HOME 大学院 計算科学・量子計算における情報圧縮

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# 計算科学・量子計算における情報圧縮

In today's computational science, various problems ranging from galaxy dynamics to entanglement between qubits are being studied. When dealing with these problems on a (classical) computer, a common issue is how to compress the vast degrees of freedom of the target problem and efficiently represent them in a finite memory. In particular, in many-body problems, the number of degrees of freedom often increases exponentially with the number of components, so how to handle the vast number of degrees of freedom has become a universally important issue. Nowadays, in addition to developments in individual scientific fields such as astronomy, physics, and chemistry, data compression methods that incorporate knowledge from applied mathematics and quantum information are attracting attention. In this lecture, we introduce linear algebra, especially low-rank approximation of matrices and tensors using singular value decomposition, which is the basis of data compression. Then, we discuss matrix product state and its generalization, i.e., tensor network state, which are used to efficiently compress degrees of freedom in material science and particle theory, the concept of entanglement in the background, and the application of tensor network to the quantum computing.

コース名

35603-0126
GSC-PH6371L2

A1 A2

2

NO

• 第1回: 計算科学・量子計算と情報圧縮 • 第2回: 線形代数の復習 • 第3回: 特異値分解 • 第4回: 特異値分解のテンソルへの拡張＋応用 • 第5回: 情報のエンタングルメントと行列積表現 • 第6回: 行列積表現の固有値問題への応用 • 第7回: テンソルネットワーク表現への発展 • 第8回: テンソルネットワーク表現の様々な応用 • 第9回: テンソルネットワーク繰り込み群 • 第10回: 量子力学と量子計算 • 第11回: 量子コンピュータ・シミュレーション • 第12回: 量子古典ハイブリッドアルゴリズムとテンソルネットワーク • 第13回: 量子誤り訂正とテンソルネットワーク #1: Computational science, quantum computing, and data compression #2: Review of linear algebra #3: Singular value decomposition #4: Application of singular value decomposition to tensor network #5: Entanglement of information and matrix product state #6: Application of matrix product state to eigenvalue problems #7: Tensor network representation #8: Applications of tensor network representations #9: Tensor network renormalization group #10: Quantum mechanics and quantum computation #11: Simulation of quantum computers #12: Quantum-classical hybrid algorithms and tensor network #13: Quantum error correction and tensor network

2回のレポート提出に基づいて成績を評価する。 Grades will be given based on 2 reports.