examples/photonics/3_Time_domain_photonic_circuits.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "attachments": {
    "oneloop.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Time-domain photonic circuits\n",
    "=============================\n",
    "\n",
    "*Authors: Fabian Laudenbach, Josh Izaac, Theodor Isacsson and Nicolas\n",
    "Quesada*\n",
    "\n",
    "We introduce the basic ideas of time-domain photonic\n",
    "systems together with the time-domain module of StrawberryFields,\n",
    "``strawberryfields.tdm``. Time-domain multiplexing allows for the\n",
    "creation of massive quantum systems having millions of entangled modes\n",
    "as shown in a number of recent experimental demonstrations [1-4].\n",
    "To motivate this architecture we follow Takeda et al. [1]  and\n",
    "study the one loop setup shown in the picture below:\n",
    "\n",
    "![oneloop.png](attachment:oneloop.png)\n",
    "\n",
    "We will first write a short standard StrawberryFields program implementing\n",
    "this. Then we will progressively modify the way this circuit is\n",
    "implemented until we are able to write it directly as a [``TDMProgram``](https://strawberryfields.readthedocs.io/en/stable/code/api/strawberryfields.TDMProgram.html).\n",
    "\n",
    "Having understood the basics of time-domain programs we will then construct a generic\n",
    "single-loop function that can be used to simulate arbitrary long programs using only two\n",
    "modes! We will use this machinery to investigate bipartite EPR states and then\n",
    "multipartite GHZ states. An important take away of this tutorial is that one can sample\n",
    "efficiently Gaussian circuits containing millions of modes with the equivalent\n",
    "computation effort of sampling Gaussian circuits with just a handful of modes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An instruction set for the time-domain architecture\n",
    "---------------------------------------------------\n",
    "\n",
    "To introduce the time domain architecture we will simulate the setup in\n",
    "the figure. We can summarize the setup as the following set of\n",
    "intructions:\n",
    "\n",
    "1. The ``i+1`` mode is squeezed by a certain amount ``r``.\n",
    "2. The ``i+1`` mode undergoes a beamsplitter transformation with its\n",
    "   preceding mode, labeled by ``i``, by a certain angle ``alpha[i]``.\n",
    "   This beamsplitter has the effect of switching in and out of the loop\n",
    "   the modes ``i+1`` and ``i`` respectively.\n",
    "3. The ``i+1`` mode has entered the loop after the beamsplitter\n",
    "   transformation and is rotated by angle ``phi[i]``.\n",
    "4. After interacting with the ``i+1`` mode, the mode in the previous\n",
    "   time bin ``i`` leaves the loop and then its rotated quadrature (by angle\n",
    "   ``theta[i]``) is measured using a homodyne detector.\n",
    "\n",
    "This circuit falls within the time-domain description because we are\n",
    "implicitly assuming that the modes are flying through the optical elements\n",
    "(squeezer, beamsplitter, rotation, measurement) in the figure above.\n",
    "Note that the loop in the figure corresponds physically to a delay line,\n",
    "typically implemented using propagation in free space or in an optical fiber.\n",
    "Thus unlike in many other physical implementations\n",
    "our modes are not labeled by a position in space but by a time label that\n",
    "tells us when they arrived to a particular optical element.\n",
    "\n",
    "Before actually trying to take advantage of the time-domain description\n",
    "of the circuit we will write a brute force simulation using the\n",
    "standard [``Program``](https://strawberryfields.readthedocs.io/en/stable/code/api/strawberryfields.Program.html).\n",
    "\n",
    "We will use ``n`` modes to represent ``n`` timebins and implement the\n",
    "setup described by the figure using a standard StrawberryFields\n",
    "program.\n",
    "\n",
    "Since we will be using a Gaussian circuit this implies that we will be using\n",
    "a covariance matrix of size ``2n`` times ``2n`` to represent our state. Thus,\n",
    "if we have for example ``n=1000`` modes we will have on the order of four million\n",
    "real numbers stored in memory. We will however, just stick to ``n=20`` for this\n",
    "concrete example.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import strawberryfields as sf\n",
    "from strawberryfields.ops import Sgate, BSgate, Rgate, MeasureHomodyne\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we assume that the parameters of the squeezing gate $(S)$\n",
    "and the angles of the beamsplitter $(BS)$ and rotation $R$\n",
