{
"cells": [
{
"cell_type": "markdown",
"id": "d26e3b44",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
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"source": [
"# Decomposing Qiskit circuits"
]
},
{
"cell_type": "markdown",
"id": "f5994d25",
"metadata": {
"pycharm": {
"name": "#%% md\n"
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"source": [
"In this notebook, we show how Qiskit circuits can be converted into Perceval circuits. To do so, we take the example of a simple gate-based circuit (a circuit producing GHZ states) and we show the translation to a linear optical circuit. We also show the equivalence between the two circuits."
]
},
{
"cell_type": "markdown",
"id": "3ed1c79e",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"As usual we start by imported the useful libraries. Note that this notebook requires the installation of Qiskit (which can be easiliy done with `pip install qiskit`)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "9dea723b",
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"import perceval as pcvl\n",
"from perceval.components import catalog\n",
"from perceval.converters import QiskitConverter\n",
"\n",
"from qiskit import QuantumCircuit\n",
"from qiskit.quantum_info import Statevector"
]
},
{
"cell_type": "markdown",
"id": "61e8fe05",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"## GHZ State generation in Qiskit"
]
},
{
"cell_type": "markdown",
"id": "57423a74",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"We first define the circuit generating GHZ states of 3 qubits with Qiskit. To do so, we first act with a Hadamard gate on qubit 0 to put in superposition of state $|0\\rangle$ and $|1\\rangle$. Then we perform two CNOT gates using qubit 0 as control and qubits 1 and 2 as targets."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "aef291d3",
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"text/plain": " ┌───┠\nq_0: ┤ H ├──■────■──\n └───┘┌─┴─┠│ \nq_1: ─────┤ X ├──┼──\n └───┘┌─┴─â”\nq_2: ──────────┤ X ├\n └───┘",
"text/html": "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: "Courier New",Courier,monospace\"> ┌───┠\nq_0: ┤ H ├──■────■──\n └───┘┌─┴─┠│ \nq_1: ─────┤ X ├──┼──\n └───┘┌─┴─â”\nq_2: ──────────┤ X ├\n └───┘</pre>"
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create a Quantum Circuit acting on the q register\n",
"circuit = QuantumCircuit(3)\n",
"\n",
"# Add a H gate on qubit 0\n",
"circuit.h(0)\n",
"\n",
"# Add CX (CNOT) gates on control qubit 0 and target qubits 1 and 2\n",
"circuit.cx(0, 1)\n",
"circuit.cx(0, 2)\n",
"\n",
"# Draw the circuit\n",
"circuit.draw()"
]
},
{
"cell_type": "markdown",
"id": "cca607ca",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"We display the final state when starting from the input state $|000\\rangle$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "7edaa2b3",
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"text/plain": "<IPython.core.display.Latex object>",
"text/latex": "$$\\frac{\\sqrt{2}}{2} |000\\rangle+\\frac{\\sqrt{2}}{2} |111\\rangle$$"
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Set the initial state of the simulator to the ground state using from_int\n",
"state = Statevector.from_int(0, 2**3)\n",
"\n",
"# Evolve the state by the quantum circuit\n",
"state = state.evolve(circuit)\n",
"\n",
"#draw using latex\n",
"state.draw('latex')"
]
},
{
"cell_type": "markdown",
"id": "9a4a941f",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"## Conversion to Perceval"
]
},
{
"cell_type": "markdown",
"id": "9d6365aa",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"With the use of `QiskitConverter`, we can transform the Qiskit circuit into a Perceval circuit. It uses 2 modes per qubit and additional modes for ancillary photons to perform deterministically two-qubit gates. Below the first six modes correspond to the three logical qubits (see the 'Spatial Modes encoding' paragraph in the 'Basics' section of the documentation) of the gate-based circuit above.\n",
"\n",
"The other modes are used to successfully implement two-qubit gates via heralding or post-selection. Heralding employs [4 ancillary modes](https://doi.org/10.1073/pnas.1018839108) while post-selection employs [2 ancillary modes](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.65.062324). With the option `use_postselection=True` in the method `.convert` on a `QiskitConverter` object, every CNOT but the last is implemented with a heralding scheme. Here it means that it would add $4+2$ ancillary modes. The option `use_postselection=False` only implements heralded CNOTs. Here it would mean $4+4$ ancillary modes. Note: the `use_postselection` option is `True` by default."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "dccbd8c9",
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"text/plain": "<drawSvg.drawing.Drawing at 0x276399b2f20>",
"image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n width=\"1750.0\" height=\"812.5\" viewBox=\"-39.0 0 1400 650\">\n<defs>\n</defs>\n<path d=\"M10,25 L25,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,75 L25,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,125 L25,125\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,175 L25,175\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,225 L25,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,275 L25,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M27,2 L123,2 L123,98 L27,98 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n<text x=\"29\" y=\"105\" font-size=\"8\" text-anchor=\"start\" dy=\"0em\">H</text>\n<path d=\"M25,25 L53,25 L72,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M78,44 L97,25 L125,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M25,75 L53,75 L72,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M78,56 L97,75 L125,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M50,43 L100,43 L100,57 L50,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"75\" y=\"90\" font-size=\"7\" text-anchor=\"middle\"><tspan x=\"75\" dy=\"0em\">Φ_tl=pi</tspan><tspan x=\"75\" dy=\"1em\">Φ_bl=pi</tspan></text>\n<text x=\"75\" y=\"26\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=5*pi/2</text>\n<path d=\"M50,53 L100,53 L100,57 L50,57 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M93,50 L103,50 L103,60 L93,60 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"98\" y=\"57\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M25,125 L125,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M25,175 L125,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M25,225 L125,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M25,275 L125,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M128,25 L172,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M125,25 L128,25 L172,125 L175,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M128,75 L172,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M125,75 L128,75 L172,175 L175,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M128,125 L172,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M125,125 L128,125 L172,225 L175,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M128,175 L172,275\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M125,175 L128,175 L172,275 L175,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M128,225 L172,425\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M125,225 L128,225 L172,425 L175,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M128,275 L172,475\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M125,275 L128,275 L172,475 L175,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M177,2 L873,2 L873,398 L177,398 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n<text x=\"179\" y=\"405\" font-size=\"8\" text-anchor=\"start\" dy=\"0em\">HERALDED CNOT</text>\n<path d=\"M178,125 L222,25\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M175,125 L178,125 L222,25 L225,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M175,225 L203,225 L222,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M228,244 L247,225 L275,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M175,275 L203,275 L222,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M228,256 L247,275 L275,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M200,243 L250,243 L250,257 L200,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"225\" y=\"285\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"225\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<path d=\"M200,243 L250,243 L250,247 L200,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M243,250 L253,250 L253,260 L243,260 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"248\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M278,275 L322,325\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M275,275 L278,275 L322,325 L325,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M175,175 L275,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M275,175 L303,175 L322,194\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M328,194 L347,175 L375,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M275,225 L303,225 L322,206\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M328,206 L347,225 L375,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M300,193 L350,193 L350,207 L300,207 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"325\" y=\"235\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"325\" y=\"176\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<path d=\"M300,193 L350,193 L350,197 L300,197 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M343,200 L353,200 L353,210 L343,210 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"348\" y=\"207\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M375,125 L403,125 L422,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M428,144 L447,125 L475,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M375,175 L403,175 L422,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M428,156 L447,175 L475,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M400,143 L450,143 L450,157 L400,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"425\" y=\"195\" font-size=\"6\" text-anchor=\"middle\"><tspan x=\"425\" dy=\"0em\">Φ_tl=3*pi/2</tspan><tspan x=\"425\" dy=\"1em\">Φ_bl=pi</tspan><tspan x=\"425\" dy=\"1em\">Φ_tr=pi/2</tspan></text>\n<text x=\"425\" y=\"126\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=2.145993</text>\n<path d=\"M400,143 L450,143 L450,147 L400,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M443,150 L453,150 L453,160 L443,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"448\" y=\"157\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M375,225 L403,225 L422,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M428,244 L447,225 L475,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M375,275 L403,275 L422,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M428,256 L447,275 L475,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M400,243 L450,243 L450,257 L400,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"425\" y=\"280\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"425\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=2.145993</text>\n<path d=\"M400,243 L450,243 L450,247 L400,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M443,250 L453,250 L453,260 L443,260 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"448\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M475,175 L503,175 L522,194\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M528,194 L547,175 L575,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M475,225 L503,225 L522,206\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M528,206 