From 43bce52457868041532988b26cbc1c0a69fc1183 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Daniel=20Kn=C3=BCttel?= Date: Fri, 22 Nov 2019 17:25:05 +0100 Subject: [PATCH] removed unnecessary notebookks --- computations/compute_lc_elements.ipynb | 406 ---- .../local_clifford_group_elements_raw.ipynb | 1807 ----------------- computations/stuff_with_sqrtiZ.ipynb | 599 ------ 3 files changed, 2812 deletions(-) delete mode 100644 computations/compute_lc_elements.ipynb delete mode 100644 computations/local_clifford_group_elements_raw.ipynb delete mode 100644 computations/stuff_with_sqrtiZ.ipynb diff --git a/computations/compute_lc_elements.ipynb b/computations/compute_lc_elements.ipynb deleted file mode 100644 index 2b6b6aa..0000000 --- a/computations/compute_lc_elements.ipynb +++ /dev/null @@ -1,406 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Computing the elements of the local clifford group" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "from itertools import product\n", - "import sympy\n", - "i = sympy.I\n", - "exp = sympy.exp\n", - "M = sympy.Matrix\n", - "simplify = sympy.simplify\n", - "from sympy.physics.quantum.dagger import Dagger\n", - "\n", - "sympy.init_printing()" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "I = M([[1, 0], [0, 1]])\n", - "X = M([[0, 1], [1, 0]])\n", - "Y = M([[0, -i], [i, 0]])\n", - "Z = M([[1, 0], [0, -1]])\n", - "O = M([[0, 0], [0, 0]])" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "H = M([[1, 1], [1, -1]]) / sympy.sqrt(2)\n", - "S = M([[1, 0], [0, i]])\n" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "C = [H, S]" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "def is_math_the_same(v):\n", - " return simplify(v[0] - v[1]) == O\n" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "from multiprocessing import Pool, cpu_count\n", - "\n", - "pool = Pool(cpu_count())" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "found Matrix([[1, 0], [0, 1]])\n", - "found Matrix([[sqrt(2)/2, sqrt(2)/2], [sqrt(2)*I/2, -sqrt(2)*I/2]])\n", - "found Matrix([[sqrt(2)/2, sqrt(2)*I/2], [sqrt(2)/2, -sqrt(2)*I/2]])\n", - "found Matrix([[1, 0], [0, -1]])\n", - "found Matrix([[1/2 + I/2, 1/2 - I/2], [1/2 - I/2, 1/2 + I/2]])\n", - "found Matrix([[sqrt(2)/2, sqrt(2)/2], [-sqrt(2)/2, sqrt(2)/2]])\n", - "found Matrix([[sqrt(2)/2, sqrt(2)*I/2], [sqrt(2)*I/2, sqrt(2)/2]])\n", - "found Matrix([[sqrt(2)/2, -sqrt(2)/2], [sqrt(2)/2, sqrt(2)/2]])\n", - "found Matrix([[1, 0], [0, -I]])\n", - "found Matrix([[1/2 + I/2, 1/2 - I/2], [1/2 + I/2, -1/2 + I/2]])\n", - "found Matrix([[0, 1], [1, 0]])\n", - "found Matrix([[sqrt(2)/2, sqrt(2)/2], [-sqrt(2)*I/2, sqrt(2)*I/2]])\n", - "found Matrix([[1/2 + I/2, 1/2 + I/2], [1/2 - I/2, -1/2 + I/2]])\n", - "found Matrix([[sqrt(2)/2, sqrt(2)*I/2], [-sqrt(2)/2, sqrt(2)*I/2]])\n", - "found Matrix([[sqrt(2)/2, -sqrt(2)/2], [sqrt(2)*I/2, sqrt(2)*I/2]])\n", - "found Matrix([[sqrt(2)/2, -sqrt(2)*I/2], [sqrt(2)/2, sqrt(2)*I/2]])\n", - "found Matrix([[sqrt(2)*(1 + I)/2, 0], [0, sqrt(2)*(1 - I)/2]])\n", - "found Matrix([[1/2 + I/2, 1/2 - I/2], [-1/2 + I/2, -1/2 - I/2]])\n", - "found Matrix([[0, 1], [I, 0]])\n", - "found Matrix([[1/2 - I/2, 1/2 + I/2], [1/2 + I/2, 1/2 - I/2]])\n", - "found Matrix([[1/2 + I/2, 1/2 + I/2], [1/2 + I/2, I*(-1 + I)/2]])\n", - "found Matrix([[0, I], [1, 0]])\n", - "found Matrix([[sqrt(2)/2, sqrt(2)*I/2], [-sqrt(2)*I/2, -sqrt(2)/2]])\n", - "found Matrix([[1/2 + I/2, -1/2 + I/2], [1/2 - I/2, I*(-1 + I)/2]])\n", - "found Matrix([[sqrt(2)/2, -sqrt(2)/2], [-sqrt(2)/2, -sqrt(2)/2]])\n", - "found Matrix([[sqrt(2)/2, -sqrt(2)*I/2], [sqrt(2)*I/2, -sqrt(2)/2]])\n" - ] - } - ], - "source": [ - "\n", - "#def list_contains_matrix(l, m):\n", - "# for elem in l:\n", - "# test = simplify(elem - m)\n", - "# if(test == 0):\n", - "# return True\n", - "# return False\n", - "\n", - "def list_contains_matrix(l, m):\n", - " #print(l, m)\n", - " for test in pool.map(is_math_the_same, [(e,m) for e in l]):\n", - " if(test):\n", - " return True\n", - "\n", - "\n", - "#for i in range(10):\n", - "while(len(C) < 24):\n", - " new_ops = ([c * H for c in C]\n", - " + [c * S for c in C])\n", - " for new_op in new_ops:\n", - " new_op.simplify()\n", - " #if(new_op not in C): # and Dagger(new_op) not in C):\n", - " if(not list_contains_matrix(C, new_op)):\n", - " print(\"found\", new_op)\n", - " C.append(new_op)\n", - " #else:\n", - " #print(new_op, \"is already known\")\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "for c in C:\n", - " c.simplify()\n", - "#C = [c for c in C if Dagger(c) not in C]" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/latex": [ - "$\\displaystyle \\left[ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & i\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\\\frac{1}{2} - \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & - i\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\\\frac{1}{2} + \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\\\\\frac{1}{2} - \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\- \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2} \\left(1 + i\\right)}{2} & 0\\\\0 & \\frac{\\sqrt{2} \\left(1 - i\\right)}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & - \\frac{1}{2} - \\frac{i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}0 & 1\\\\i & 0\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} - \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\\\\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\\\\\frac{1}{2} + \\frac{i}{2} & \\frac{i \\left(-1 + i\\right)}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}0 & i\\\\1 & 0\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\- \\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\\\\\frac{1}{2} - \\frac{i}{2} & \\frac{i \\left(-1 + i\\right)}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]\\right]$" - ], - "text/plain": [ - "⎡⎡√2 √2 ⎤ ⎡ √2 √2 ⎤ ⎡√2 √2⋅ⅈ ⎤ ⎡1 ⅈ 1 \n", - "⎢⎢── ── ⎥ ⎢ ── ── ⎥ ⎢── ──── ⎥ ⎢─ + ─ ─ \n", - "⎢⎢2 2 ⎥ ⎡1 0⎤ ⎡1 0⎤ ⎢ 2 2 ⎥ ⎢2 2 ⎥ ⎡1 0 ⎤ ⎢2 2 2 \n", - "⎢⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ \n", - "⎢⎢√2 -√2 ⎥ ⎣0 ⅈ⎦ ⎣0 1⎦ ⎢√2⋅ⅈ -√2⋅ⅈ ⎥ ⎢√2 -√2⋅ⅈ ⎥ ⎣0 -1⎦ ⎢1 ⅈ 1 \n", - "⎢⎢── ────⎥ ⎢──── ──────⎥ ⎢── ──────⎥ ⎢─ - ─ ─ \n", - "⎣⎣2 2 ⎦ ⎣ 2 2 ⎦ ⎣2 2 ⎦ ⎣2 2 2 \n", - "\n", - " ⅈ⎤ ⎡ √2 √2⎤ ⎡ √2 √2⋅ⅈ⎤ ⎡√2 -√2 ⎤ ⎡1 ⅈ 1 ⅈ ⎤ \n", - "- ─⎥ ⎢ ── ──⎥ ⎢ ── ────⎥ ⎢── ────⎥ ⎢─ + ─ ─ - ─ ⎥ \n", - " 2⎥ ⎢ 2 2 ⎥ ⎢ 2 2 ⎥ ⎢2 2 ⎥ ⎡1 0 ⎤ ⎢2 2 2 2 ⎥ ⎡0 1⎤ \n", - " ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥,\n", - " ⅈ⎥ ⎢-√2 √2⎥ ⎢√2⋅ⅈ √2 ⎥ ⎢√2 √2 ⎥ ⎣0 -ⅈ⎦ ⎢1 ⅈ 1 ⅈ⎥ ⎣1 0⎦ \n", - "+ ─⎥ ⎢──── ──⎥ ⎢──── ── ⎥ ⎢── ── ⎥ ⎢─ + ─ - ─ + ─⎥ \n", - " 2⎦ ⎣ 2 2 ⎦ ⎣ 2 2 ⎦ ⎣2 2 ⎦ ⎣2 2 2 2⎦ \n", - "\n", - " ⎡ √2 √2 ⎤ ⎡1 ⅈ 1 ⅈ ⎤ ⎡ √2 √2⋅ⅈ⎤ ⎡ √2 -√2 ⎤ ⎡√2 -√2⋅ⅈ ⎤ ⎡\n", - " ⎢ ── ── ⎥ ⎢─ + ─ ─ + ─ ⎥ ⎢ ── ────⎥ ⎢ ── ────⎥ ⎢── ──────⎥ ⎢\n", - " ⎢ 2 2 ⎥ ⎢2 2 2 2 ⎥ ⎢ 2 2 ⎥ ⎢ 2 2 ⎥ ⎢2 2 ⎥ ⎢\n", - " ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢\n", - " ⎢-√2⋅ⅈ √2⋅ⅈ⎥ ⎢1 ⅈ 1 ⅈ⎥ ⎢-√2 √2⋅ⅈ⎥ ⎢√2⋅ⅈ √2⋅ⅈ⎥ ⎢√2 √2⋅ⅈ ⎥ ⎢\n", - " ⎢────── ────⎥ ⎢─ - ─ - ─ + ─⎥ ⎢──── ────⎥ ⎢──── ────⎥ ⎢── ──── ⎥ ⎢\n", - " ⎣ 2 2 ⎦ ⎣2 2 2 2⎦ ⎣ 2 2 ⎦ ⎣ 2 2 ⎦ ⎣2 2 ⎦ ⎣\n", - "\n", - "√2⋅(1 + ⅈ) ⎤ ⎡ 1 ⅈ 1 ⅈ ⎤ ⎡1 ⅈ 1 ⅈ⎤ ⎡1 ⅈ \n", - "────────── 0 ⎥ ⎢ ─ + ─ ─ - ─ ⎥ ⎢─ - ─ ─ + ─⎥ ⎢─ + ─ \n", - " 2 ⎥ ⎢ 2 2 2 2 ⎥ ⎡0 1⎤ ⎢2 2 2 2⎥ ⎢2 2 \n", - " ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ \n", - " √2⋅(1 - ⅈ)⎥ ⎢ 1 ⅈ 1 ⅈ⎥ ⎣ⅈ 0⎦ ⎢1 ⅈ 1 ⅈ⎥ ⎢1 ⅈ ⅈ\n", - " 0 ──────────⎥ ⎢- ─ + ─ - ─ - ─⎥ ⎢─ + ─ ─ - ─⎥ ⎢─ + ─ ─\n", - " 2 ⎦ ⎣ 2 2 2 2⎦ ⎣2 2 2 2⎦ ⎣2 2 \n", - "\n", - " 1 ⅈ ⎤ ⎡ √2 √2⋅ⅈ⎤ ⎡1 ⅈ 1 ⅈ ⎤ ⎡ √2 -√2 ⎤ ⎡ √2 \n", - " ─ + ─ ⎥ ⎢ ── ────⎥ ⎢─ + ─ - ─ + ─ ⎥ ⎢ ── ────⎥ ⎢ ── \n", - " 2 2 ⎥ ⎡0 ⅈ⎤ ⎢ 2 2 ⎥ ⎢2 2 2 2 ⎥ ⎢ 2 2 ⎥ ⎢ 2 \n", - " ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ \n", - "⋅(-1 + ⅈ)⎥ ⎣1 0⎦ ⎢-√2⋅ⅈ -√2 ⎥ ⎢1 ⅈ ⅈ⋅(-1 + ⅈ)⎥ ⎢-√2 -√2 ⎥ ⎢√2⋅ⅈ \n", - "─────────⎥ ⎢────── ────⎥ ⎢─ - ─ ──────────⎥ ⎢──── ────⎥ ⎢──── \n", - " 2 ⎦ ⎣ 2 2 ⎦ ⎣2 2 2 ⎦ ⎣ 2 2 ⎦ ⎣ 2 \n", - "\n", - "-√2⋅ⅈ ⎤⎤\n", - "──────⎥⎥\n", - " 2 ⎥⎥\n", - " ⎥⎥\n", - " -√2 ⎥⎥\n", - " ──── ⎥⎥\n", - " 2 ⎦⎦" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "\n", - "C" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAAOCAYAAADNGCeJAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABZklEQVQ4EXWTgVHDMAxFHY4BcmWDdoMCE5ARwgqwAT1GgA06Q9mgXaHdgG5A0w3Ce8HKNSTV3Y+tL/lbke2ibdtUFMU8pbQC2gM4gRWxg0QYeSXzd/AD7oD+hrwdY2cKSaQA/gdoQRWcI7a+9DO3ga/zPOmUE0kNfBM88xcRfoyuBXv9GyYVaPIvMO3N0svcAskFeHZyzRRz0RHl85Ukd9a2oEJ8+29jW7I2oe9TlB0joe+/8KCXtsTmiTegSNcv102KkbAE3YIQjxE+Dsf4Hsz7WEwuRxKsaurkanjFvAH+toKiO/VRZQQsfUrI0xzw+Ior5smXAzGI0YKoOBaEHyO8VSpY3/LpjBNylwVJr5mKl6Hri/Aujk4c7sjaL+Izr4aLbPgjgXhS0pobnLLImTyrmDKvz67gE83s31fOnjEuEfKyuqGX2+Y/ZXFpeVtj1Z+KebxWNmUHku4jkP/Ah+5vh/UP/Rd43VK9lG9blAAAAABJRU5ErkJggg==\n", - "text/latex": [ - "$\\displaystyle 28$" - ], - "text/plain": [ - "28" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(C)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is bad. Does one have to ignore global phases? Note that the matrices 10 and 18 are the same, disregarding a phase of $pi/4$:" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & - i\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡1 0 ⎤\n", - "⎢ ⎥\n", - "⎣0 -ⅈ⎦" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "C[10]" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2} \\left(1 + i\\right)}{2} & 0\\\\0 & \\frac{\\sqrt{2} \\left(1 - i\\right)}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡√2⋅(1 + ⅈ) ⎤\n", - "⎢────────── 0 ⎥\n", - "⎢ 2 ⎥\n", - "⎢ ⎥\n", - "⎢ √2⋅(1 - ⅈ)⎥\n", - "⎢ 0 ──────────⎥\n", - "⎣ 2 ⎦" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "C[18]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "XXX: continue here with computations" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "lookup_table = [ca * cb for ca, cb in product(C, C)]\n", - "for l in lookup_table:\n", - " l.simplify()" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "False" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(lookup_table) == 24*24" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [], - "source": [ - "ltb = []\n", - "row = []\n", - "for i, result in enumerate(lookup_table):\n", - " if(i % 24):\n", - " ltb.append(row)\n", - " row = []\n", - " row.append(result)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [], - "source": [ - "#lookup_table = [[C.index(i) for i in row] for row in ltb]\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/computations/local_clifford_group_elements_raw.ipynb b/computations/local_clifford_group_elements_raw.ipynb deleted file mode 100644 index 9c9a976..0000000 --- a/computations/local_clifford_group_elements_raw.ipynb +++ /dev/null @@ -1,1807 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Computing the Elements of the Local Clifford Group\n", - "\n", - "From Anders&Briegel 2005 it is known, that the Local Clifford Group (LC) has 24 elements.\n", - "Also one can disregrad a global phase. Below are the computed elements." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from itertools import product\n", - "from functools import reduce\n", - "from operator import iconcat\n", - "import sympy\n", - "i = sympy.I\n", - "exp = sympy.exp\n", - "M = sympy.Matrix\n", - "simplify = sympy.simplify\n", - "from sympy.physics.quantum.dagger import Dagger\n", - "\n", - "sympy.init_printing()" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "I = M([[1, 0], [0, 1]])\n", - "X = M([[0, 1], [1, 0]])\n", - "Y = M([[0, -i], [i, 0]])\n", - "Z = M([[1, 0], [0, -1]])\n", - "O = M([[0, 0], [0, 0]])" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "H = M([[1, 1], [1, -1]]) / sympy.sqrt(2)\n", - "S = M([[1, 0], [0, i]])\n" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡√2 √2 ⎤\n", - "⎢── ── ⎥\n", - "⎢2 2 ⎥\n", - "⎢ ⎥\n", - "⎢√2 -√2 ⎥\n", - "⎢── ────⎥\n", - "⎣2 2 ⎦" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "H" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & i\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡1 