{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# States and measurements" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Qubit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Qubits are vectors in $\\mathbb C^2$ and so they are defined by two complex numbers. One degree of freedom is removed because we do not care about complex unit prefactor of the vector and another is removed because we want our states to be normalized, $\\langle\\psi|\\psi\\rangle=1$. We will now look at different ways of looking at states in *Qiskit*." ] }, { "cell_type": "code", "execution_count": 117, "metadata": {}, "outputs": [], "source": [ "import qiskit\n", "import random\n", "import math\n", "from qiskit.visualization import plot_histogram, plot_state_city, plot_state_paulivec, plot_bloch_vector\n", "from qiskit.visualization import plot_state_hinton, plot_state_qsphere, plot_bloch_multivector\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us start with a simple circuit having one qubit and no classical register." ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circ = qiskit.QuantumCircuit(1, 1)\n", "circ.h(0)\n", "circ.draw(output=\"mpl\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can define measurement separately." ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "measure_z = qiskit.QuantumCircuit(1, 1)\n", "measure_z.measure(0, 0)\n", "measure_z.draw(output=\"mpl\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The basic circuit can now be composed with the measurement into larger circuit." ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAL4AAAB7CAYAAADKUTqaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAACQlJREFUeJzt3WtMU3kexvGnXAaRcil0AEG8QNVAFVYBB42XdGaTQdcNBtigKCqKBMOqYDQriSYbX8Au4rqbGMcuY4yrYwwIRKImBhIhJviixkBEGxEhoRBuozDKrLhiuy9QnFouRVtO4f98EhI8PaU/zdd/zmnLqcxkMplAJBgnqQcgkgLDJyExfBISwychMXwSEsMnITF8EhLDJyExfBISwychMXwSEsMnITF8EhLDJyExfBISwychMXwSEsMnITF8EhLDJyExfBISwychMXwSEsMnITF8EhLDJyExfBKSi9QDTAc5P0nzuP/c9mX3l8lkthlkEqbLpVi54pOQGD4JieGTkBg+CYnhk5AYPgmJ4dNnk8vlcHKangnxeXyCUqlEUlISYmNjsXTpUnh4eGBwcBB6vR73799HeXk52tvbze7j7e2Nqqoq6PV6pKenw2g0SjT955Hxw98mNlNfwAoODkZ+fj5SUlLg5uY25n5DQ0OorKxEXl4empqaRqKPjY3Fs2fPsGrVKvT29gLgC1iTZjQaUVRUhEWLFmHWrFmIiopCbW0tlixZgszMTKnHm5Qf/xyExprzZttMJhN+yPBCs65CoqnMbd++HY2NjdixYwdcXV1x48YNHDhwAOvWrUNkZCRWr16NrKwslJSUwGQyITExEfX19Th69KhZ9BqNZiT66cRhDnV2796NiooKHD9+HNHR0airq8PWrVvR29uLQ4cOST2e1QZedODX/k58PS/KbPsvPS343+ArBITGSDTZR0eOHEFhYSEAoLKyEjk5OWhtbbXY7969e9BqtQgMDERBQQF27dqFgoICABiJ3mAwTOnstuIQ4V+5cgUXL15ETU0N1q9fDwDQaDR48OABysvLER0dLfGE1utu0UHm5Ay/uWqz7T+3NWC2dwA8/UIkmmxYamoqCgsLYTQakZ2djXPnzk14n66uLuTk5GDNmjVQqVQAgKtXr07b6AEHOdQpKChAfHz8SPQfqFQquLq6YtmyZRJNNnndLTooAhfD5St3s+29bQ3wXyjtaj9nzhycOXMGALB//36rogc+nsiqVCp0dXUBAA4fPoyIiAi7zWpvkq/47e3taGxsRG5ursVtbW1tUKvV4554fSlr3sF48LL1J2zdLTr0dzdDm6U02/72zQBi/phn89km48SJE1AoFLh58ybOnj1r1X0+PZHVaDQ4duwYMjMzUVRUhI0bN9p15smy9uTaIcIHgMDAQLPtr1+/Rm1trcU/rKPrbr2PbxL/ivA1O8y2/5S3DAESrvg+Pj7Ytm34aaLRFpnRjBa9wWBAXl4e0tLSsGHDBoSGhqKlpcWeo9uF5Ic6SuXwytjU1GS2vbCwEJ2dnVixYoVdH99kMk34Za3+rma8+bUP8yO/h6ff3JGvd28H8ea//fCf5ImtNbNZO3dCQgLc3d1RVVWFp0+fTvjYY0UPAC9evEBJSQkAICUlxaYz2/LvPB7JV/zQ0FBERkYiPz8fvr6+CA4OxrVr13Dr1i0AmHYnti5usy2e0el8Wge5Xwg8vAMkmgyIiRn+T1ddXT3hvuNF/0FVVRV27tw58nOnG8lXfCcnJ5SWlkKtVmPfvn1IT0+HUqlEdnY2XFxcEBkZKfWIVutu0SFgYSycnM3Xk87me5Ie5gCAWj38LFNDQ8O4+1kTPQDU19eb/dzpRvIVHwAWL16MO3fumG1LS0tDeHg43N3dx7iX41m3/R+jbv82/YcpnsTSpUuXUFdXB71eP+5+p06dmjB6YPjcLD8/Hz09PfYY1+4c9i0L4eHhiIuLw4ULF6QeZca+ZWE0CoUCxcXFyM3N/azn6R00JwuSH+qMZmBgAE1NTXY/sSVLfX19SE5OntYvTlnDIQ51PiWXy/Hu3Tupx6AZzCFXfCJ7Y/gkJIZPQmL4JCSGT0Ji+CQkhk9CcthXbmnqHf37vwEAf/tLptn3MxFXfBISwychMXwSEsMnITF8EhLDJyExfBISwychMXwSEsMnITF8EhLDJyExfBISwychMXwSEsMnm6mpqYFarYZKpUJGRoZDXxuJ4ZNNGI1GZGRkoLS0FM3NzXj58iUuX74s9VhjYvhkEzqdDkFBQSMfD7Rnzx6UlZVJPNXYGD7ZRHt7O0JCPn6w3bx58xz6+psOee1Mmhr9Lwfwn/Lb+PS3rv91oWzU7/+0cT2CAsw/2+sDk8lkdnVmR/9Vbq74AvPxkiMoQInOnufo7Hk+sv3T7zt7nsNLPnvM6AEgJCQEbW1tI382GAyYO3eufQa3AYYvuO/XxcLtK9dx93GSyfAHTdy4+8TExKCjowOPHz8GAJw/fx6JiYk2m9PWGL7gPD1mQ7Nq+bj7xK1Qw1+pGHcfZ2dnFBcXIzk5GWFhYZDL5UhLS7PlqDbF6+oQ3g4N4fSPpXjxyyuL29xnueFIZgpmu8+SYDL74YpPcHVxwQbNN6Pe9vs10TMueoDhW7h+/To2bdoEf39/uLm5Yf78+UhNTcXDhw+lHs2uli5eiIUhc8y2fe3rg7jfRUg0kX0x/PeGhoawZcsWbN68GQ0NDUhMTMTBgwexfPlylJWVoaOjQ+oR7Uomk2HTd6vw24+L2/RtHJydZ2YiPMZ/LysrC1qtFnv37sXp06fh4eExcpvBYICPjw88PT3t8tgfrlNJX87aa33yBSwAd+/ehVarRXx8PLRarcXHZP72FUmaGbjiA0hKSkJ5eTnq6+sRFRUl9TiS6/65DwETPH053TF8AF5eXvDz80Nra6skj89DHdux9lBnZp65TEJ/fz9evXqFBQsWSD0KTSHhV/y+vj74+voiIiICjx49knocmiLCr/gKhQJhYWHQ6/Worq62uP3JkycSTEX2JvyKDwAlJSVISUmBs7MzEhISoFKp0NPTg7q6OkRERKCiokLqEcnGGP57t2/fxsmTJ6HT6TA4OAh/f3+sXLkSOTk5WLt2rdTjkY0xfBKS8Mf4JCaGT0Ji+CQkhk9CYvgkJIZPQmL4JCSGT0Ji+CQkhk9CYvgkJIZPQmL4JCSGT0Ji+CQkhk9CYvgkJIZPQmL4JCSGT0Ji+CQkhk9CYvgkJIZPQmL4JCSGT0Ji+CSk/wOQRmeqI+NdNQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circZ = circ + measure_z\n", "circZ.draw(output=\"mpl\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have seen this circuit previously and we know what we will measure." ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "backend = qiskit.Aer.get_backend(\"qasm_simulator\")\n", "job = qiskit.execute(circZ, backend, shots=1024)\n", "plot_histogram(job.result().get_counts())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Previous simulation performed 1024 experimental runs on given circuit, which is something that a real experiment (and real quantum computer) would give us. But this information is not complete - single measurement gives us only partial information and only in a statistical form. What we find are the probabilities of obtaining given outcomes. In previous case in circ we prepared the $|+\\rangle=\\frac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle)$ state. But the measurements measures in $\\{|0\\rangle,|1\\rangle\\}$ basis. The probabilities are given by the *Born rule:* having a state $|\\psi\\rangle$, the probability of measuring it in state $|\\phi\\rangle$ is $p(\\phi | \\psi)=\\|\\langle\\phi | \\psi\\rangle\\|$. In this case we find $p(0 | +)=p(1| +)=1/2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Previous description via simulation does offer a good way of comparing with experiments, but we can gat full information about the state (before measurement) by invoking the statevector_simulator backend." ] }, { "cell_type": "code", "execution_count": 105, "metadata": {}, "outputs": [], "source": [ "backend = qiskit.Aer.get_backend('statevector_simulator')\n", "job = qiskit.execute(circ, backend)\n", "result = job.result()\n", "psi = result.get_statevector(circ)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The output state (before measurement) is now stored in psi and we can visualise it in several different ways. For now we will use Bloch vector representation - each state can be represented as a vector on a sphere (vis. two free parameters described at the beginning)." ] }, { "cell_type": "code", "execution_count": 106, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_bloch_multivector(psi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Other forms include functions plot_state_paulivec(psi), plot_state_hinton(psi), plot_state_city(psi) and others. Some of these also have interactive versions, for example:" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [], "source": [ "from qiskit.visualization import iplot_state_city" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "iplot_state_city(psi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Random state" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sometimes it is useful to be able to prepare a random state. States $|0\\rangle$, $|1\\rangle$, $|+\\rangle$ or $|-\\rangle$ are just some possibilities. Since the initial state is always $|0\\rangle$ to get other states, just like above, we need to transform them. We saw that we could use $H$ to get the $|+\\rangle$ state. We can use $\\sigma_x$ that acts as NOT, etc. Useful is a set of unitary rotations of qubits." ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rotx = qiskit.QuantumCircuit(1)\n", "rotx.rx(0.823, 0)\n", "job = qiskit.execute(rotx, backend)\n", "result = job.result()\n", "plot_bloch_multivector(result.get_statevector(rotx))" ] }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "roty = qiskit.QuantumCircuit(1)\n", "roty.ry(math.pi / 2, 0)\n", "job = qiskit.execute(roty, backend)\n", "result = job.result()\n", "plot_bloch_multivector(result.get_statevector(roty))" ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rnd_circ = qiskit.QuantumCircuit(1)\n", "rnd_circ.rx(math.pi * random.random(), 0)\n", "rnd_circ.ry(math.pi * random.random(), 0)\n", "rnd_circ.ry(math.pi * random.random(), 0)\n", "rnd_circ.draw(output=\"mpl\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.0" } }, "nbformat": 4, "nbformat_minor": 2 }