L547,225 L575,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M500,193 L550,193 L550,207 L500,207 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"525\" y=\"235\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"525\" y=\"176\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<path d=\"M500,193 L550,193 L550,197 L500,197 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M543,200 L553,200 L553,210 L543,210 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"548\" y=\"207\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M325,325 L475,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M478,325 L522,325\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M475,325 L478,325 L522,325 L525,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M575,125 L603,125 L622,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M628,144 L647,125 L675,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M575,175 L603,175 L622,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M628,156 L647,175 L675,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M600,143 L650,143 L650,157 L600,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"625\" y=\"180\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"625\" y=\"126\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=1.028622</text>\n<path d=\"M600,143 L650,143 L650,147 L600,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M643,150 L653,150 L653,160 L643,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"648\" y=\"157\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M575,225 L603,225 L622,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M628,244 L647,225 L675,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M575,275 L603,275 L622,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M628,256 L647,275 L675,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M600,243 L650,243 L650,257 L600,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"625\" y=\"295\" font-size=\"6\" text-anchor=\"middle\"><tspan x=\"625\" dy=\"0em\">Φ_tl=3*pi/2</tspan><tspan x=\"625\" dy=\"1em\">Φ_bl=pi</tspan><tspan x=\"625\" dy=\"1em\">Φ_tr=pi/2</tspan></text>\n<text x=\"625\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=1.028622</text>\n<path d=\"M600,243 L650,243 L650,247 L600,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M643,250 L653,250 L653,260 L643,260 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"648\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M525,325 L675,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M678,325 L722,275\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M675,325 L678,325 L722,275 L725,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M675,225 L725,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M725,225 L753,225 L772,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M778,244 L797,225 L825,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M725,275 L753,275 L772,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M778,256 L797,275 L825,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M750,243 L800,243 L800,257 L750,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"775\" y=\"285\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"775\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<path d=\"M750,243 L800,243 L800,247 L750,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M793,250 L803,250 L803,260 L793,260 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"798\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M828,225 L872,275\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M825,225 L828,225 L872,275 L875,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M828,275 L872,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M825,275 L828,275 L872,225 L875,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M225,25 L675,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M678,25 L722,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M675,25 L678,25 L722,125 L725,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M725,125 L875,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M675,175 L875,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M175,425 L875,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M175,475 L875,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M878,125 L922,75\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M875,125 L878,125 L922,75 L925,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M878,175 L922,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M875,175 L878,175 L922,125 L925,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M878,225 L922,325\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M875,225 L878,225 L922,325 L925,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M878,275 L922,375\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M875,275 L878,275 L922,375 L925,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M878,425 L922,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M875,425 L878,425 L922,175 L925,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M878,475 L922,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M875,475 L878,475 L922,225 L925,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M927,2 L1223,2 L1223,298 L927,298 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n<text x=\"929\" y=\"305\" font-size=\"8\" text-anchor=\"start\" dy=\"0em\">POSTPROCESSED CNOT</text>\n<path d=\"M925,25 L953,25 L972,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M978,44 L997,25 L1025,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M925,75 L953,75 L972,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M978,56 L997,75 L1025,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M950,43 L1000,43 L1000,57 L950,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"975\" y=\"95\" font-size=\"6\" text-anchor=\"middle\"><tspan x=\"975\" dy=\"0em\">Φ_tl=3*pi/2</tspan><tspan x=\"975\" dy=\"1em\">Φ_bl=pi</tspan><tspan x=\"975\" dy=\"1em\">Φ_tr=pi/2</tspan></text>\n<text x=\"975\" y=\"26\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=1.910633</text>\n<path d=\"M950,43 L1000,43 L1000,47 L950,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M993,50 L1003,50 L1003,60 L993,60 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"998\" y=\"57\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M925,175 L953,175 L972,194\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M978,194 L997,175 L1025,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M925,225 L953,225 L972,206\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M978,206 L997,225 L1025,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M950,193 L1000,193 L1000,207 L950,207 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"975\" y=\"235\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"975\" y=\"176\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<path d=\"M950,193 L1000,193 L1000,197 L950,197 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M993,200 L1003,200 L1003,210 L993,210 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"998\" y=\"207\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M925,125 L1025,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1025,125 L1053,125 L1072,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1078,144 L1097,125 L1125,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1025,175 L1053,175 L1072,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1078,156 L1097,175 L1125,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1050,143 L1100,143 L1100,157 L1050,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1075\" y=\"195\" font-size=\"6\" text-anchor=\"middle\"><tspan x=\"1075\" dy=\"0em\">Φ_tl=3*pi/2</tspan><tspan x=\"1075\" dy=\"1em\">Φ_bl=pi</tspan><tspan x=\"1075\" dy=\"1em\">Φ_tr=pi/2</tspan></text>\n<text x=\"1075\" y=\"126\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=1.910633</text>\n<path d=\"M1050,143 L1100,143 L1100,147 L1050,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1093,150 L1103,150 L1103,160 L1093,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"1098\" y=\"157\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M1025,225 L1053,225 L1072,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1078,244 L1097,225 L1125,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1025,275 L1053,275 L1072,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1078,256 L1097,275 L1125,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1050,243 L1100,243 L1100,257 L1050,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1075\" y=\"280\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1075\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=1.910633</text>\n<path d=\"M1050,243 L1100,243 L1100,247 L1050,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1093,250 L1103,250 L1103,260 L1093,260 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"1098\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M1125,175 L1153,175 L1172,194\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1178,194 L1197,175 L1225,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1125,225 L1153,225 L1172,206\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1178,206 L1197,225 L1225,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1150,193 L1200,193 L1200,207 L1150,207 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1175\" y=\"235\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1175\" y=\"176\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<path d=\"M1150,193 L1200,193 L1200,197 L1150,197 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1193,200 L1203,200 L1203,210 L1193,210 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n<text x=\"1198\" y=\"207\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">H</text>\n<path d=\"M1025,75 L1225,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1125,125 L1225,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M925,325 L1225,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M925,375 L1225,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1228,75 L1272,25\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M1225,75 L1228,75 L1272,25 L1275,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1228,125 L1272,75\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M1225,125 L1228,125 L1272,75 L1275,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1228,175 L1272,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M1225,175 L1228,175 L1272,225 L1275,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1228,225 L1272,275\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M1225,225 L1228,225 L1272,275 L1275,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1228,325 L1272,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M1225,325 L1228,325 L1272,125 L1275,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1228,375 L1272,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n<path d=\"M1225,375 L1228,375 L1272,175 L1275,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1275,25 L1290,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M1275,75 L1290,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M1275,125 L1290,125\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M1275,175 L1290,175\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M1275,225 L1290,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M1275,275 L1290,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M-2,15 L10,15 L10,85 L-2,85 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<text x=\"4\" y=\"27\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">0</text>\n<text