0⎤\n", - "⎢ ⎥\n", - "⎣0 ⅈ⎦" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "S" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "s2m = {\"H\": H, \"S\": S}" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "def evalstr(s):\n", - " m = I\n", - " \n", - " for c in s:\n", - " m *= s2m[c]\n", - " \n", - " m.simplify()\n", - " \n", - " return m" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡√2 √2⋅ⅈ ⎤\n", - "⎢── ──── ⎥\n", - "⎢2 2 ⎥\n", - "⎢ ⎥\n", - "⎢√2 -√2⋅ⅈ ⎥\n", - "⎢── ──────⎥\n", - "⎣2 2 ⎦" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"HS\")" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ √2 √2 ⎤\n", - "⎢ ── ── ⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢√2⋅ⅈ -√2⋅ⅈ ⎥\n", - "⎢──── ──────⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SH\")" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡√2 -√2 ⎤\n", - "⎢── ────⎥\n", - "⎢2 2 ⎥\n", - "⎢ ⎥\n", - "⎢√2 √2 ⎥\n", - "⎢── ── ⎥\n", - "⎣2 2 ⎦" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"HSS\")" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ √2 √2⎤\n", - "⎢ ── ──⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢-√2 √2⎥\n", - "⎢──── ──⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SSH\")" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & - i\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡1 0 ⎤\n", - "⎢ ⎥\n", - "⎣0 -ⅈ⎦" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SSS\")" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡√2 -√2⋅ⅈ ⎤\n", - "⎢── ──────⎥\n", - "⎢2 2 ⎥\n", - "⎢ ⎥\n", - "⎢√2 √2⋅ⅈ ⎥\n", - "⎢── ──── ⎥\n", - "⎣2 2 ⎦" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"HSSS\")" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ √2 √2 ⎤\n", - "⎢ ── ── ⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢-√2⋅ⅈ √2⋅ⅈ⎥\n", - "⎢────── ────⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SSSH\")" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ √2 √2⋅ⅈ⎤\n", - "⎢ ── ────⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢√2⋅ⅈ √2 ⎥\n", - "⎢──── ── ⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SHS\")" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ √2 -√2 ⎤\n", - "⎢ ── ────⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢√2⋅ⅈ √2⋅ⅈ⎥\n", - "⎢──── ────⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SHSS\")" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\- \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ √2 √2⋅ⅈ⎤\n", - "⎢ ── ────⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢-√2 √2⋅ⅈ⎥\n", - "⎢──── ────⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SSHS\")" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ √2 -√2 ⎤\n", - "⎢ ── ────⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢-√2 -√2 ⎥\n", - "⎢──── ────⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SSHSS\")" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\- \\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ √2 -√2⋅ⅈ ⎤\n", - "⎢ ── ──────⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢-√2 -√2⋅ⅈ ⎥\n", - "⎢──── ──────⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SSHSSS\")" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\\\frac{1}{2} - \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡1 ⅈ 1 ⅈ⎤\n", - "⎢─ + ─ ─ - ─⎥\n", - "⎢2 2 2 2⎥\n", - "⎢ ⎥\n", - "⎢1 ⅈ 1 ⅈ⎥\n", - "⎢─ - ─ ─ + ─⎥\n", - "⎣2 2 2 2⎦" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"HSH\") # = exp(i*pi/4) SSSHSSS" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡0 1⎤\n", - "⎢ ⎥\n", - "⎣1 0⎦" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"HSSH\")" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}0 & 1\\\\i & 0\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡0 1⎤\n", - "⎢ ⎥\n", - "⎣ⅈ 0⎦" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SHSSH\")" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}0 & i\\\\1 & 0\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡0 ⅈ⎤\n", - "⎢ ⎥\n", - "⎣1 0⎦" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"HSSHS\")" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}0 & i\\\\i & 0\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡0 ⅈ⎤\n", - "⎢ ⎥\n", - "⎣ⅈ 0⎦" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SHSSHS\") # = exp(i*pi/2) HSSH" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡√2⋅ⅈ -√2⋅ⅈ ⎤\n", - "⎢──── ──────⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢ √2 √2 ⎥\n", - "⎢ ── ── ⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"HSSHSH\")" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ √2⋅ⅈ √2⎤\n", - "⎢ ──── ──⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢-√2⋅ⅈ √2⎥\n", - "⎢────── ──⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"HSHSSH\") # = exp(-i*pi/2) SSHSSS" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGQAAAA/CAYAAAAWq21gAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAGeklEQVR4Ae2bi3HcNhCG7zQuwLkS5A7spINzB1IJsjtwxhVknA6cFlSCU4KVDuwOYquDy/czAIYEXwAJgOQNMQMRz8X+u1iA3FsdD4fDmfyF7Kfvl8vlld+41+dL4Hg8PkHldQel+xe1xre1soo/vPpeTSeBB0idPHKVUTiFYA1/ewNmV9kJlzEirHscG7PWfvA9wtvdGH8+Rur/+HOg9ay2G78jVZ0F3kHrvZgZyqnWK03H4PsyhM32xfDmLCRmUuDYexjyj8HBqYB8yYAT874PDlxHZzS+ELazKATBfmDxz2LACPmjYebWPB8QemWipm4fGvcv+U/bsMZnHZ/4i8Q4CunMCORz0Z8kGXoy5YoW5c+2rKfq5G/1tq2V4d/hs5jqGKZgZM5PcnUfJVUIRGUdd5ZBytLCuVaXlajttW3b0hO+G/jEu8EzCyM0KoUkPbKM6b6Fyfrd8Z7FvorrvsQ8bQq9l//G3Pu+cUu39+ATW6MYY3iPshAIa4e/69rVtH8iu50yMKZxZJl5utC13V52zSvVxvqz8IlPkuTQwDjGP+PjjywmSXlarCU42iTQxtnqM0G/rOCbxto+yhKA5ur8jAJhaaR6sv4sfOKD1MIYwh/z4hViCTNZn/6fbN0wosu6916gT4LX16hThjdffR/qbUuV4SMan5HBIMYhPKw5SyHazc5KKA9aB/1i9NEyRFm76LZWd8eV+mz7Uk94iMInPoWH3ItxDAtzpyvEMKCjp7ISnr3WQZ/dNVKCzRrvLIWyBPBk6DYsbwxIrn74CcJneB7FOMYn681WiIQoIhKy2xn+wmaMtlAj18fRJwuRX0ivlM5y6mNKl+EjCJ/4IkkODXyqx/BsaNzJsaeLrPLJ8IxKvAZqF53Ib1h8C+6O1eJDllLqw4soDtuDf6dJ3x1XpwwDtTi+WRbS1s/eMlUC0RbChOqwnLpg7DysrujvJLnwxeIIPrJiCccqYOnxa8F3s7Qg9vWbEgi2kOa0/hqmr1fYj2aE3s+V+n7/+L93A39L4UquEGSrDzt5P6sEEH0EyhWx9QiWYrjOCAsZJvtxSpe/8/hSlpWobXGXyByMBkM2XNCvvtRz3CFJfxuA0bWkIriSH1nswr88CQqIgu5aoS/euFVXS+HKYSFOsNwf8nPJJ/TGNV5BISeubAqBad0d+jFLfq7nK9BDBSE3ruRHlri2TKOI6rd1s6OeqW/a51UCV3ILMUzrVfcPKcIoQ/fIpmOFS+FK7lyEcb2+6eOwkbCOor6pxuIJKrlxGfqz3e8tqAj+l1bjFTSUwpX8yOqTPTvgMpb75q6pHQyPYzjUP5XnIgqBwauIhDc4ql9XdQQP5akKyfKW1cFMlkjxjnVyN0XjQIm6T08oL+gNM7tCYGhqJHxu4UbRr+PQRCPoEK+2xkRF9J+ZgALTOBd9OtB20YyUNxsJX8chjKmxQK9yLopwNoVAuxEpTn2TnmAfh1FIUiysUSkk25FlTDo6Eh7GVpV6cIjHQe8v87TR5cuLjuifbCEsJn9V0kh4/8grUZ+Lw1hMI+IdmqrrQpcluSjNPjyMmXdkQUCKTBoJ38dszva5OIwyZAkuqp+yNqqUIU93UEQ/4+YpxAoJQtGR4swRw72R8JZ2yecUHEYZvVgMxqCIfsYmU4h2gTNLytoZ7s3KFyp9AuBigSlrdy0ezwsPUThqyujEAj13XAmjLwe/zpg0CjGMBUWKs6jdTVKCzfIMj56xPoAcdfgIwmEwD2KBlhQcHNHP2KQK0eIiKCG7HeMLzYyRNTWyP26pOnwF4TAKEd4GDtUt75RlIcER/YytFJLM/c5r3lVEwi+Fg3WlkKTu9+KR4gDIkRbFMenDEG3KVDsTffLsTkqYe9EfsXLh6AMfgm+SQkII9zG1pvY14rhZk4B2Xg6HSRYyJDiOAb1dhLilh8isrq8UruQKQZLFgpILa60YrjPAOE7T/B4iWuRsQcmp+IylkxsX9KvvkBx3yKBbmoW3morgSn5ksfP2YOsZWy6HhTh2uAjlSpE7Yg+2dlIZLmRTCMq4Zek92HpY/q3e5EeWVrDK4Pjag61bIh9uSG4hRhlyqe/B1sOy7+xN5u211FGIXt/0cdhIWEtRP1Vj8QSV3LgM/aTe3go2gt+DrWdsAHdkoSE/GFq/b+wpgwSQ9ZMvb5apThUdIyr82rHuD3b7pv9RswPTKppQhj4HTh3MfP0PQGFN59x03VEAAAAASUVORK5CYII=\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡√2⋅ⅈ √2 ⎤\n", - "⎢──── ── ⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢ √2 √2⋅ⅈ⎥\n", - "⎢ ── ────⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"HSSHSHS\") # = exp(-i*pi/2) SSSHSSS" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\\\frac{1}{2} + \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡1 ⅈ 1 ⅈ ⎤\n", - "⎢─ + ─ ─ - ─ ⎥\n", - "⎢2 2 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢1 ⅈ 1 ⅈ⎥\n", - "⎢─ + ─ - ─ + ─⎥\n", - "⎣2 2 2 2⎦" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SHSH\")" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\\\\\frac{1}{2} + \\frac{i}{2} & \\frac{i \\left(-1 + i\\right)}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡1 ⅈ 1 ⅈ ⎤\n", - "⎢─ + ─ ─ + ─ ⎥\n", - "⎢2 2 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢1 ⅈ ⅈ⋅(-1 + ⅈ)⎥\n", - "⎢─ + ─ ──────────⎥\n", - "⎣2 2 2 ⎦" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SHSHS\")" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\\\\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡1 ⅈ 1 ⅈ⎤\n", - "⎢─ + ─ - ─ + ─⎥\n", - "⎢2 2 2 2⎥\n", - "⎢ ⎥\n", - "⎢1 ⅈ 1 ⅈ ⎥\n", - "⎢─ + ─ ─ - ─ ⎥\n", - "⎣2 2 2 2 ⎦" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SHSHSS\") # = SHSH" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & - \\frac{1}{2} - \\frac{i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ 1 ⅈ 1 ⅈ ⎤\n", - "⎢ ─ + ─ ─ - ─ ⎥\n", - "⎢ 2 2 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢ 1 ⅈ 1 ⅈ⎥\n", - "⎢- ─ + ─ - ─ - ─⎥\n", - "⎣ 2 2 2 2⎦" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"SSHSH\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Using the string representation:" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [], - "source": [ - "LC = [\"H\", \"S\", \"SS\", \"HH\", \"HS\", \"SH\", \"HSS\", \"SSH\", \"SSS\", \"HSSS\", \"SSSH\",\n", - " \"SHS\", \"SHSS\", \"SSHS\", \"SSHSS\", \"SSHSSS\", \"HSH\", \"HSSH\", \"SHSSH\",\n", - " \"HSSHS\", \"HSSHSH\", \"SHSH\", \"SHSHS\", \"SSHSH\"]" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle 24$" - ], - "text/plain": [ - "24" - ] - }, - "execution_count": 33, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(LC)" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/latex": [ - "$\\displaystyle \\left[ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & i\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & - i\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\- \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\- \\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\\\frac{1}{2} - \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right], \\ \\left[\\begin{matrix}0 & 1\\\\i & 0\\end{matrix}\\right], \\ \\left[\\begin{matrix}0 & i\\\\1 & 0\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\\\frac{1}{2} + \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\\\\\frac{1}{2} + \\frac{i}{2} & \\frac{i \\left(-1 + i\\right)}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & - \\frac{1}{2} - \\frac{i}{2}\\end{matrix}\\right]\\right]$" - ], - "text/plain": [ - "⎡⎡√2 √2 ⎤ ⎡√2 √2⋅ⅈ ⎤ ⎡ √2 √2 ⎤ ⎡√2 -√2 ⎤\n", - "⎢⎢── ── ⎥ ⎢── ──── ⎥ ⎢ ── ── ⎥ ⎢── ────⎥\n", - "⎢⎢2 2 ⎥ ⎡1 0⎤ ⎡1 0 ⎤ ⎡1 0⎤ ⎢2 2 ⎥ ⎢ 2 2 ⎥ ⎢2 2 ⎥\n", - "⎢⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥\n", - "⎢⎢√2 -√2 ⎥ ⎣0 ⅈ⎦ ⎣0 -1⎦ ⎣0 1⎦ ⎢√2 -√2⋅ⅈ ⎥ ⎢√2⋅ⅈ -√2⋅ⅈ ⎥ ⎢√2 √2 ⎥\n", - "⎢⎢── ────⎥ ⎢── ──────⎥ ⎢──── ──────⎥ ⎢── ── ⎥\n", - "⎣⎣2 2 ⎦ ⎣2 2 ⎦ ⎣ 2 2 ⎦ ⎣2 2 ⎦\n", - "\n", - " ⎡ √2 √2⎤ ⎡√2 -√2⋅ⅈ ⎤ ⎡ √2 √2 ⎤ ⎡ √2 √2⋅ⅈ⎤ ⎡ √2 -√2 \n", - " ⎢ ── ──⎥ ⎢── ──────⎥ ⎢ ── ── ⎥ ⎢ ── ────⎥ ⎢ ── ────\n", - " ⎢ 2 2 ⎥ ⎡1 0 ⎤ ⎢2 2 ⎥ ⎢ 2 2 ⎥ ⎢ 2 2 ⎥ ⎢ 2 2 \n", - ", ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ \n", - " ⎢-√2 √2⎥ ⎣0 -ⅈ⎦ ⎢√2 √2⋅ⅈ ⎥ ⎢-√2⋅ⅈ √2⋅ⅈ⎥ ⎢√2⋅ⅈ √2 ⎥ ⎢√2⋅ⅈ √2⋅ⅈ\n", - " ⎢──── ──⎥ ⎢── ──── ⎥ ⎢────── ────⎥ ⎢──── ── ⎥ ⎢──── ────\n", - " ⎣ 2 2 ⎦ ⎣2 2 ⎦ ⎣ 2 2 ⎦ ⎣ 2 2 ⎦ ⎣ 2 2 \n", - "\n", - "⎤ ⎡ √2 √2⋅ⅈ⎤ ⎡ √2 -√2 ⎤ ⎡ √2 -√2⋅ⅈ ⎤ ⎡1 ⅈ 1 ⅈ⎤ \n", - "⎥ ⎢ ── ────⎥ ⎢ ── ────⎥ ⎢ ── ──────⎥ ⎢─ + ─ ─ - ─⎥ \n", - "⎥ ⎢ 2 2 ⎥ ⎢ 2 2 ⎥ ⎢ 2 2 ⎥ ⎢2 2 2 2⎥ ⎡0 1⎤ ⎡0 1⎤ \n", - "⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥,\n", - "⎥ ⎢-√2 √2⋅ⅈ⎥ ⎢-√2 -√2 ⎥ ⎢-√2 -√2⋅ⅈ ⎥ ⎢1 ⅈ 1 ⅈ⎥ ⎣1 0⎦ ⎣ⅈ 0⎦ \n", - "⎥ ⎢──── ────⎥ ⎢──── ────⎥ ⎢──── ──────⎥ ⎢─ - ─ ─ + ─⎥ \n", - "⎦ ⎣ 2 2 ⎦ ⎣ 2 2 ⎦ ⎣ 2 2 ⎦ ⎣2 2 2 2⎦ \n", - "\n", - " ⎡√2⋅ⅈ -√2⋅ⅈ ⎤ ⎡1 ⅈ 1 ⅈ ⎤ ⎡1 ⅈ 1 ⅈ ⎤ ⎡ 1 ⅈ 1 \n", - " ⎢──── ──────⎥ ⎢─ + ─ ─ - ─ ⎥ ⎢─ + ─ ─ + ─ ⎥ ⎢ ─ + ─ ─ -\n", - " ⎡0 ⅈ⎤ ⎢ 2 2 ⎥ ⎢2 2 2 2 ⎥ ⎢2 2 2 2 ⎥ ⎢ 2 2 2 \n", - " ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ \n", - " ⎣1 0⎦ ⎢ √2 √2 ⎥ ⎢1 ⅈ 1 ⅈ⎥ ⎢1 ⅈ ⅈ⋅(-1 + ⅈ)⎥ ⎢ 1 ⅈ 1 \n", - " ⎢ ── ── ⎥ ⎢─ + ─ - ─ + ─⎥ ⎢─ + ─ ──────────⎥ ⎢- ─ + ─ - ─ \n", - " ⎣ 