| [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 $z_n$, |
#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
| #!/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' |
| 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 + |
| import tensorflow as tf | |
| import numpy as np | |
| import os | |
| import zconfig | |
| import utils | |
| class RBM(object): |
| 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() { | |
| $(this)[0].CodeMirror.addKeyMap(map); |
| import progressbar | |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| import qutip | |
| def average_fidelity(U, V, sample_size): | |
| total = 0 | |
| for idx in range(sample_size): | |
| psi = qutip.rand_ket_haar(8) | |
| total += np.abs((psi.dag() * U.dag() * V * psi)[0, 0])**2 |
| import argparse | |
| import os | |
| import sys | |
| import re | |
| def printBold(msg): | |
| HEADER = '\033[95m' | |
| BOLD = '\033[1m' | |
| print(HEADER + BOLD + msg + '\x1b[0m') |
| #!/bin/sh | |
| arg=${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 |
| (* 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]}; | |