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[toc]


Mittag-Leffler expansions
============

Let $f(z)$ be a complex function with an infinite number of *simple* poles $z_n$, and holomorphic at the origin. Suppose also that the poles are ordered in the following way
$$ 0 < | z_1| \leq | z_2 | \le \dots \le | z_n| \le \dots $$
If
1. $\mathcal{C}_n$ is a contour encircling all poles up to $z_n$,

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#Linear Harmonic Oscillator [toc]

Consider the linear oscillator equation $$ \tag{LHO} y'' + \omega^2 y = 0. $$ We want to solve this equation using a series expansion around the origin. ##Frobenius Solution Method Start with the Ansatz $$ y(x) = x^\rho \sum_{n=0}^\infty c_n x^n, $$ where $c_0 \neq 0$ by definition (otherwise we would just rename the coefficients and absorb into $\rho$ the lowest power of $x$). Using this into the original differential equation gives the condition

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base6ToBase10Conversion[n_Integer] := 
 ToExpression[StringJoin["6^^", ToString@n]]

labelToIndex[label_String] := With[{
   elementsConversionRules = {"H" -> 0, "V" -> 1, "D" -> 2, "A" -> 3, 
     "L" -> 4, "R" -> 5}
   },
  If[
   StringLength@label == 4,
   -(1 +

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#!/usr/bin/python3
import struct
import os
import time

start_time = time.time()
# ============ CONSTANTS TO (OPTIONALLY) SET =============
WINDOW_SIZE = 100
INPUT_FILE_NAME = 'data_lab\\timetags5byte.bin'
# OUTPUT_FILE_NAME = 'output.txt'

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import tensorflow as tf
import numpy as np
import os

import zconfig
import utils


class RBM(object):

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var script = document.createElement('script');
script.src = "https://ajax.googleapis.com/ajax/libs/jquery/2.2.0/jquery.min.js";
document.getElementsByTagName('head')[0].appendChild(script);
map = {'Cmd-I': function(cm) {
        var s = cm.getSelection(),
            t = s.slice(0, 1) === '*' && s.slice(-1) === '*';
        cm.replaceSelection(t ? s.slice(1, -1) : '*' + s + '*', 'around');
    }};
$('.CodeMirror').each(function() {
    $(this)[0].CodeMirror.addKeyMap(map);

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import progressbar
import numpy as np
import matplotlib.pyplot as plt
import qutip

def average_fidelity(U, V, sample_size):
    total = 0
    for idx in range(sample_size):
        psi = qutip.rand_ket_haar(8)
        total += np.abs((psi.dag() * U.dag() * V * psi)[0, 0])**2

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#!/bin/sh

arg=${1:-.}
exts="aux bbl blg brf idx ilg ind lof log lol lot out toc synctex.gz fls fdb_latexmk run.xml bcf"

if [ -d $arg ]; then
    for ext in $exts; do
         rm -f $arg/*.$ext
    done
    rm -f $arg/*Notes.bib

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(* Create the expressions that must be satisfied by the d_s coefficients to generate a specific target
   state after the coin is projected onto the + state. *)
generateConditionsForDs[n_, s_] := Sum[
    Conjugate[u[i] - d[i]] (u[i + n - s] - d[i + n - s]) + Conjugate[d[i + 1]] d[i + n - s + 1],
    {i, 1, s}
] /. {d[1] -> 0, d[n + 1] -> u[n + 1]};

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displacedFockProbs[n_, mu_, k_] := Times[
    k! / n! * mu^(k - n),
    Exp[-mu],
    Sum[Binomial[n, j] (-mu)^j / (k - n + j)!, {j, n - k, n}]^2
];