\backslash chi\; =\; 1$. For states that are translationally symmetric, we can choose: : $$ A_1^ = A_2^ = \cdots = A_N^ \equiv A^. In general, every state can be written in the MPS form (with $\backslash chi$ growing exponentially with the particle number ''N''). However, MPS are practical when $\backslash chi$ is small – for example, does not depend on the particle number. Except for a small number of specific cases (some mentioned in the section Examples), such thing is not possible. Though, in many cases it serves as a good approximation. MPS decomposition is not unique. Introductions in.〔 and.〔 In the context of finite automata:〔 == Obtaining MPS == One method to obtain MPS is to use Schmidt decomposition times. 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「matrix product state」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.