x=\"4\" y=\"77\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">1</text>\n<text x=\"-2\" y=\"91\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\" dy=\"0em\">[q0]</text>\n<path d=\"M-2,115 L10,115 L10,185 L-2,185 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<text x=\"4\" y=\"127\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">2</text>\n<text x=\"4\" y=\"177\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">3</text>\n<text x=\"-2\" y=\"191\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\" dy=\"0em\">[q1]</text>\n<path d=\"M-2,215 L10,215 L10,285 L-2,285 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<text x=\"4\" y=\"227\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">4</text>\n<text x=\"4\" y=\"277\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">5</text>\n<text x=\"-2\" y=\"291\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\" dy=\"0em\">[q2]</text>\n<path d=\"M557,125 C557,125,557,115,567,115 L575,115 L575,135 L567,135 C557,135,557,125,557,125 L557,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n<text x=\"563\" y=\"141\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\" dy=\"0em\">[herald0]</text>\n<text x=\"567\" y=\"128\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">0</text>\n<path d=\"M357,125 C357,125,357,115,367,115 L375,115 L375,135 L367,135 C357,135,357,125,357,125 L357,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n<text x=\"363\" y=\"141\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\" dy=\"0em\">[herald1]</text>\n<text x=\"367\" y=\"128\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">1</text>\n<path d=\"M557,275 C557,275,557,265,567,265 L575,265 L575,285 L567,285 C557,285,557,275,557,275 L557,275\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n<text x=\"563\" y=\"291\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\" dy=\"0em\">[herald2]</text>\n<text x=\"567\" y=\"278\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">0</text>\n<path d=\"M357,275 C357,275,357,265,367,265 L375,265 L375,285 L367,285 C357,285,357,275,357,275 L357,275\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n<text x=\"363\" y=\"291\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\" dy=\"0em\">[herald3]</text>\n<text x=\"367\" y=\"278\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">1</text>\n<path d=\"M907,25 C907,25,907,15,917,15 L925,15 L925,35 L917,35 C907,35,907,25,907,25 L907,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n<text x=\"913\" y=\"41\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\" dy=\"0em\">[herald4]</text>\n<text x=\"917\" y=\"28\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">0</text>\n<path d=\"M1007,275 C1007,275,1007,265,1017,265 L1025,265 L1025,285 L1017,285 C1007,285,1007,275,1007,275 L1007,275\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n<text x=\"1013\" y=\"291\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\" dy=\"0em\">[herald5]</text>\n<text x=\"1017\" y=\"278\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">0</text>\n<path d=\"M1290,15 L1302,15 L1302,85 L1290,85 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<text x=\"1296\" y=\"27\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">0</text>\n<text x=\"1296\" y=\"77\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">1</text>\n<text x=\"1302\" y=\"91\" font-size=\"6\" text-anchor=\"end\" font-style=\"italic\" dy=\"0em\">[q0]</text>\n<path d=\"M1290,115 L1302,115 L1302,185 L1290,185 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<text x=\"1296\" y=\"127\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">2</text>\n<text x=\"1296\" y=\"177\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">3</text>\n<text x=\"1302\" y=\"191\" font-size=\"6\" text-anchor=\"end\" font-style=\"italic\" dy=\"0em\">[q1]</text>\n<path d=\"M1290,215 L1302,215 L1302,285 L1290,285 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<text x=\"1296\" y=\"227\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">4</text>\n<text x=\"1296\" y=\"277\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">5</text>\n<text x=\"1302\" y=\"291\" font-size=\"6\" text-anchor=\"end\" font-style=\"italic\" dy=\"0em\">[q2]</text>\n<path d=\"M683,135 L675,135 L675,115 L683,115 C683,115,693,115,693,125 C693,135,683,135,683,135 L683,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n<text x=\"688\" y=\"141\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\" dy=\"0em\">[herald0]</text>\n<text x=\"683\" y=\"128\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">0</text>\n<path d=\"M483,135 L475,135 L475,115 L483,115 C483,115,493,115,493,125 C493,135,483,135,483,135 L483,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n<text x=\"488\" y=\"141\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\" dy=\"0em\">[herald1]</text>\n<text x=\"483\" y=\"128\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">1</text>\n<path d=\"M683,285 L675,285 L675,265 L683,265 C683,265,693,265,693,275 C693,285,683,285,683,285 L683,285\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n<text x=\"688\" y=\"291\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\" dy=\"0em\">[herald2]</text>\n<text x=\"683\" y=\"278\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">0</text>\n<path d=\"M483,285 L475,285 L475,265 L483,265 C483,265,493,265,493,275 C493,285,483,285,483,285 L483,285\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n<text x=\"488\" y=\"291\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\" dy=\"0em\">[herald3]</text>\n<text x=\"483\" y=\"278\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">1</text>\n<path d=\"M1033,35 L1025,35 L1025,15 L1033,15 C1033,15,1043,15,1043,25 C1043,35,1033,35,1033,35 L1033,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n<text x=\"1038\" y=\"41\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\" dy=\"0em\">[herald4]</text>\n<text x=\"1033\" y=\"28\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">0</text>\n<path d=\"M1133,285 L1125,285 L1125,265 L1133,265 C1133,265,1143,265,1143,275 C1143,285,1133,285,1133,285 L1133,285\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" 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},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qiskit_converter = QiskitConverter(catalog, backend_name=\"Naive\")\n",
"quantum_processor = qiskit_converter.convert(circuit, use_postselection=True)\n",
"pcvl.pdisplay(quantum_processor, recursive=True)"
]
},
{
"cell_type": "markdown",
"id": "88ff50bd",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"With this converted circuit, we can now check that the resulting state is the same as before the conversion. By default, the input is the logical state $|000\\rangle_L$. Note that where Qiskit displays state in the order $|q_2q_1q_0\\rangle_L$, Perceval uses the reverse order $|q_0q_1q_2\\rangle_L$, but still shown as Fock states. Here, it doesn't change anything since we end with only $|000\\rangle_L$ and $|111\\rangle_L$ states."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "8ddb1457",
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"text/plain": "<IPython.core.display.HTML object>",
"text/html": "<table>\n<thead>\n<tr><th>state </th><th>probability </th></tr>\n</thead>\n<tbody>\n<tr><td>|1,0,1,0,1,0></td><td>1/2 </td></tr>\n<tr><td>|0,1,0,1,0,1></td><td>1/2 </td></tr>\n<tr><td>|1,0,0,1,1,0></td><td>0 </td></tr>\n<tr><td>|0,1,1,0,0,1></td><td>0 </td></tr>\n</tbody>\n</table>"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Not necessary here\n",
"quantum_processor.with_input(pcvl.LogicalState([0,0,0]))\n",
"\n",
"sampler = pcvl.algorithm.Sampler(quantum_processor)\n",
"\n",
"output_distribution = sampler.probs()[\"results\"]\n",
"pcvl.pdisplay(output_distribution, precision=1e-2, max_v = 4)"
]
},
{
"cell_type": "markdown",
"id": "2f14a1c5",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"This circuit can now be converted using a general interferometer decomposition so it can be implemented on a generic photonic chip."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "d15ff2ba",
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"u = quantum_processor.linear_circuit().compute_unitary(use_symbolic=False)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "1de600cb",
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"text/plain": "<drawSvg.drawing.Drawing at 0x27639e51f90>",
"image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n width=\"1437.5\" height=\"406.25\" viewBox=\"-35.0 0 2300 650\">\n<defs>\n</defs>\n<path d=\"M10,25 L25,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,75 L25,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,125 L25,125\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,175 L25,175\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,225 L25,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,275 L25,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,325 L25,325\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,375 L25,375\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,425 L25,425\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,475 L25,475\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,525 L25,525\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,575 L25,575\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M25,25 L53,25 L72,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M78,44 L97,25 L125,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M25,75 L53,75 L72,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M78,56 L97,75 L125,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M50,43 L100,43 L100,57 L50,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"75\" y=\"80\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"75\" y=\"26\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi/2</text>\n<path d=\"M50,43 L100,43 L100,47 L50,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M93,50 L103,50 L103,60 L93,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"98\" y=\"57\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M125,25 L175,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M130,40 L139,40 L153,10 L144,10 L130,40 L139,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"147\" y=\"38\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=2*pi</text>\n<path d=\"M25,125 L125,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M125,75 L153,75 L172,94\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M178,94 L197,75 L225,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M125,125 L153,125 L172,106\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M178,106 L197,125 L225,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M150,93 L200,93 L200,107 L150,107 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"175\" y=\"130\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"175\" y=\"76\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M150,93 L200,93 L200,97 L150,97 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M193,100 L203,100 L203,110 L193,110 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"198\" y=\"107\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M225,75 L275,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M230,90 L239,90 L253,60 L244,60 L230,90 L239,90 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"247\" y=\"88\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=3.586284</text>\n<path d=\"M175,25 L275,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M275,25 L303,25 L322,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M328,44 L347,25 L375,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M275,75 L303,75 L322,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M328,56 