2 2 ⎦ ⎣2 2 2 2⎦ ⎣2 2 2 ⎦ ⎣ 2 2 2 \n", - "\n", - " ⅈ ⎤⎤\n", - " ─ ⎥⎥\n", - " 2 ⎥⎥\n", - " ⎥⎥\n", - " ⅈ⎥⎥\n", - "- ─⎥⎥\n", - " 2⎦⎦" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "[simplify(evalstr(c)) for c in LC]" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}0 & i\\\\1 & 0\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡0 ⅈ⎤\n", - "⎢ ⎥\n", - "⎣1 0⎦" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "[simplify(evalstr(c)) for c in LC][19]" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [], - "source": [ - "product_table = []\n", - "row = []\n", - "\n", - "for i,p in enumerate(product(LC, LC)):\n", - " if(i % 24 == 0):\n", - " product_table.append(row)\n", - " row = []\n", - " row.append(p[0] + p[1])\n", - " \n", - "product_table = product_table[1:]" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": {}, - "outputs": [], - "source": [ - "def simplify_str(s):\n", - " # Start with removing obvious identities.\n", - " s = s.replace(\"HH\", \"\").replace(\"SSSS\", \"\").replace(\"HH\", \"\")\n", - " # We precomputed some other stuff. Use that now:\n", - " s = s.replace(\"SSSHSSS\", \"HSH\")\n", - " s = s.replace(\"SHSSHS\", \"HSSH\")\n", - " s = s.replace(\"HSSHSHS\", \"HSH\")\n", - " \n", - " # Check for identities again:\n", - " s = s.replace(\"HH\", \"\").replace(\"SSSS\", \"\").replace(\"HH\", \"\")\n", - " s = s.replace(\"HH\", \"\").replace(\"SSSS\", \"\").replace(\"HH\", \"\")\n", - " return s" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": {}, - "outputs": [], - "source": [ - "product_table = [[simplify_str(s) for s in row] for row in product_table]" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[['',\n", - " 'HS',\n", - " 'HSS',\n", - " 'H',\n", - " 'S',\n", - " 'HSH',\n", - " 'SS',\n", - " 'HSSH',\n", - " 'HSSS',\n", - " 'SSS',\n", - " 'HSSSH',\n", - " 'HSHS',\n", - " 'HSHSS',\n", - " 'HSSHS',\n", - " 'HSSHSS',\n", - " 'HSSHSSS',\n", - " 'SH',\n", - " 'SSH',\n", - " 'HSHSSH',\n", - " 'SSHS',\n", - " 'SSHSH',\n", - " 'HSHSH',\n", - " 'HSHSHS',\n", - " 'HSSHSH'],\n", - " ['SH',\n", - " 'SS',\n", - " 'SSS',\n", - " 'S',\n", - " 'SHS',\n", - " 'SSH',\n", - " 'SHSS',\n", - " 'SSSH',\n", - " '',\n", - " 'SHSSS',\n", - " 'H',\n", - " 'SSHS',\n", - " 'SSHSS',\n", - " 'SSSHS',\n", - " 'SSSHSS',\n", - " 'HSH',\n", - " 'SHSH',\n", - " 'SHSSH',\n", - " 'SSHSSH',\n", - " 'HSSH',\n", - " 'HSS',\n", - " 'SSHSH',\n", - " 'SSHSHS',\n", - " 'SSSHSH'],\n", - " ['SSH',\n", - " 'SSS',\n", - " '',\n", - " 'SS',\n", - " 'SSHS',\n", - " 'SSSH',\n", - " 'SSHSS',\n", - " 'H',\n", - " 'S',\n", - " 'SSHSSS',\n", - " 'SH',\n", - " 'SSSHS',\n", - " 'SSSHSS',\n", - " 'HS',\n", - " 'HSS',\n", - " 'HSSS',\n", - " 'SSHSH',\n", - " 'SSHSSH',\n", - " 'SSSHSSH',\n", - " 'SHSSH',\n", - " 'SHSS',\n", - " 'SSSHSH',\n", - " 'SSSHSHS',\n", - " 'HSH'],\n", - " ['H',\n", - " 'S',\n", - " 'SS',\n", - " '',\n", - " 'HS',\n", - " 'SH',\n", - " 'HSS',\n", - " 'SSH',\n", - " 'SSS',\n", - " 'HSSS',\n", - " 'SSSH',\n", - " 'SHS',\n", - " 'SHSS',\n", - " 'SSHS',\n", - " 'SSHSS',\n", - " 'SSHSSS',\n", - " 'HSH',\n", - " 'HSSH',\n", - " 'SHSSH',\n", - " 'HSSHS',\n", - " 'HSSHSH',\n", - " 'SHSH',\n", - " 'SHSHS',\n", - " 'SSHSH'],\n", - " ['HSH',\n", - " 'HSS',\n", - " 'HSSS',\n", - " 'HS',\n", - " 'HSHS',\n", - " 'HSSH',\n", - " 'HSHSS',\n", - " 'HSSSH',\n", - " 'H',\n", - " 'HSHSSS',\n", - " '',\n", - " 'HSSHS',\n", - " 'HSSHSS',\n", - " 'HSSSHS',\n", - " 'HSSSHSS',\n", - " 'SH',\n", - " 'HSHSH',\n", - " 'HSHSSH',\n", - " 'HSSHSSH',\n", - " 'SSH',\n", - " 'SS',\n", - " 'HSSHSH',\n", - " 'HSH',\n", - " 'HSSSHSH'],\n", - " ['S',\n", - " 'SHS',\n", - " 'SHSS',\n", - " 'SH',\n", - " 'SS',\n", - " 'SHSH',\n", - " 'SSS',\n", - " 'SHSSH',\n", - " 'SHSSS',\n", - " '',\n", - " 'SHSSSH',\n", - " 'SHSHS',\n", - " 'SHSHSS',\n", - " 'HSSH',\n", - " 'HSSHS',\n", - " 'HSSHSS',\n", - " 'SSH',\n", - " 'SSSH',\n", - " 'SHSHSSH',\n", - " 'SSSHS',\n", - " 'SSSHSH',\n", - " 'SHSHSH',\n", - " 'SHSHSHS',\n", - " 'HSS'],\n", - " ['HSSH',\n", - 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" 'SHSHS',\n", - " 'SHSSH',\n", - " 'SHSHSS',\n", - " 'SHSSSH',\n", - " 'SH',\n", - " 'SHSHSSS',\n", - " 'S',\n", - " 'HSSH',\n", - " 'HSSHS',\n", - " 'SHSSSHS',\n", - " 'SHSSSHSS',\n", - " 'SSH',\n", - " 'SHSHSH',\n", - " 'SHSHSSH',\n", - " 'HSSHSH',\n", - " 'SSSH',\n", - " 'SSS',\n", - " 'HSS',\n", - " 'HSSS',\n", - " 'SHSSSHSH'],\n", - " ['SHSSH',\n", - " 'SHSSS',\n", - " 'SH',\n", - " 'SHSS',\n", - " 'HSSH',\n", - " 'SHSSSH',\n", - " 'HSSHS',\n", - " 'S',\n", - " 'SHS',\n", - " 'HSSHSS',\n", - " 'SHSH',\n", - " 'SHSSSHS',\n", - " 'SHSSSHSS',\n", - " 'SS',\n", - " 'SSS',\n", - " '',\n", - " 'HSS',\n", - " 'HSSHSH',\n", - " 'SHSSSHSSH',\n", - " 'HSH',\n", - " 'HS',\n", - " 'SHSSSHSH',\n", - " 'SHSSSHSHS',\n", - " 'SSH'],\n", - " ['SSHSH',\n", - " 'SSHSS',\n", - " 'SSHSSS',\n", - " 'SSHS',\n", - " 'SSHSHS',\n", - " 'SSHSSH',\n", - " 'SSHSHSS',\n", - " 'SSHSSSH',\n", - " 'SSH',\n", - " 'SSHSHSSS',\n", - " 'SS',\n", - " 'SHSSH',\n", - " 'SHSSHS',\n", - " 'SSHSSSHS',\n", - " 'SSHSSSHSS',\n", - " 'SSSH',\n", - " 'SSHSHSH',\n", - " 'SSHSHSSH',\n", - " 'SHSSHSH',\n", - " 'H',\n", - " '',\n", - " 'SHSS',\n", - " 'SHSSS',\n", - " 'SSHSSSHSH'],\n", - " ['SSHSSH',\n", - " 'SSHSSS',\n", - " 'SSH',\n", - " 'SSHSS',\n", - " 'SHSSH',\n", - " 'SSHSSSH',\n", - " 'SHSSHS',\n", - " 'SS',\n", - " 'SSHS',\n", - " 'SHSSHSS',\n", - " 'SSHSH',\n", - " 'SSHSSSHS',\n", - " 'SSHSSSHSS',\n", - " 'SSS',\n", - " '',\n", - " 'S',\n", - " 'SHSS',\n", - " 'SHSSHSH',\n", - " 'SSHSSSHSSH',\n", - " 'SHSH',\n", - " 'SHS',\n", - " 'SSHSSSHSH',\n", - " 'SSHSSSHSHS',\n", - " 'SSSH'],\n", - " ['SSHSSSH',\n", - " 'SSH',\n", - " 'SSHS',\n", - " 'SSHSSS',\n", - " 'SSHSSSHS',\n", - " 'SS',\n", - " 'SSHSSSHSS',\n", - " 'SSHSH',\n", - " 'SSHSS',\n", - " 'SSSH',\n", - " 'SSHSSH',\n", - " 'SSS',\n", - " '',\n", - " 'SSHSHS',\n", - " 'SSHSHSS',\n", - " 'SSHSHSSS',\n", - " 'SSHSSSHSH',\n", - " 