Convert str(array) back to numpy array

Posted on Sun 21 May 2017 in Physics

If we print a numpy array, which actually use str(), we will find it almost irreversible.

In [74]:
print('l is printed as:\n', l)
l is printed as:
 [[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]
 [12 13 14 …

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DMRG Notes

Posted on Tue 16 May 2017 in Physics

The density matrix renormalization group (DMRG) is a numerical variational technique devised to obtain the low energy physics of quantum many-body systems with high accuracy. It was invented in 1992 by Steven R. White and it is nowadays the most efficient method for 1-dimensional systems.

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Reduced density matrix and partial trace

Posted on Wed 03 May 2017 in Physics

The reduced matrix is defined as the partial trace of the density matrix. In linear algebra and functional analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar valued function on operators, the partial trace is an operator-valued function. The partial trace has applications in quantum information and decoherence which is relevant for quantum measurement and thereby to the decoherent approaches to interpretations of quantum mechanics, including consistent histories and the relative state interpretation.

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Transverse Ising Model

Posted on Sat 25 March 2017 in Physics

In [1]:
%matplotlib inline
%config InlineBackend.figure_format = 'svg'
Using matplotlib backend: agg
Populating the interactive namespace from numpy and matplotlib
In [2]:
import scipy.sparse as sp
from scipy.sparse.linalg import eigsh
from functools import reduce
In [3]:
s0=array([[1,0], [0,1]], dtype=int8)
sx=array …

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One way quantum computer

Posted on Sat 18 February 2017 in Physics

The one-way or measurement based quantum computer (MBQC) is a method of quantum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is "one-way" because the resource state is destroyed by the measurements.

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Cluster States

Posted on Wed 01 February 2017 in Physics

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

Posted on Tue 17 January 2017 in Physics

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

Posted on Thu 05 January 2017 in Physics

Fermat’s Principle

Fermat’s Principle is

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

If we choose the path connecting two points to be

$$\bm r=\bm r(t),\quad t_0\leq t\leq t_1$$

We can write

$$s …

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Invariance of Euler-Lagrange Equations

Posted on Sun 30 October 2016 in Physics

E-L is deduced from the Hamilton’s principle

$$\delta S=\delta\int L(\bm q, \dot{\bm q}, t)dt=0$$

It is easy to find that, for \(L'=L+\dd f(\bm q, t)/\dd t\) or change of …

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Jacobi Identity for Classical Possion Bracket

Posted on Sun 30 October 2016 in Physics

Definition of Classical Possion Bracket:

$$[f, g]=\sum_{i=1, 2,\ldots, n}\frac{\pp(f, g)}{\pp(p_i, q_i)}=\sum_{i=1, 2,\ldots, n}\left(\frac{\pp f}{\pp p_i}\frac{\pp g}{\pp q_i}-\frac …

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