L347,75 L375,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M300,43 L350,43 L350,57 L300,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"325\" y=\"80\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"325\" y=\"26\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=10.655737</text>\n<path d=\"M300,43 L350,43 L350,47 L300,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M343,50 L353,50 L353,60 L343,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"348\" y=\"57\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M375,25 L425,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M380,40 L389,40 L403,10 L394,10 L380,40 L389,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"397\" y=\"38\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=pi</text>\n<path d=\"M25,175 L225,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M225,125 L253,125 L272,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M278,144 L297,125 L325,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M225,175 L253,175 L272,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M278,156 L297,175 L325,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M250,143 L300,143 L300,157 L250,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"275\" y=\"180\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"275\" y=\"126\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M250,143 L300,143 L300,147 L250,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M293,150 L303,150 L303,160 L293,160 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"298\" y=\"157\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M325,125 L375,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M330,140 L339,140 L353,110 L344,110 L330,140 L339,140 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"347\" y=\"138\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=5.789269</text>\n<path d=\"M375,75 L403,75 L422,94\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M428,94 L447,75 L475,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M375,125 L403,125 L422,106\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M428,106 L447,125 L475,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M400,93 L450,93 L450,107 L400,107 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"425\" y=\"130\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"425\" y=\"76\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=10*pi/3</text>\n<path d=\"M400,93 L450,93 L450,97 L400,97 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M443,100 L453,100 L453,110 L443,110 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"448\" y=\"107\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M475,75 L525,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M480,90 L489,90 L503,60 L494,60 L480,90 L489,90 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"497\" y=\"88\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=pi</text>\n<path d=\"M425,25 L525,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M525,25 L553,25 L572,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M578,44 L597,25 L625,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M525,75 L553,75 L572,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M578,56 L597,75 L625,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M550,43 L600,43 L600,57 L550,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"575\" y=\"80\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"575\" y=\"26\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=4.372552</text>\n<path d=\"M550,43 L600,43 L600,47 L550,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M593,50 L603,50 L603,60 L593,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"598\" y=\"57\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M625,25 L675,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M630,40 L639,40 L653,10 L644,10 L630,40 L639,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"647\" y=\"38\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=0</text>\n<path d=\"M25,225 L53,225 L72,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M78,244 L97,225 L125,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M25,275 L53,275 L72,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M78,256 L97,275 L125,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M50,243 L100,243 L100,257 L50,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"75\" y=\"280\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"75\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi/2</text>\n<path d=\"M50,243 L100,243 L100,247 L50,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M93,250 L103,250 L103,260 L93,260 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"98\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M125,225 L175,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M130,240 L139,240 L153,210 L144,210 L130,240 L139,240 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"147\" y=\"238\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=0.376182</text>\n<path d=\"M175,225 L325,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M325,175 L353,175 L372,194\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M378,194 L397,175 L425,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M325,225 L353,225 L372,206\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M378,206 L397,225 L425,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M350,193 L400,193 L400,207 L350,207 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"375\" y=\"230\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"375\" y=\"176\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M350,193 L400,193 L400,197 L350,197 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M393,200 L403,200 L403,210 L393,210 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"398\" y=\"207\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M425,175 L475,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M430,190 L439,190 L453,160 L444,160 L430,190 L439,190 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"447\" y=\"188\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=0.062973</text>\n<path d=\"M475,125 L503,125 L522,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M528,144 L547,125 L575,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M475,175 L503,175 L522,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M528,156 L547,175 L575,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M500,143 L550,143 L550,157 L500,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"525\" y=\"180\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"525\" y=\"126\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M500,143 L550,143 L550,147 L500,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M543,150 L553,150 L553,160 L543,160 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"548\" y=\"157\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M575,125 L625,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M580,140 L589,140 L603,110 L594,110 L580,140 L589,140 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"597\" y=\"138\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=3.081369</text>\n<path d=\"M625,75 L653,75 L672,94\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M678,94 L697,75 L725,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M625,125 L653,125 L672,106\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M678,106 L697,125 L725,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M650,93 L700,93 L700,107 L650,107 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"675\" y=\"130\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"675\" y=\"76\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M650,93 L700,93 L700,97 L650,97 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M693,100 L703,100 L703,110 L693,110 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"698\" y=\"107\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M725,75 L775,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M730,90 L739,90 L753,60 L744,60 L730,90 L739,90 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"747\" y=\"88\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=5.904254</text>\n<path d=\"M25,325 L125,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M125,275 L153,275 L172,294\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M178,294 L197,275 L225,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M125,325 L153,325 L172,306\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M178,306 L197,325 L225,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M150,293 L200,293 L200,307 L150,307 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"175\" y=\"330\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"175\" y=\"276\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M150,293 L200,293 L200,297 L150,297 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M193,300 L203,300 L203,310 L193,310 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"198\" y=\"307\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M225,275 L275,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M230,290 L239,290 L253,260 L244,260 L230,290 L239,290 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"247\" y=\"288\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=3.460472</text>\n<path d=\"M275,275 L425,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M425,225 L453,225 L472,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M478,244 L497,225 L525,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M425,275 L453,275 L472,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M478,256 L497,275 L525,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M450,243 L500,243 L500,257 L450,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"475\" y=\"280\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"475\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M450,243 L500,243 L500,247 L450,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M493,250 L503,250 L503,260 L493,260 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"498\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M525,225 L575,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M530,240 L539,240 L553,210 L544,210 L530,240 L539,240 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"547\" y=\"238\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=0.982393</text>\n<path d=\"M575,175 L603,175 L622,194\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M628,194 L647,175 L675,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M575,225 L603,225 L622,206\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M628,206 L647,225 L675,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M600,193 L650,193 L650,207 L600,207 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"625\" y=\"230\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"625\" y=\"176\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M600,193 L650,193 L650,197 L600,197 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M643,200 L653,200 L653,210 L643,210 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"648\" y=\"207\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M675,175 L725,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M680,190 L689,190 L703,160 L694,160 L680,190 L689,190 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"697\" y=\"188\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=4.856823</text>\n<path d=\"M725,125 L753,125 L772,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M778,144 L797,125 L825,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M725,175 