'SSHSSSHSSH',\n", - " 'H',\n", - " 'SSHSSHSSH',\n", - " 'SSHSSHSS',\n", - " 'SSSH',\n", - " 'SSSHS',\n", - " 'SSHSHSH'],\n", - " ['HS',\n", - " 'HSHS',\n", - " 'HSHSS',\n", - " 'HSH',\n", - " 'HSS',\n", - " 'HSHSH',\n", - " 'HSSS',\n", - " 'HSHSSH',\n", - " 'HSHSSS',\n", - " 'H',\n", - " 'HSHSSSH',\n", - " 'HSHSHS',\n", - " 'HSHSHSS',\n", - " 'SSH',\n", - " 'SSHS',\n", - " 'SSHSS',\n", - " 'HSSH',\n", - " 'HSSSH',\n", - " 'HSHSHSSH',\n", - " 'HSSSHS',\n", - " 'HSSSHSH',\n", - " 'HSHSHSH',\n", - " 'HSHSHSHS',\n", - " 'SS'],\n", - " ['HSS',\n", - " 'HSSHS',\n", - " 'HSSHSS',\n", - " 'HSSH',\n", - " 'HSSS',\n", - " 'HSSHSH',\n", - " 'H',\n", - " 'HSSHSSH',\n", - " 'HSSHSSS',\n", - " 'HS',\n", - " 'HSSHSSSH',\n", - " 'HSH',\n", - " 'HSHS',\n", - " 'HSHSSH',\n", - " 'HSHSSHS',\n", - " 'HSHSSHSS',\n", - " 'HSSSH',\n", - " '',\n", - " 'HSHSH',\n", - " 'S',\n", - " 'SH',\n", - " 'HS',\n", - " 'HSS',\n", - " 'HSHSS'],\n", - " ['SHSS',\n", - " 'HSSH',\n", - " 'HSSHS',\n", - " 'SHSSH',\n", - " 'SHSSS',\n", - " 'HSS',\n", - " 'SH',\n", - " 'HSSHSH',\n", - " 'HSSHSS',\n", - " 'SHS',\n", - " 'HSSHSSH',\n", - " 'HSSS',\n", - " 'H',\n", - " 'HSH',\n", - " 'HSHS',\n", - " 'HSHSS',\n", - " 'SHSSSH',\n", - " 'S',\n", - " '',\n", - " 'SS',\n", - " 'SSH',\n", - " 'HSSSH',\n", - " 'HSSSHS',\n", - " 'HS'],\n", - " ['HSSHSH',\n", - " 'HSSHSS',\n", - " 'HSSHSSS',\n", - " 'HSSHS',\n", - " 'HSH',\n", - " 'HSSHSSH',\n", - " 'HSHS',\n", - " 'HSSHSSSH',\n", - " 'HSSH',\n", - " 'HSHSS',\n", - " 'HSS',\n", - " 'HSHSSH',\n", - " 'HSHSSHS',\n", - " 'HSSHSSSHS',\n", - " 'HSSHSSSHSS',\n", - " 'HSSSH',\n", - " 'HS',\n", - " 'HSHSH',\n", - " 'HSHSSHSH',\n", - " '',\n", - " 'H',\n", - " 'HSHSS',\n", - " 'HSHSSS',\n", - " 'HSSHSSSHSH'],\n", - " ['HSSHS',\n", - " 'HSH',\n", - " 'HSHS',\n", - " 'HSSHSH',\n", - " 'HSSHSS',\n", - " 'HS',\n", - " 'HSSHSSS',\n", - " 'HSHSH',\n", - " 'HSHSS',\n", - " 'HSSH',\n", - " 'HSHSSH',\n", - " 'HSS',\n", - " 'HSSS',\n", - " '',\n", - " 'S',\n", - " 'SS',\n", - " 'HSSHSSH',\n", - " 'HSSHSSSH',\n", - " 'HSSSH',\n", - " 'HSSHSSSHS',\n", - " 'HSSHSSSHSH',\n", - " 'HSSH',\n", - " 'HSSHS',\n", - " 'H'],\n", - " ['SHS',\n", - " 'SHSHS',\n", - " 'SHSHSS',\n", - " 'SHSH',\n", - " 'SHSS',\n", - " 'SHSHSH',\n", - " 'SHSSS',\n", - " 'SHSHSSH',\n", - " 'SHSHSSS',\n", - " 'SH',\n", - " 'SHSHSSSH',\n", - " 'SHSHSHS',\n", - " 'SHSHSHSS',\n", - " 'SSSH',\n", - " 'SSSHS',\n", - " 'SSSHSS',\n", - " 'SHSSH',\n", - " 'SHSSSH',\n", - " 'SHSHSHSSH',\n", - " 'SHSSSHS',\n", - " 'SHSSSHSH',\n", - " 'SHSHSHSH',\n", - " 'SHSHSHSHS',\n", - " 'SSS'],\n", - " ['SHSHSH',\n", - " 'SHSHSS',\n", - " 'SHSHSSS',\n", - " 'SHSHS',\n", - " 'SHSHSHS',\n", - " 'SHSHSSH',\n", - " 'SHSHSHSS',\n", - " 'SHSHSSSH',\n", - " 'SHSH',\n", - " 'SHSHSHSSS',\n", - " 'SHS',\n", - " 'SSSH',\n", - " 'SSSHS',\n", - " 'SHSHSSSHS',\n", - " 'SHSHSSSHSS',\n", - " 'SHSSH',\n", - " 'SHSHSHSH',\n", - " 'SHSHSHSSH',\n", - " 'SSSHSH',\n", - " 'SHSSSH',\n", - " 'SHSSS',\n", - " 'SSS',\n", - " '',\n", - " 'SHSHSSSHSH']]" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "product_table" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'H': 0,\n", - " 'S': 1,\n", - " 'SS': 2,\n", - " 'HH': 3,\n", - " 'HS': 4,\n", - " 'SH': 5,\n", - " 'HSS': 6,\n", - " 'SSH': 7,\n", - " 'SSS': 8,\n", - " 'HSSS': 9,\n", - " 'SSSH': 10,\n", - " 'SHS': 11,\n", - " 'SHSS': 12,\n", - " 'SSHS': 13,\n", - " 'SSHSS': 14,\n", - " 'SSHSSS': 15,\n", - " 'HSH': 16,\n", - " 'HSSH': 17,\n", - " 'SHSSH': 18,\n", - " 'HSSHS': 19,\n", - " 'HSSHSH': 20,\n", - " 'SHSH': 21,\n", - " 'SHSHS': 22,\n", - " 'SSHSH': 23,\n", - " '': 3}" - ] - }, - "execution_count": 38, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "LC_indices = {c:i for i,c in enumerate(LC)}\n", - "LC_indices[\"\"] = 3\n", - "\n", - "LC_indices" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": {}, - "outputs": [], - "source": [ - "product_table = [[LC_indices[p] if p in LC_indices else p for p in row] for row in product_table]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we have to compute the missing elements manually. But at first flatten the list and remove duplicates." - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "['HSHS',\n", - " 'SSSHS',\n", - " 'HSHSS',\n", - " 'HSSSH',\n", - " 'SHSSS',\n", - " 'HSHSH',\n", - " 'SHSHSH',\n", - " 'HSHSSS',\n", - " 'HSHSSH',\n", - " 'HSHSHS',\n", - " 'SSSHSH',\n", - " 'SSHSSH',\n", - " 'HSSSHS',\n", - " 'SHSHSS',\n", - " 'HSSHSS',\n", - " 'SHSSSH',\n", - " 'SHSSHS',\n", - " 'SSSHSS',\n", - " 'SSHSHS',\n", - " 'HSSSHSH',\n", - " 'SSSHSSH',\n", - " 'HSHSSSH',\n", - " 'SHSHSSH',\n", - " 'HSHSSHS',\n", - " 'HSHSHSH',\n", - " 'SSSHSHS',\n", - " 'HSHSHSS',\n", - " 'SHSSHSS',\n", - " 'SHSHSSS',\n", - " 'HSSHSSS',\n", - " 'HSSSHSS',\n", - " 'SSHSHSS',\n", - " 'SHSSHSH',\n", - " 'SSHSHSH',\n", - " 'SSHSSHS',\n", - " 'HSSHSSH',\n", - " 'SHSSSHS',\n", - " 'SHSHSHS',\n", - " 'SSHSSSH',\n", - " 'SHSSSHSS',\n", - " 'HSHSSHSS',\n", - " 'SHSHSHSS',\n", - " 'SSHSHSSS',\n", - " 'HSSSHSSH',\n", - " 'HSHSHSHS',\n", - " 'HSHSHSSH',\n", - " 'HSSSHSHS',\n", - " 'SSHSHSSH',\n", - " 'SHSSSHSH',\n", - " 'SSSHSHSH',\n", - " 'SSHSHSHS',\n", - " 'HSSHSSSH',\n", - " 'SHSHSSSH',\n", - " 'SSHSSHSS',\n", - " 'SSSHSHSS',\n", - " 'HSHSSHSH',\n", - " 'SHSHSHSH',\n", - " 'SSHSSSHS',\n", - " 'SSSHSHSHS',\n", - " 'SSHSSHSSH',\n", - " 'SSHSSSHSH',\n", - " 'SHSHSHSSS',\n", - " 'SSSHSHSSH',\n", - " 'SHSHSHSHS',\n", - " 'HSSHSSSHS',\n", - " 'SSHSSSHSS',\n", - " 'SHSSSHSHS',\n", - " 'SHSSSHSSH',\n", - " 'SHSHSHSSH',\n", - " 'SHSHSSSHS',\n", - " 'SHSHSSSHSS',\n", - " 'SHSHSSSHSH',\n", - " 'SSHSSSHSSH',\n", - " 'HSSHSSSHSS',\n", - " 'HSSHSSSHSH',\n", - " 'SSHSSSHSHS']" - ] - }, - "execution_count": 40, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "unresolved_products = [[p for p in row if not isinstance(p, int)] for row in product_table]\n", - "unresolved_products = reduce(iconcat, unresolved_products)\n", - "unresolved_products = list(sorted(set(unresolved_products), key=lambda x: len(x)))\n", - "unresolved_products" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that we can now add new identities, which will allow us to reduce the re" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\\\\\frac{1}{2} - \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡1 ⅈ 1 ⅈ ⎤\n", - "⎢─ + ─ ─ + ─ ⎥\n", - "⎢2 2 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢1 ⅈ 1 ⅈ⎥\n", - "⎢─ - ─ - ─ + ─⎥\n", - "⎣2 2 2 2⎦" - ] - }, - "execution_count": 41, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "evalstr(\"HSHS\")" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/computations/stuff_with_sqrtiZ.ipynb b/computations/stuff_with_sqrtiZ.ipynb deleted file mode 100644 index 171f561..0000000 --- a/computations/stuff_with_sqrtiZ.ipynb +++ /dev/null @@ -1,599 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import sympy\n", - "sympy.init_printing()" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "a, b, c, d = sympy.symbols(\"a b c d\")\n", - "i = sympy.I" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "X = sympy.Matrix([[0, 1], [1, 0]])\n", - "Z = sympy.Matrix([[1, 0], [0, -1]])\n", - "\n", - "M = sympy.Matrix([[a, b], [c, d]])" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡0 1⎤\n", - "⎢ ⎥\n", - "⎣1 0⎦" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "X" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡1 0 ⎤\n", - "⎢ ⎥\n", - "⎣0 -1⎦" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "Z" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}a & b\\\\c & d\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡a b⎤\n", - "⎢ ⎥\n", - "⎣c d⎦" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "M" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "term_X = M*M + i*X\n", - "term_Z = M*M - i*Z" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}a^{2} + b c & a b + b d + i\\\\a c + c d + i & b c + d^{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ 2 ⎤\n", - "⎢ a + b⋅c a⋅b + b⋅d + ⅈ⎥\n", - "⎢ ⎥\n", - "⎢ 2 ⎥\n", - "⎣a⋅c + c⋅d + ⅈ b⋅c + d ⎦" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "term_X" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}a^{2} + b c - i & a b + b d\\\\a c + c d & b c + d^{2} + i\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ 2 ⎤\n", - "⎢a + b⋅c - ⅈ a⋅b + b⋅d ⎥\n", - "⎢ ⎥\n", - "⎢ 2 ⎥\n", - "⎣ a⋅c + c⋅d b⋅c + d + ⅈ⎦" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "term_Z" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/latex": [ - "$\\displaystyle \\left[ \\left\\{ a : - \\frac{\\sqrt{2}}{2}, \\ b : \\frac{\\sqrt{2} i}{2}, \\ c : \\frac{\\sqrt{2} i}{2}, \\ d : - \\frac{\\sqrt{2}}{2}\\right\\}, \\ \\left\\{ a : \\frac{\\sqrt{2}}{2}, \\ b : - \\frac{\\sqrt{2} i}{2}, \\ c : - \\frac{\\sqrt{2} i}{2}, \\ d : \\frac{\\sqrt{2}}{2}\\right\\}, \\ \\left\\{ a : - \\frac{\\sqrt{2} i}{2}, \\ b : \\frac{\\sqrt{2}}{2}, \\ c : \\frac{\\sqrt{2}}{2}, \\ d : - \\frac{\\sqrt{2} i}{2}\\right\\}, \\ \\left\\{ a : \\frac{\\sqrt{2} i}{2}, \\ b : - \\frac{\\sqrt{2}}{2}, \\ c : - \\frac{\\sqrt{2}}{2}, \\ d : \\frac{\\sqrt{2} i}{2}\\right\\}\\right]$" - ], - "text/plain": [ - "⎡⎧ -√2 √2⋅ⅈ √2⋅ⅈ -√2 ⎫ ⎧ √2 -√2⋅ⅈ -√2⋅ⅈ √2⎫ ⎧\n", - "⎢⎨a: ────, b: ────, c: ────, d: ────⎬, ⎨a: ──, b: ──────, c: ──────, d: ──⎬, ⎨\n", - "⎣⎩ 2 2 2 2 ⎭ ⎩ 2 2 2 2 ⎭ ⎩\n", - "\n", - " -√2⋅ⅈ √2 √2 -√2⋅ⅈ ⎫ ⎧ √2⋅ⅈ -√2 -√2 √2⋅ⅈ⎫⎤\n", - "a: ──────, b: ──, c: ──, d: ──────⎬, ⎨a: ────, b: ────, c: ────, d: ────⎬⎥\n", - " 2 2 2 2 ⎭ ⎩ 2 2 2 2 ⎭⎦" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sympy.solve(term_X)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/latex": [ - "$\\displaystyle \\left[ \\left\\{ a : - \\sqrt{i}, \\ b : 0, \\ c : 0, \\ d : - \\sqrt{- i}\\right\\}, \\ \\left\\{ a : - \\sqrt{i}, \\ b : 0, \\ c : 0, \\ d : \\sqrt{- i}\\right\\}, \\ \\left\\{ a : \\sqrt{i}, \\ b : 0, \\ c : 0, \\ d : - \\sqrt{- i}\\right\\}, \\ \\left\\{ a : \\sqrt{i}, \\ b : 0, \\ c : 0, \\ d : \\sqrt{- i}\\right\\}\\right]$" - ], - "text/plain": [ - "⎡⎧ ____⎫ ⎧ ____⎫ ⎧ \n", - "⎢⎨a: -√ⅈ, b: 0, c: 0, d: -╲╱ -ⅈ ⎬, ⎨a: -√ⅈ, b: 0, c: 0, d: ╲╱ -ⅈ ⎬, ⎨a: √ⅈ, b:\n", - "⎣⎩ ⎭ ⎩ ⎭ ⎩ \n", - "\n", - " ____⎫ ⎧ ____⎫⎤\n", - " 0, c: 0, d: -╲╱ -ⅈ ⎬, ⎨a: √ⅈ, b: 0, c: 0, d: ╲╱ -ⅈ ⎬⎥\n", - " ⎭ ⎩ ⎭⎦" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sympy.solve(term_Z)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}- \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡-√2 √2⋅ⅈ⎤\n", - "⎢──── ────⎥\n", - "⎢ 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢√2⋅ⅈ -√2 ⎥\n", - "⎢──── ────⎥\n", - "⎣ 2 2 ⎦" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sqrt_miX = sympy.Matrix([[-sympy.sqrt(2)/2, i*sympy.sqrt(2)/2], [i*sympy.sqrt(2)/2, -sympy.sqrt(2)/2]])\n", - "sqrt_miX" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}- \\sqrt{i} & 0\\\\0 & - \\sqrt{- i}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡-√ⅈ 0 ⎤\n", - "⎢ ⎥\n", - "⎢ ____⎥\n", - "⎣ 0 -╲╱ -ⅈ ⎦" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sqrt_iZ = sympy.Matrix([[-sympy.sqrt(i), 0], [0, -sympy.sqrt(-i)]])\n", - "sqrt_iZ" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}0 & - i\\\\- i & 0\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡0 -ⅈ⎤\n", - "⎢ ⎥\n", - "⎣-ⅈ 0 ⎦" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sqrt_miX**2" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}i & 0\\\\0 & - i\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ⅈ 0 ⎤\n", - "⎢ ⎥\n", - "⎣0 -ⅈ⎦" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sqrt_iZ**2" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}- \\frac{i \\sqrt{- i}}{2} - \\frac{\\sqrt{i} i}{2} & - \\frac{\\sqrt{i}}{2} + \\frac{\\sqrt{- i}}{2}\\\\- \\frac{\\sqrt{i}}{2} + \\frac{\\sqrt{- i}}{2} & \\frac{\\sqrt{i} i}{2} + \\frac{i \\sqrt{- i}}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ ____ ____ ⎤\n", - "⎢ ⅈ⋅╲╱ -ⅈ √ⅈ⋅ⅈ √ⅈ ╲╱ -ⅈ ⎥\n", - "⎢- ──────── - ──── - ── + ────── ⎥\n", - "⎢ 2 2 