Cluster States

In quantum information and quantum computing, a cluster state is a type of highly entangled state of multiple qubits. Cluster states are generated in lattices of qubits with Ising type interactions. A cluster C is a connected subset of a d-dimensional lattice, and a cluster state is a pure state of the qubits located on C. Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice. Cluster states are especially useful in the context of the one-way quantum computer.

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Renyi entropy of the wormholes

In information theory, the Rényi entropy generalizes the Hartley entropy, the Shannon entropy, the collision entropy and the min entropy. Entropies quantify the diversity, uncertainty, or randomness of a system. The Rényi entropy is named after Alfréd Rényi.

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Geometrical Optics in Continuum

Fermat’s Principle

Fermat’s Principle is

$$\delta s=\delta\int n\dd \ell=0$$

If we choose the path …

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Javascript 学习小记


  • 支持Markdown
    • 支持嵌入代码块的语法高亮
    • 支持latex输入一些基本的数学公式
  • 电脑上使用起来方便
  • 方便用手机查看
  • 方便分享给其他人
  • 软件稳定,无明显BUG,体积小,依赖少

最终我发现了NBViewer+Jupyter Notebook+Github/Gist的组合。

注:现在更倾向于用Jupyter Notebook+Pelican的组合了,参见Blogging with Jupyter and Pelican

  • 存在的问题:刷新麻烦,需要手动加?flush=true
  • 解决方案:UserScript脚本Refresh NBViewer Button。具体请看描述。


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Jupyter Notebook的配置

# 默认目录

jupyter notebook --generate-config
vim /home/zpj/.jupyter/查找dir设定notebook根目录


# 配置pylab, matplotlib默认载入


%matplotlib inline
%config InlineBackend.figure_format = 'svg'

# 配置ipython

# 目的

  • 设置pylab环境自动载入
  • 为notebook设置inline显示,使得图片嵌入在文档中
  • 设置矢量svg格式可以使生成的图像在任何屏幕下获得清晰的显示

# 步骤


ipython profile create


vim ~/.ipython/profile_default/


c.InteractiveShellApp.pylab = "inline"
c.InlineBackend.figure_formats = ['svg']
c.InteractiveShellApp.pylab_import_all = True
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In [2]:
def maxsum(l):
    for i in l:
        s=max(s, 0)
        m=max(m, s)
    return m
In [3]:
def maxprod(l):
    for i in l:
        pos=max(1, pos)*i
        if i<0:
            pos, neg=neg, pos
        m=max(m, pos)
    return m
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Invariance of Euler-Lagrange Equations

E-L is deduced from the Hamilton’s principle

$$\delta S=\delta\int L(\bm q, \dot{\bm q}, t)dt …
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From d’Alembert to Lagrange


Assume \(\bm F\) is active force and \(\bm R\) is constraint force. Then for …

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