L753,175 L772,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M778,156 L797,175 L825,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M750,143 L800,143 L800,157 L750,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"775\" y=\"180\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"775\" y=\"126\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M750,143 L800,143 L800,147 L750,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M793,150 L803,150 L803,160 L793,160 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"798\" y=\"157\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M825,125 L875,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M830,140 L839,140 L853,110 L844,110 L830,140 L839,140 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"847\" y=\"138\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=1.354757</text>\n<path d=\"M25,375 L225,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M225,325 L253,325 L272,344\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M278,344 L297,325 L325,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M225,375 L253,375 L272,356\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M278,356 L297,375 L325,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M250,343 L300,343 L300,357 L250,357 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"275\" y=\"380\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"275\" y=\"326\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M250,343 L300,343 L300,347 L250,347 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M293,350 L303,350 L303,360 L293,360 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"298\" y=\"357\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M325,325 L375,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M330,340 L339,340 L353,310 L344,310 L330,340 L339,340 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"347\" y=\"338\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=2.007123</text>\n<path d=\"M375,325 L525,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M525,275 L553,275 L572,294\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M578,294 L597,275 L625,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M525,325 L553,325 L572,306\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M578,306 L597,325 L625,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M550,293 L600,293 L600,307 L550,307 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"575\" y=\"330\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"575\" y=\"276\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M550,293 L600,293 L600,297 L550,297 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M593,300 L603,300 L603,310 L593,310 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"598\" y=\"307\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M625,275 L675,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M630,290 L639,290 L653,260 L644,260 L630,290 L639,290 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"647\" y=\"288\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=1.274398</text>\n<path d=\"M675,225 L703,225 L722,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M728,244 L747,225 L775,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M675,275 L703,275 L722,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M728,256 L747,275 L775,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M700,243 L750,243 L750,257 L700,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"725\" y=\"280\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"725\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M700,243 L750,243 L750,247 L700,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M743,250 L753,250 L753,260 L743,260 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"748\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M775,225 L825,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M780,240 L789,240 L803,210 L794,210 L780,240 L789,240 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"797\" y=\"238\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=5.501469</text>\n<path d=\"M825,175 L853,175 L872,194\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M878,194 L897,175 L925,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M825,225 L853,225 L872,206\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M878,206 L897,225 L925,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M850,193 L900,193 L900,207 L850,207 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"875\" y=\"230\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"875\" y=\"176\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=11.570771</text>\n<path d=\"M850,193 L900,193 L900,197 L850,197 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M893,200 L903,200 L903,210 L893,210 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"898\" y=\"207\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M925,175 L975,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M930,190 L939,190 L953,160 L944,160 L930,190 L939,190 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"947\" y=\"188\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=3*pi/2</text>\n<path d=\"M25,425 L325,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M325,375 L353,375 L372,394\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M378,394 L397,375 L425,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M325,425 L353,425 L372,406\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M378,406 L397,425 L425,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M350,393 L400,393 L400,407 L350,407 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"375\" y=\"430\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"375\" y=\"376\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M350,393 L400,393 L400,397 L350,397 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M393,400 L403,400 L403,410 L393,410 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"398\" y=\"407\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M425,375 L475,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M430,390 L439,390 L453,360 L444,360 L430,390 L439,390 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"447\" y=\"388\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=1.808302</text>\n<path d=\"M475,375 L625,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M625,325 L653,325 L672,344\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M678,344 L697,325 L725,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M625,375 L653,375 L672,356\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M678,356 L697,375 L725,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M650,343 L700,343 L700,357 L650,357 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"675\" y=\"380\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"675\" y=\"326\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M650,343 L700,343 L700,347 L650,347 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M693,350 L703,350 L703,360 L693,360 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"698\" y=\"357\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M725,325 L775,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M730,340 L739,340 L753,310 L744,310 L730,340 L739,340 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"747\" y=\"338\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=2.764924</text>\n<path d=\"M775,275 L803,275 L822,294\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M828,294 L847,275 L875,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M775,325 L803,325 L822,306\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M828,306 L847,325 L875,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M800,293 L850,293 L850,307 L800,307 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"825\" y=\"330\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"825\" y=\"276\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M800,293 L850,293 L850,297 L800,297 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M843,300 L853,300 L853,310 L843,310 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"848\" y=\"307\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M875,275 L925,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M880,290 L889,290 L903,260 L894,260 L880,290 L889,290 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"897\" y=\"288\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=5.623088</text>\n<path d=\"M925,225 L953,225 L972,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M978,244 L997,225 L1025,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M925,275 L953,275 L972,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M978,256 L997,275 L1025,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M950,243 L1000,243 L1000,257 L950,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"975\" y=\"280\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"975\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=11.806155</text>\n<path d=\"M950,243 L1000,243 L1000,247 L950,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M993,250 L1003,250 L1003,260 L993,260 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"998\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1025,225 L1075,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1030,240 L1039,240 L1053,210 L1044,210 L1030,240 L1039,240 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1047\" y=\"238\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=5.500548</text>\n<path d=\"M975,175 L1075,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1075,175 L1103,175 L1122,194\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1128,194 L1147,175 L1175,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1075,225 L1103,225 L1122,206\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1128,206 L1147,225 L1175,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1100,193 L1150,193 L1150,207 L1100,207 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1125\" y=\"230\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1125\" y=\"176\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M1100,193 L1150,193 L1150,197 L1100,197 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1143,200 L1153,200 L1153,210 L1143,210 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1148\" y=\"207\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1175,175 L1225,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1180,190 L1189,190 L1203,160 L1194,160 L1180,190 L1189,190 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1197\" y=\"188\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=2.353433</text>\n<path d=\"M875,125 L1225,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1225,125 L1253,125 L1272,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1278,144 L1297,125 L1325,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1225,175 L1253,175 L1272,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1278,156 L1297,175 L1325,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1250,143 L1300,143 L1300,157 L1250,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1275\" y=\"180\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1275\" y=\"126\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3.852148</text>\n<path d=\"M1250,143 L1300,143 L1300,147 L1250,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1293,150 L1303,150 L1303,160 L1293,160 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1298\" y=\"157\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1325,125 L1375,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1330,140 L1339,140 