    "do not change with the timebin.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We set the seed to facilitate later comparison\n",
    "# since the samples are stochastic.\n",
    "np.random.seed(42)\n",
    "n = 20\n",
    "\n",
    "r = 1.0\n",
    "length = n - 1\n",
    "alpha = [np.pi / 4] * length\n",
    "phi = [0] * length\n",
    "theta = [0] * length\n",
    "\n",
    "prog0 = sf.Program(n)\n",
    "with prog0.context as q:\n",
    "    for i in range(n - 1):\n",
    "        Sgate(r) | q[i + 1]\n",
    "        BSgate(alpha[i]) | (q[i], q[i + 1])\n",
    "        Rgate(phi[i]) | q[i + 1]\n",
    "        MeasureHomodyne(theta[i]) | q[i]\n",
    "eng0 = sf.Engine(\"gaussian\")\n",
    "result0 = eng0.run(prog0)"
   ]
  },
  {
   "attachments": {
    "unrolled.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can look at an unrolled version of the program above in terms of\n",
    "a circuit diagram as\n",
    "\n",
    "![unrolled.png](attachment:unrolled.png)\n",
    "\n",
    "where, for clarity, we have reduced the number of displayed modes to ``n=5``.\n",
    "\n",
    "Finally, we can also look at the samples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.10417347  0.60228311 -0.00316101  0.34561221  0.25296546 -0.13280689\n",
      "  -0.67985316 -0.19192785  0.12600941 -0.51235116 -0.07813559 -0.52072239\n",
      "   0.04318271  0.13989725 -0.10611505  0.68226231 -0.38850925 -0.44870008\n",
      "  -0.72062428]]\n"
     ]
    }
   ],
   "source": [
    "print(result0.samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this program we follow each and every time-bin mode (a total of\n",
    "``n=20`` modes) as they progress through the different operations.\n",
    "However, at most only two modes are interacting at the same time. The\n",
    "rest of the modes either have not been squeezed (and thus are in the\n",
    "vacuum state) or have been measured (and thus reset to vacuum).\n",
    "\n",
    "Reducing simulation resources: shifting modes\n",
    "-----------------------------------------------\n",
    "\n",
    "Instead of keeping track of the modes using labels telling us their time\n",
    "bin, we can label them in terms of the position that they occupy in the\n",
    "circuit above. A convenient choice of labels is to look at the two modes\n",
    "that enter into the beamsplitter. We can use ``0`` for the mode that\n",
    "enters in the top port of the beamsplitter and which has been\n",
    "circulating in the loop. We can use the label ``1`` for the mode that\n",
    "has just been squeezed and is about to enter the beamsplitter in the\n",
    "bottom port. These two modes, which have fixed positions in the circuit,\n",
    "we call concurrent modes; they are, at all times, the only two modes\n",
    "that are not in vacuum in the circuit.\n",
    "\n",
    "To make a closed loop of modes going in and out of the circuit one can\n",
    "recycle the mode that is measured (mode ``0``) and plug it back in as a\n",
    "vacuum mode re-entering the circuit. As it turns out the Gaussian\n",
    "backend of Strawberry Fields automatically resets to vacuum a mode that\n",
    "has been measured thus the resetting is automatically taken care of.\n",
    "\n",
    "To implement the recycling we will need a function that takes the mode\n",
    "that is measured (which sits at the  beginning of the mode list ``q``)\n",
    "and moves it back to the end of the list after it is measured.\n",
    "This functionality is\n",
    "provided by the function ``shift_by`` in the module\n",
    "``strawberryfield.tdm.tdmprogram`` as illustrated below:\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 0]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from strawberryfields.tdm.program import shift_by\n",
    "\n",
    "l = [0, 1, 2, 3, 4]\n",
    "shift_by(l, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now ready to simulate an ``n=20`` mode circuit using only two\n",
    "concurrent modes:\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.72062428 -0.44870008]]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(42)  # We set the seed to facilitate comparison\n",
    "prog1 = sf.Program(2)\n",
    "n = 20\n",
    "with prog1.context as q:\n",
    "    for i in range(n - 1):\n",
    "        Sgate(r) | q[1]\n",
    "        BSgate(alpha[i]) | (q[0], q[1])\n",
    "        Rgate(phi[i]) | q[1]\n",
    "        MeasureHomodyne(theta[i]) | q[0]\n",
    "        # Note that only position 0 of q is measured\n",
    "        q = shift_by(q, 1)\n",
    "eng1 = sf.Engine(\"gaussian\")\n",
    "result1 = eng1.run(prog1)\n",
    "print(result1.samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though we measured ``n-1`` times we only get 2 values. This is\n",
    "because the ``samples`` attribute only contains the last ever measured\n",
