175 lines
10 KiB
Plaintext
175 lines
10 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"from itertools import product\n",
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"from functools import reduce\n",
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"from operator import iconcat\n",
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"import sympy\n",
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"i = sympy.I\n",
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"exp = sympy.exp\n",
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"M = sympy.Matrix\n",
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"simplify = sympy.simplify\n",
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"from sympy.physics.quantum.dagger import Dagger\n",
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"\n",
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"sympy.init_printing()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"I = M([[1, 0], [0, 1]])\n",
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"X = M([[0, 1], [1, 0]])\n",
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"Y = M([[0, -i], [i, 0]])\n",
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"Z = M([[1, 0], [0, -1]])\n",
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"O = M([[0, 0], [0, 0]])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"H = M([[1, 1], [1, -1]]) / sympy.sqrt(2)\n",
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"S = M([[1, 0], [0, i]])\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"s2m = {\"H\": H, \"S\": S}\n",
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"def evalstr(s):\n",
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" m = I\n",
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" \n",
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" for c in s:\n",
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" m *= s2m[c]\n",
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" \n",
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" m.simplify()\n",
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" return m"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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\n",
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"text/latex": [
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"$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$"
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],
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"text/plain": [
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"⎡ √2⋅ⅈ √2⎤\n",
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"⎢ ──── ──⎥\n",
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"⎢ 2 2 ⎥\n",
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"⎢ ⎥\n",
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"⎢-√2⋅ⅈ √2⎥\n",
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"⎢────── ──⎥\n",
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"⎣ 2 2 ⎦"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"evalstr(\"HSHSSH\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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\n",
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"text/latex": [
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"$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right]$"
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],
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"text/plain": [
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"⎡√2 √2⋅ⅈ ⎤\n",
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"⎢── ──── ⎥\n",
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"⎢2 2 ⎥\n",
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"⎢ ⎥\n",
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"⎢√2 -√2⋅ⅈ ⎥\n",
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"⎢── ──────⎥\n",
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"⎣2 2 ⎦"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"evalstr(\"HS\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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\n",
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"text/latex": [
|
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"$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$"
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],
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"text/plain": [
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"⎡ √2 -√2 ⎤\n",
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"⎢ ── ────⎥\n",
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"⎢ 2 2 ⎥\n",
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"⎢ ⎥\n",
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"⎢-√2 -√2 ⎥\n",
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"⎢──── ────⎥\n",
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"⎣ 2 2 ⎦"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"evalstr(\"SSHSS\")"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
|