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢ ____ ____⎥\n", - "⎢ √ⅈ ╲╱ -ⅈ √ⅈ⋅ⅈ ⅈ⋅╲╱ -ⅈ ⎥\n", - "⎢ - ── + ────── ──── + ────────⎥\n", - "⎣ 2 2 2 2 ⎦" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "H_ = sqrt_miX * sqrt_iZ**3 * sqrt_miX\n", - "H_" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{i \\left(- \\sqrt{i} + \\left(- i\\right)^{\\frac{5}{2}}\\right)}{2} & - \\frac{\\sqrt{i}}{2} + \\frac{\\sqrt{- i}}{2}\\\\- \\frac{\\sqrt{i}}{2} + \\frac{\\sqrt{- i}}{2} & \\frac{i \\left(\\sqrt{- i} + \\sqrt{i}\\right)}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ ⎛ 5/2⎞ ____ ⎤\n", - "⎢ⅈ⋅⎝-√ⅈ + (-ⅈ) ⎠ √ⅈ ╲╱ -ⅈ ⎥\n", - "⎢───────────────── - ── + ────── ⎥\n", - "⎢ 2 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢ ____ ⎛ ____ ⎞⎥\n", - "⎢ √ⅈ ╲╱ -ⅈ ⅈ⋅⎝╲╱ -ⅈ + √ⅈ⎠⎥\n", - "⎢ - ── + ────── ───────────────⎥\n", - "⎣ 2 2 2 ⎦" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "H_.simplify()\n", - "H_" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGkAAAA/CAYAAADjVebQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAF6UlEQVR4Ae2ci5EUNxCGb68IAF8IOANwCEsGEMJBBnYRgYsQcAoXAnYG4AwgBHwZrL9/kFQa3bzVmodqp0o3kkZq9d+/WjOrx51ubm7OhM+E9Pp+uVx+TTOv6TIWOJ1OX5H8skP622dR5usoruiPJH1NlrXAPeLvkiYa5wkk4TV/JwWyk/SOy5gQ2j2Nldnjc7A9oNebMd2m4qPcv6ks2nhU3m36wCpNA++Q9V5KDgWr9taU47B9HsLln1noFTzJQlgi4y2KpkNoUuSwyVWxFSGJnvY75v8kCog/5/ZBca4XP2839xDYuLJLH+YWY5PSa+E70xY2u+iPSUCehoJGFvFPPq670oRvcd6R4ugesHk8sf6W+JD1H6F575mShFB50RuvOHExc47S8iblvfR5R7mjcwub9HZYiuBDdkOS6XDnXP81ysfvovc09kVojnz1YBOkVfDN8iSUkie86+r95H8khF41UGaXw10uNudZsoEJPuTMH+5EAEFKyM+fxyQoTWiN1/FzB0C/qL+lddNyW6TRKQtbCXzoNJ8kbzwqawrjo087BfVB0Pue4Zk8UL+gW+TGMvYQR7/Z2Bx+c3zokkWSvjiCN8nwhF4v4pkAPHgSiMujXvj0nu7oNQtbRJA5PnRZTpJTTMNW403ce72IZ76HiRgfVH63HoVuk7BFBGmE8Nh0N8GHnGyS1OMkREqFXpR6hSsjr2uFtNye0ug6CZsjSTZoYVPaAg9yGpI0uakXpoaq2ROdfJaqx90RXlH/O/dqrj1gQweRdP8s06p/UF+/i6oiyNlkN9iyPCmT4Gv1EQvM9iQqaNw1v5YMs9ZK7B3b5OFuD8a0JsfL2zu2W6/o9b5fC0z2pCEIDBdVrRmlWLfGZ0ISoPSjVrPBzQUo/ZjT9Eotu402x3fGmNh4+YKf6hPC7DdxzTIor3cuL6e9tes6LKvjo93mx6zVO2mVNRWU3uraFJ/JcEfP/iuxnkBpc+WTbUpJuUMkt8Zn5UnB2LyPNJenua9XIbOiyBb4TEkCgN5FWhTUXN4hdwMN9aet8JkMdwLmAUBOs7/B9bhH0lXM622Jz8STHAB9dv8pchxBei9VsZ98a3wmE6yA0KeiftC2Lrxo9vJHS8BOElvhc+1mL1U0ZoSMX3ZizyJqbI3PZLjrsww94TIW+uoePR/cD2PY9XwKzmIkoUC1pyrGDOuwN6vdGvKHwpgsPTf7uutobNWTBx3tb5llir0ISfSkak9VjDEfY1dZ0iYrBGdk4ZHLJ1jTusgLe/CIV3WqIsWapmPsepaDn7rNBKuEmJKEvNbJA9JVz5DHJKXYHUmL8SOvIcl0uHOuXeWpCgw2ePVgVx2TGfRZnkSjmp+r8lRF7BVd8VzszrMmn7qgvfnDHZVEaJWnKrpIifNysTuCtEIw+VQJZeeT5JWm8uyTB9SRB+7+VIXH2Hdfgt0RNBs/bWWRNOvkgSMo7BcnrR61y1MVfeT4fPSehT0iaDZ+2lpOkmt40skDkUEocurAG27tO3gmYY8IWoTfgqRJJw9cQ/oMbYW1DWvZHlgmYXckyRta2JWeog/lGk/KWqrgs7PaUxUYaPBaAzttiKTspYrdnDwYtGiZh6thn/xjFlblsp0XzzTjvejC7YsuDKKb5s7+ITxZlBxQWBOkYafT1tgnk1TamAMGy3qE3o8IyNq5tDX22ywLXCuvYoHJnjSkjRtSPrgy+uTWddh/8vRT/el/S+M3IQk4m29on27SIiWL4z+jNsPu8vUk1SesvqE9R2fLuqXwI7f5nWT1TjKZjkepo15F8ZsMd/TKqjfsj/Wc0vitPCng4CVa9Yb9ALQnUgK/KUkoqC+7ajfs9/ASskvhNxnupKVXENevcsN+YKInUhK/iSc5BavdsN/DS8gujT9rFtxriZL6VHwyN4ZXFZ2X8+1vfS+F38nNngVv7AMZVW/YH+sEpfGH4Q7W0s31Wiu6XitZAPt/TTmg6WZ00nCkyG8duvygh4Tp+o7n1yxDC0CQfrrcdYj88j/xBryWF0SjzAAAAABJRU5ErkJggg==\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡√2 √2 ⎤\n", - "⎢── ── ⎥\n", - "⎢2 2 ⎥\n", - "⎢ ⎥\n", - "⎢√2 -√2 ⎥\n", - "⎢── ────⎥\n", - "⎣2 2 ⎦" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "H = sympy.Matrix([[1, 1], [1, -1]]) / sympy.sqrt(2)\n", - "H" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [], - "source": [ - "phi = sympy.symbols(\"phi\")" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAVCAYAAAB7R6/OAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAARUlEQVQoFWNgYGAoA+K7UGyEhc/QCRR0+f//PwMyBoqBxZmADLxgVAEkeEbDgchwYIEmp5mMjIwgZigQuwBxOhALAfFuAP68FOR8/BSoAAAAAElFTkSuQmCC\n", - "text/latex": [ - "$\\displaystyle \\left[ \\right]$" - ], - "text/plain": [ - "[]" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sympy.solve(sympy.exp(i*phi)*H_ - H)" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{i \\left(\\left(- i\\right)^{\\frac{9}{2}} + \\sqrt{i}\\right)}{2} & \\frac{\\left(- i\\right)^{\\frac{5}{2}}}{2} + \\frac{\\sqrt{i}}{2}\\\\\\frac{\\left(- i\\right)^{\\frac{5}{2}}}{2} + \\frac{\\sqrt{i}}{2} & \\frac{i \\left(- \\sqrt{i} + \\left(- i\\right)^{\\frac{5}{2}}\\right)}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ ⎛ 9/2 ⎞ 5/2 ⎤\n", - "⎢ⅈ⋅⎝(-ⅈ) + √ⅈ⎠ (-ⅈ) √ⅈ ⎥\n", - "⎢──────────────── ─────── + ── ⎥\n", - "⎢ 2 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢ 5/2 ⎛ 5/2⎞⎥\n", - "⎢ (-ⅈ) √ⅈ ⅈ⋅⎝-√ⅈ + (-ⅈ) ⎠⎥\n", - "⎢ ─────── + ── ─────────────────⎥\n", - "⎣ 2 2 2 ⎦" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "H__ = H_ * sympy.exp(i * sympy.pi )\n", - "H__.simplify()\n", - "H__" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Some other calculatuions:" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAcAAAAOCAYAAADjXQYbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAo0lEQVQYGX2QARGCQBBF9xgDkAErGMEIWEEb0AEaaAVtYATHCFhBGpzv3+ydDCPuzGd3///HfbAYo81hZh04i6sYlnWCmEQGOdbq18ni/StuZAsh1LQj2IKRqwa6paS03u/eM781CxWnGogHUB3AK03+qLOTXdG7spfBrHXxa56JT8Rr3tVzIKXVK9tEesD8nTsEGW8ecNRefh/knV2YMF0kfgByKG0w9dMLeQAAAABJRU5ErkJggg==\n", - "text/latex": [ - "$\\displaystyle i$" - ], - "text/plain": [ - "ⅈ" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sympy.exp(i * sympy.pi/2)" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}- \\frac{\\sqrt{i}}{2} + \\frac{\\sqrt{- i}}{2} & \\frac{\\sqrt{i} i}{2} + \\frac{i \\sqrt{- i}}{2}\\\\\\frac{\\sqrt{i} i}{2} + \\frac{i \\sqrt{- i}}{2} & - \\frac{\\sqrt{- i}}{2} + \\frac{\\sqrt{i}}{2}\\end{matrix}\\right]$" - ], - "text/plain": [ - "⎡ ____ ____⎤\n", - "⎢ √ⅈ ╲╱ -ⅈ √ⅈ⋅ⅈ ⅈ⋅╲╱ -ⅈ ⎥\n", - "⎢ - ── + ────── ──── + ────────⎥\n", - "⎢ 2 2 2 2 ⎥\n", - "⎢ ⎥\n", - "⎢ ____ ____ ⎥\n", - "⎢√ⅈ⋅ⅈ ⅈ⋅╲╱ -ⅈ ╲╱ -ⅈ √ⅈ ⎥\n", - "⎢──── + ──────── - ────── + ── ⎥\n", - "⎣ 2 2 2 2 ⎦" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sqrt_miX * sqrt_iZ * sqrt_miX" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -}