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Issue #1208 Test #106

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Test under issue #1208
mlaguna10 Mar 23, 2020
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mlaguna10 Apr 1, 2020
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333 changes: 333 additions & 0 deletions examples/Pauli-X, Y, Z and S,T Quantum Gates using QuTiP (Test under #1208).ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"from qutip import *\n",
"from qutip.qip import *\n",
"from IPython.display import Image"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Pauli-X, Y and Z Quantum Gates"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Pauli-X gate is one of the most basic and fundamentals gates in quantum circuits. The Pauli-X gate is a single-qubit rotation through pi radians around the x-axis. Here you can see how to create this gate through a QObj."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 1.0\\\\1.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
"Qobj data =\n",
"[[0. 1.]\n",
" [1. 0.]]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x_gate()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Pauli-Y gate is a single-qubit rotation through pi radians around the y-axis. Here you can see how to create this gate through a QObj."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & -1.0j\\\\1.0j & 0.0\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
"Qobj data =\n",
"[[0.+0.j 0.-1.j]\n",
" [0.+1.j 0.+0.j]]"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_gate()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Pauli-Z gate is a single-qubit rotation through pi radians around the z-axis. Here you can see how to create this gate through a QObj."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & -1.0\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
"Qobj data =\n",
"[[ 1. 0.]\n",
" [ 0. -1.]]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"z_gate()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## S and T Quantum Gates"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The S gate is also known as the phase gate or the Z90 gate, because it represents a 90 degree rotation around the z-axis. Here you can see how to create this gate through a QObj."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & -1.0j\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\n",
"Qobj data =\n",
"[[1.+0.j 0.+0.j]\n",
" [0.+0.j 0.-1.j]]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s_gate()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The T gate is just another phase gate that satisfies the property S=T*T. Here you can see how to create this gate through a QObj."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & (0.707+0.707j)\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\n",
"Qobj data =\n",
"[[1. +0.j 0. +0.j ]\n",
" [0. +0.j 0.70710678+0.70710678j]]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t_gate()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Adding previous gates to a QubitCircuit"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Gate(X, targets=[0], controls=None)]"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"q = QubitCircuit(1)\n",
"q.add_gate(\"X\", targets=[0])\n",
"q.gates"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Gate(Y, targets=[0], controls=None)]"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"q = QubitCircuit(1)\n",
"q.add_gate(\"Y\", targets=[0])\n",
"q.gates"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Gate(Z, targets=[0], controls=None)]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"q = QubitCircuit(1)\n",
"q.add_gate(\"Z\", targets=[0])\n",
"q.gates"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Gate(S, targets=[0], controls=None)]"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"q = QubitCircuit(1)\n",
"q.add_gate(\"S\", targets=[0])\n",
"q.gates"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Gate(T, targets=[0], controls=None)]"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"q = QubitCircuit(1)\n",
"q.add_gate(\"T\", targets=[0])\n",
"q.gates"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "qutip-dev-py3",
"language": "python",
"name": "qutip-dev-py3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.1"
}
},
"nbformat": 4,
"nbformat_minor": 4
}