L1353,110 L1344,110 L1330,140 L1339,140 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1347\" y=\"138\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=pi</text>\n<path d=\"M775,75 L1375,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1375,75 L1403,75 L1422,94\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1428,94 L1447,75 L1475,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1375,125 L1403,125 L1422,106\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1428,106 L1447,125 L1475,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1400,93 L1450,93 L1450,107 L1400,107 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1425\" y=\"130\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1425\" y=\"76\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=5*pi/2</text>\n<path d=\"M1400,93 L1450,93 L1450,97 L1400,97 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1443,100 L1453,100 L1453,110 L1443,110 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1448\" y=\"107\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1475,75 L1525,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1480,90 L1489,90 L1503,60 L1494,60 L1480,90 L1489,90 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1497\" y=\"88\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=pi/2</text>\n<path d=\"M675,25 L1525,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1525,25 L1553,25 L1572,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1578,44 L1597,25 L1625,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1525,75 L1553,75 L1572,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1578,56 L1597,75 L1625,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1550,43 L1600,43 L1600,57 L1550,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1575\" y=\"80\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1575\" y=\"26\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=8.497483</text>\n<path d=\"M1550,43 L1600,43 L1600,47 L1550,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1593,50 L1603,50 L1603,60 L1593,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1598\" y=\"57\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1625,25 L1675,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1630,40 L1639,40 L1653,10 L1644,10 L1630,40 L1639,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1647\" y=\"38\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=3*pi/2</text>\n<path d=\"M25,475 L425,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M425,425 L453,425 L472,444\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M478,444 L497,425 L525,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M425,475 L453,475 L472,456\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M478,456 L497,475 L525,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M450,443 L500,443 L500,457 L450,457 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"475\" y=\"480\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"475\" y=\"426\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M450,443 L500,443 L500,447 L450,447 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M493,450 L503,450 L503,460 L493,460 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"498\" y=\"457\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M525,425 L575,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M530,440 L539,440 L553,410 L544,410 L530,440 L539,440 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"547\" y=\"438\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=1.005773</text>\n<path d=\"M575,425 L725,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M725,375 L753,375 L772,394\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M778,394 L797,375 L825,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M725,425 L753,425 L772,406\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M778,406 L797,425 L825,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M750,393 L800,393 L800,407 L750,407 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"775\" y=\"430\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"775\" y=\"376\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M750,393 L800,393 L800,397 L750,397 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M793,400 L803,400 L803,410 L793,410 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"798\" y=\"407\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M825,375 L875,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M830,390 L839,390 L853,360 L844,360 L830,390 L839,390 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"847\" y=\"388\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=3.232767</text>\n<path d=\"M875,325 L903,325 L922,344\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M928,344 L947,325 L975,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M875,375 L903,375 L922,356\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M928,356 L947,375 L975,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M900,343 L950,343 L950,357 L900,357 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"925\" y=\"380\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"925\" y=\"326\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=2.145993</text>\n<path d=\"M900,343 L950,343 L950,347 L900,347 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M943,350 L953,350 L953,360 L943,360 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"948\" y=\"357\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M975,325 L1025,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M980,340 L989,340 L1003,310 L994,310 L980,340 L989,340 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"997\" y=\"338\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=0</text>\n<path d=\"M1025,275 L1053,275 L1072,294\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1078,294 L1097,275 L1125,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1025,325 L1053,325 L1072,306\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1078,306 L1097,325 L1125,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1050,293 L1100,293 L1100,307 L1050,307 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1075\" y=\"330\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1075\" y=\"276\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=2.431038</text>\n<path d=\"M1050,293 L1100,293 L1100,297 L1050,297 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1093,300 L1103,300 L1103,310 L1093,310 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1098\" y=\"307\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1125,275 L1175,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1130,290 L1139,290 L1153,260 L1144,260 L1130,290 L1139,290 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1147\" y=\"288\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=3.3554</text>\n<path d=\"M1175,225 L1203,225 L1222,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1228,244 L1247,225 L1275,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1175,275 L1203,275 L1222,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1228,256 L1247,275 L1275,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1200,243 L1250,243 L1250,257 L1200,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1225\" y=\"280\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1225\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M1200,243 L1250,243 L1250,247 L1200,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1243,250 L1253,250 L1253,260 L1243,260 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1248\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1275,225 L1325,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1280,240 L1289,240 L1303,210 L1294,210 L1280,240 L1289,240 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1297\" y=\"238\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=1.356989</text>\n<path d=\"M1325,175 L1353,175 L1372,194\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1378,194 L1397,175 L1425,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1325,225 L1353,225 L1372,206\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1378,206 L1397,225 L1425,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1350,193 L1400,193 L1400,207 L1350,207 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1375\" y=\"230\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1375\" y=\"176\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=2.381377</text>\n<path d=\"M1350,193 L1400,193 L1400,197 L1350,197 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1393,200 L1403,200 L1403,210 L1393,210 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1398\" y=\"207\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1425,175 L1475,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1430,190 L1439,190 L1453,160 L1444,160 L1430,190 L1439,190 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1447\" y=\"188\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=pi</text>\n<path d=\"M1475,125 L1503,125 L1522,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1528,144 L1547,125 L1575,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1475,175 L1503,175 L1522,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1528,156 L1547,175 L1575,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1500,143 L1550,143 L1550,157 L1500,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1525\" y=\"180\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1525\" y=\"126\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=8.193819</text>\n<path d=\"M1500,143 L1550,143 L1550,147 L1500,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1543,150 L1553,150 L1553,160 L1543,160 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1548\" y=\"157\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1575,125 L1625,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1580,140 L1589,140 L1603,110 L1594,110 L1580,140 L1589,140 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1597\" y=\"138\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=pi/2</text>\n<path d=\"M1625,75 L1653,75 L1672,94\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1678,94 L1697,75 L1725,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1625,125 L1653,125 L1672,106\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1678,106 L1697,125 L1725,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1650,93 L1700,93 L1700,107 L1650,107 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1675\" y=\"130\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1675\" y=\"76\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=10.742894</text>\n<path d=\"M1650,93 L1700,93 L1700,97 L1650,97 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1693,100 L1703,100 L1703,110 L1693,110 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1698\" y=\"107\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1725,75 L1775,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1730,90 L1739,90 L1753,60 L1744,60 L1730,90 L1739,90 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1747\" y=\"88\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=pi/2</text>\n<path d=\"M1675,25 L1775,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1775,25 L1803,25 L1822,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1828,44 L1847,25 L1875,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1775,75 L1803,75 L1822,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1828,56 L1847,75 L1875,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1800,43 L1850,43 L1850,57 L1800,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1825\" y=\"80\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1825\" y=\"26\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=4.913747</text>\n<path d=\"M1800,43 L1850,43 L1850,47 L1800,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1843,50 L1853,50 L1853,60 L1843,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1848\" y=\"57\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1875,25 L1925,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1880,40 L1889,40 L1903,10 L1894,10 L1880,40 L1889,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1897\" y=\"38\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=pi/2</text>\n<path d=\"M25,525 L525,525\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M525,475 L553,475 L572,494\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M578,494 L597,475 L625,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M525,525 L553,525 L572,506\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M578,506 L597,525 L625,525\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M550,493 L600,493 L600,507 L550,507 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"575\" y=\"530\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"575\" y=\"476\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M550,493 L600,493 L600,497 L550,497 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M593,500 L603,500 L603,510 L593,510 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"598\" y=\"507\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M625,475 L675,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M630,490 L639,490 L653,460 L644,460 L630,490 L639,490 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"647\" y=\"488\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=4.704143</text>\n<path d=\"M675,475 L825,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M825,425 L853,425 L872,444\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M878,444 L897,425 L925,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M825,475 L853,475 L872,456\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M878,456 L897,475 L925,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M850,443 L900,443 L900,457 L850,457 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"875\" y=\"480\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"875\" y=\"426\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=1.910633</text>\n<path d=\"M850,443 L900,443 L900,447 L850,447 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M893,450 L903,450 L903,460 L893,460 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"898\" y=\"457\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M925,425 L975,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M930,440 L939,440 L953,410 L944,410 L930,440 L939,440 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"947\" y=\"438\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=5.019366</text>\n<path d=\"M975,375 L1003,375 L1022,394\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1028,394 L1047,375 L1075,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M975,425 L1003,425 L1022,406\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1028,406 L1047,425 L1075,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1000,393 L1050,393 L1050,407 L1000,407 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1025\" y=\"430\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1025\" y=\"376\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M1000,393 L1050,393 L1050,397 L1000,397 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1043,400 L1053,400 L1053,410 L1043,410 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1048\" y=\"407\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1075,375 L1125,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1080,390 L1089,390 L1103,360 L1094,360 L1080,390 L1089,390 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1097\" y=\"388\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=2.278419</text>\n<path d=\"M1125,325 L1153,325 L1172,344\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1178,344 L1197,325 L1225,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1125,375 L1153,375 L1172,356\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1178,356 L1197,375 L1225,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1150,343 L1200,343 L1200,357 L1150,357 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1175\" y=\"380\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1175\" y=\"326\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M1150,343 L1200,343 L1200,347 L1150,347 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1193,350 L1203,350 L1203,360 L1193,360 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1198\" y=\"357\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1225,325 L1275,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1230,340 L1239,340 L1253,310 L1244,310 L1230,340 L1239,340 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1247\" y=\"338\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=0.876857</text>\n<path d=\"M1275,275 L1303,275 L1322,294\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1328,294 L1347,275 L1375,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1275,325 L1303,325 L1322,306\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1328,306 L1347,325 L1375,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1300,293 L1350,293 L1350,307 L1300,307 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1325\" y=\"330\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1325\" y=\"276\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M1300,293 L1350,293 L1350,297 L1300,297 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1343,300 L1353,300 L1353,310 L1343,310 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1348\" y=\"307\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1375,275 L1425,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1380,290 L1389,290 L1403,260 L1394,260 L1380,290 L1389,290 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1397\" y=\"288\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=3.698707</text>\n<path d=\"M1425,225 L1453,225 L1472,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1478,244 L1497,225 L1525,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1425,275 L1453,275 L1472,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1478,256 L1497,275 L1525,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1450,243 L1500,243 L1500,257 L1450,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1475\" y=\"280\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1475\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M1450,243 L1500,243 L1500,247 L1450,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1493,250 L1503,250 L1503,260 L1493,260 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1498\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1525,225 L1575,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1530,240 L1539,240 L1553,210 L1544,210 L1530,240 L1539,240 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1547\" y=\"238\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=1.698868</text>\n<path d=\"M1575,175 L1603,175 L1622,194\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1628,194 L1647,175 L1675,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1575,225 L1603,225 L1622,206\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1628,206 L1647,225 L1675,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1600,193 L1650,193 L1650,207 L1600,207 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1625\" y=\"230\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1625\" y=\"176\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M1600,193 L1650,193 L1650,197 L1600,197 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1643,200 L1653,200 L1653,210 L1643,210 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1648\" y=\"207\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1675,175 L1725,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1680,190 L1689,190 L1703,160 L1694,160 L1680,190 L1689,190 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1697\" y=\"188\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=1.773002</text>\n<path d=\"M1725,125 L1753,125 L1772,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1778,144 L1797,125 L1825,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1725,175 L1753,175 L1772,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1778,156 L1797,175 L1825,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1750,143 L1800,143 L1800,157 L1750,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1775\" y=\"180\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1775\" y=\"126\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M1750,143 L1800,143 L1800,147 L1750,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1793,150 L1803,150 L1803,160 L1793,160 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1798\" y=\"157\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1825,125 L1875,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1830,140 L1839,140 L1853,110 L1844,110 L1830,140 L1839,140 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1847\" y=\"138\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=4.082134</text>\n<path d=\"M1875,75 L1903,75 L1922,94\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1928,94 L1947,75 L1975,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1875,125 L1903,125 L1922,106\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1928,106 L1947,125 L1975,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1900,93 L1950,93 L1950,107 L1900,107 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1925\" y=\"130\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1925\" y=\"76\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M1900,93 L1950,93 L1950,97 L1900,97 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1943,100 L1953,100 L1953,110 L1943,110 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1948\" y=\"107\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1975,75 L2025,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1980,90 L1989,90 L2003,60 L1994,60 L1980,90 L1989,90 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1997\" y=\"88\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=5.319738</text>\n<path d=\"M1925,25 L2025,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M2025,25 L2053,25 L2072,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M2078,44 L2097,25 L2125,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M2025,75 L2053,75 L2072,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M2078,56 L2097,75 L2125,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M2050,43 L2100,43 L2100,57 L2050,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"2075\" y=\"80\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"2075\" y=\"26\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M2050,43 L2100,43 L2100,47 L2050,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M2093,50 L2103,50 L2103,60 L2093,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"2098\" y=\"57\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M2125,25 L2175,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M2130,40 L2139,40 L2153,10 L2144,10 L2130,40 L2139,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"2147\" y=\"38\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=1.956447</text>\n<path d=\"M25,575 L625,575\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M625,525 L653,525 L672,544\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M678,544 L697,525 L725,525\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M625,575 L653,575 L672,556\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M678,556 L697,575 L725,575\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M650,543 L700,543 L700,557 L650,557 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"675\" y=\"580\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"675\" y=\"526\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=1.910633</text>\n<path d=\"M650,543 L700,543 L700,547 L650,547 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M693,550 L703,550 L703,560 L693,560 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"698\" y=\"557\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M725,525 L775,525\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M730,540 L739,540 L753,510 L744,510 L730,540 L739,540 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"747\" y=\"538\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=2.517287</text>\n<path d=\"M775,525 L925,525\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M925,475 L953,475 L972,494\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M978,494 L997,475 L1025,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M925,525 L953,525 L972,506\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M978,506 L997,525 L1025,525\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M950,493 L1000,493 L1000,507 L950,507 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"975\" y=\"530\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"975\" y=\"476\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M950,493 L1000,493 L1000,497 L950,497 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M993,500 L1003,500 L1003,510 L993,510 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"998\" y=\"507\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1025,475 L1075,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1030,490 L1039,490 L1053,460 L1044,460 L1030,490 L1039,490 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1047\" y=\"488\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=5.456853</text>\n<path d=\"M1075,425 L1103,425 L1122,444\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1128,444 L1147,425 L1175,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1075,475 L1103,475 L1122,456\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1128,456 L1147,475 L1175,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1100,443 L1150,443 L1150,457 L1100,457 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1125\" y=\"480\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1125\" y=\"426\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M1100,443 L1150,443 L1150,447 L1100,447 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1143,450 L1153,450 L1153,460 L1143,460 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1148\" y=\"457\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1175,425 L1225,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1180,440 L1189,440 L1203,410 L1194,410 L1180,440 L1189,440 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1197\" y=\"438\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=2.055497</text>\n<path d=\"M1225,375 L1253,375 L1272,394\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1278,394 L1297,375 L1325,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1225,425 L1253,425 L1272,406\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1278,406 L1297,425 L1325,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1250,393 L1300,393 L1300,407 L1250,407 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1275\" y=\"430\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1275\" y=\"376\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M1250,393 L1300,393 L1300,397 L1250,397 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1293,400 L1303,400 L1303,410 L1293,410 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1298\" y=\"407\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1325,375 L1375,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1330,390 L1339,390 L1353,360 L1344,360 L1330,390 L1339,390 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1347\" y=\"388\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=0.966679</text>\n<path d=\"M1375,325 L1403,325 L1422,344\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1428,344 L1447,325 L1475,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1375,375 L1403,375 L1422,356\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1428,356 L1447,375 L1475,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1400,343 L1450,343 L1450,357 L1400,357 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1425\" y=\"380\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1425\" y=\"326\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=3*pi</text>\n<path d=\"M1400,343 L1450,343 L1450,347 L1400,347 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1443,350 L1453,350 L1453,360 L1443,360 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1448\" y=\"357\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1475,325 L1525,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1480,340 L1489,340 L1503,310 L1494,310 L1480,340 L1489,340 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1497\" y=\"338\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=0.853832</text>\n<path d=\"M1525,275 L1553,275 L1572,294\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1578,294 L1597,275 L1625,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1525,325 L1553,325 L1572,306\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1578,306 L1597,325 L1625,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1550,293 L1600,293 L1600,307 L1550,307 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1575\" y=\"330\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1575\" y=\"276\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=pi</text>\n<path d=\"M1550,293 L1600,293 L1600,297 L1550,297 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1593,300 L1603,300 L1603,310 L1593,310 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1598\" y=\"307\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1625,275 L1675,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1630,290 L1639,290 L1653,260 L1644,260 L1630,290 L1639,290 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1647\" y=\"288\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=0.716222</text>\n<path d=\"M1675,225 L1703,225 L1722,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1728,244 L1747,225 L1775,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1675,275 L1703,275 L1722,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1728,256 L1747,275 L1775,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1700,243 L1750,243 L1750,257 L1700,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1725\" y=\"280\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\"></text>\n<text x=\"1725\" y=\"226\" font-size=\"7\" text-anchor=\"middle\" dy=\"0em\">Θ=7*pi/2</text>\n<path d=\"M1700,243 L1750,243 L1750,247 L1700,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1743,250 L1753,250 L1753,260 L1743,260 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1748\" y=\"257\" font-size=\"6\" text-anchor=\"middle\" dy=\"0em\">Rx</text>\n<path d=\"M1775,225 L1825,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1780,240 L1789,240 L1803,210 L1794,210 L1780,240 L1789,240 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1797\" y=\"238\" font-size=\"7\" text-anchor=\"start\" dy=\"0em\">Φ=3*pi/2</text>\n<path d=\"M2125,75 L2175,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1975,125 L2175,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1825,175 L2175,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1825,225 L2175,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1775,275 L2175,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1625,325 L2175,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1475,375 L2175,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1325,425 L2175,425\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1175,475 L2175,475\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1025,525 L2175,525\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M725,575 L2175,575\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M2175,25 L2190,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M2175,75 L2190,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M2175,125 L2190,125\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M2175,175 L2190,175\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M2175,225 L2190,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M2175,275 L2190,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M2175,325 L2190,325\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M2175,375 L2190,375\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M2175,425 L2190,425\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M2175,475 L2190,475\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M2175,525 L2190,525\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M2175,575 L2190,575\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<text x=\"2200\" y=\"28\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">0</text>\n<text x=\"2200\" y=\"78\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">1</text>\n<text x=\"2200\" y=\"128\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">2</text>\n<text x=\"2200\" y=\"178\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">3</text>\n<text x=\"2200\" y=\"228\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">4</text>\n<text x=\"2200\" y=\"278\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">5</text>\n<text x=\"2200\" y=\"328\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">6</text>\n<text x=\"2200\" y=\"378\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">7</text>\n<text x=\"2200\" y=\"428\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">8</text>\n<text x=\"2200\" y=\"478\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">9</text>\n<text x=\"2200\" y=\"528\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">10</text>\n<text x=\"2200\" y=\"578\" font-size=\"10\" text-anchor=\"end\" dy=\"0em\">11</text>\n<text x=\"0\" y=\"28\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">0</text>\n<text x=\"0\" y=\"78\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">1</text>\n<text x=\"0\" y=\"128\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">2</text>\n<text x=\"0\" y=\"178\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">3</text>\n<text x=\"0\" y=\"228\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">4</text>\n<text x=\"0\" y=\"278\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">5</text>\n<text x=\"0\" y=\"328\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">6</text>\n<text x=\"0\" y=\"378\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">7</text>\n<text x=\"0\" y=\"428\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">8</text>\n<text x=\"0\" y=\"478\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">9</text>\n<text x=\"0\" y=\"528\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">10</text>\n<text x=\"0\" y=\"578\" font-size=\"10\" text-anchor=\"start\" dy=\"0em\">11</text>\n</svg>"
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ub = (pcvl.Circuit(2)\n",
" // pcvl.BS(theta=pcvl.Parameter(\"theta\"))\n",
" // (0, pcvl.PS(phi=pcvl.Parameter(\"φ_a\"))))\n",
"\n",
"pc_norm = pcvl.Circuit.decomposition(u, ub, shape=\"triangle\")\n",
"pcvl.pdisplay(pc_norm, compact=True, render_size=0.5)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}