    "value(s) in our modes; since we only have two concurrent modes we only get\n",
    "two numbers. To obtain the complete sample record we use the attribute\n",
    "``samples_dict``, which contains all measured samples inside of a dict.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: [array([-0.10417347]), array([-0.00316101]), array([0.25296546]), array([-0.67985316]), array([0.12600941]), array([-0.07813559]), array([0.04318271]), array([-0.10611505]), array([-0.38850925]), array([-0.72062428])], 1: [array([0.60228311]), array([0.34561221]), array([-0.13280689]), array([-0.19192785]), array([-0.51235116]), array([-0.52072239]), array([0.13989725]), array([0.68226231]), array([-0.44870008])]}\n"
     ]
    }
   ],
   "source": [
    "print(result1.samples_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we obtain the same samples as in ``result0.samples`` except\n",
    "that they are ordered in a slightly different arrangement. We can put\n",
    "them in the correct order by using ``reshape_samples``\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: array([[-0.10417347,  0.60228311, -0.00316101,  0.34561221,  0.25296546,\n",
       "         -0.13280689, -0.67985316, -0.19192785,  0.12600941, -0.51235116,\n",
       "         -0.07813559, -0.52072239,  0.04318271,  0.13989725, -0.10611505,\n",
       "          0.68226231, -0.38850925, -0.44870008, -0.72062428]])}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from strawberryfields.tdm.program import reshape_samples\n",
    "\n",
    "reshape_samples(result1.samples_dict, [0], [2], n - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second argument ``[0]`` gives the label of the\n",
    "concurrent mode where a measurement happened,\n",
    "while the third argument ``[2]`` indicates, for this simple one loop program,\n",
    "that there are only two concurrent modes in a single loop.\n",
    "Finally, the last argument gives the information on the number of\n",
    "time bins measured. Notice that it is ``n-1`` and not ``n``.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the measurement outcomes are now attached to the only mode\n",
    "that we ever measured, namely ``0``. Note that in ``result1.samples_dict``\n",
    "the samples are attached to different modes. This is an artifact of the\n",
    "recycling.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By recycling the modes we are now able to simulate very long circuits\n",
    "with just two modes. Going back to our hypothetical one thousand mode example,\n",
    "we would need to keep in memory millions of real numbers, instead by using\n",
    "a time-domain strategy where we only worry about concurrent modes we only ever\n",
    "need to consider covariances matrices of size four by four, which results\n",
    "in massive speed and memory gains!\n",
    "\n",
    "\n",
    "The TDMProgram\n",
    "----------------\n",
    "\n",
    "Rather than performing the mode shifting and sample reshaping manually,\n",
    "Strawberry Fields provides the [``TDMProgram``](https://strawberryfields.readthedocs.io/en/stable/code/api/strawberryfields.TDMProgram.html) program class for automating this procedure, making it easy to construct and simulate time-domain multiplexing algorithms.\n",
    "\n",
    "In this class one needs to specify the number of\n",
    "active modes (``N=2`` for the example above) and then the class takes\n",
    "care of automatically shifting the modes and reshaping the samples. Thus\n",
    "the program above could have been rewritten as\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[-0.10417347  0.60228311 -0.00316101  0.34561221  0.25296546\n",
      "   -0.13280689 -0.67985316 -0.19192785  0.12600941 -0.51235116\n",
      "   -0.07813559 -0.52072239  0.04318271  0.13989725 -0.10611505\n",
      "    0.68226231 -0.38850925 -0.44870008 -0.72062428]]]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(42)  # We set the seed to facilitate comparison\n",
    "N = 2  # Number of concurrent modes\n",
    "prog2 = sf.TDMProgram(N=N)\n",
    "\n",
    "with prog2.context(alpha, phi, theta) as (p, q):\n",
    "    Sgate(r, 0) | q[1]\n",
    "    BSgate(p[0]) | (q[0], q[1])\n",
    "    Rgate(p[1]) | q[1]\n",
    "    MeasureHomodyne(p[2]) | q[0]\n",
    "eng2 = sf.Engine(\"gaussian\")\n",
    "result2 = eng2.run(prog2)\n",
    "print(result2.samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a ``TDMProgram`` we need to specify the number of concurrent modes\n",
    "``N``. Then we pass to the ``context`` the sequences of\n",
    "the different parameters that will be used in the program, in our case\n",
    "the lists ``alpha``, ``phi`` and ``theta``. The three variables in the\n",
    "list ``p`` will cycle through the corresponding values of these lists.\n",
    "For example, ``p[0]`` will go through the values of ``alpha`` as the\n",
    "simulation progresses.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A single-loop architecture\n",
    "--------------------------\n",
    "\n",
    "We will now write a simple function that\n",
    "encapsulates the single loop architecture using a ``TDMprogram``. Then we\n",
    "will use it to generate samples of interesting quantum states and\n",
    "investigate their correlations.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def singleloop(r, alpha, phi, theta, shots):\n",
    "    \"\"\"Single loop program.\n",
    "\n",
    "    Args:\n",
    "        r (float): squeezing parameter\n",
    "        alpha (Sequence[float]): beamsplitter angles\n",
    "        phi (Sequence[float]): rotation angles\n",
    "        theta (Sequence[float]): homodyne measurement angles\n",
    "        shots (int): number of times the circuit is sampled\n",
    "    Returns:\n",
    "        list: homodyne samples from the single loop simulation\n",
    "    \"\"\"\n",
    "\n",
    "    prog = sf.TDMProgram(N=2)\n",
    "    with prog.context(alpha, phi, theta) as (p, q):\n",
    "        Sgate(r, 0) | q[1]\n",
    "        BSgate(p[0]) | (q[0], q[1])\n",
    "        Rgate(p[1]) | q[1]\n",
    "        MeasureHomodyne(p[2]) | q[0]\n",
    "    eng = sf.Engine(\"gaussian\")\n",
    "    result = eng.run(prog, shots=shots)\n",
    "    # We only want the samples from concurrent mode 0\n",
    "    return result.samples_dict[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the function we just developed to reproduce for the fourth\n",
    "time the results of our very simple experiment:\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.10417347,  0.60228311, -0.00316101,  0.34561221,  0.25296546,\n",
       "        -0.13280689, -0.67985316, -0.19192785,  0.12600941, -0.51235116,\n",
       "        -0.07813559, -0.52072239,  0.04318271,  0.13989725, -0.10611505,\n",
       "         0.68226231, -0.38850925, -0.44870008, -0.72062428]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(42)  # We set the seed to facilitate comparison\n",
    "singleloop(r, alpha, phi, theta, 1)  # We want 1 shot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generation of EPR states\n",
    "------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the single loop architecture we can easily generate\n",
    "Einstein-Podolsky-Rosen (EPR) states [5]. In this section we will create\n",
    "this bipartite state and probe it using homodyne measurements.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = 2.0\n",
    "alpha = [np.pi / 4, 0]\n",
    "phi = [0, np.pi / 2]\n",
    "theta = [0, 0]  # We will measure the positions by setting theta = [0,0]\n",
    "shots = 2500\n",
    "\n",
    "samplesEPRxx = singleloop(r, alpha, phi, theta, shots)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To process the samples we simply transpose the array in which they\n",
    "are stored. This gives us easier access to the values corresponding\n",
    "to the two halves of an EPR state.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "samplesxx = samplesEPRxx.T\n",
    "x0 = samplesxx[0]\n",
    "x1 = samplesxx[1]\n",
    "\n",
    "# We now want to look at the samples\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "plt.plot(x0, x1, \".\")\n",
    "plt.xlabel(r\"$x_0$\")\n",
    "plt.ylabel(r\"$x_{1}$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can put this observation in more quantitative terms by looking at the\n",
    "variance of $x_1-x_0$:\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.036501533171290304"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_var_xx = np.var(x0 - x1)\n",
    "sample_var_xx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As it turns out the variance of the operator $N_1 = x_1 - x_0$ is\n",
    "related to the amount of squeezing used to prepare the state. One can\n",
    "easily find that $\\text{Var}(N_1) = 2 e^{-2 r}$.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03663127777746836"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expected_var_xx = 2 * np.exp(-2 * r)\n",
    "expected_var_xx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the literature, the operator $N$ for which one finds a relation\n",
    "like the one above, is called a *Nullifier* of the state. A way to\n",
    "understand this name is that the variance of this operator approaches\n",
    "zero (or *nullifies*) as the squeezing in the state grows [1].\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The EPR state has a second nullifier, $N_2 = p_1+p_2$. We can\n",
    "confirm this by running our circuit again, but this time measuring\n",
    "in the $P$ quadrature\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = [np.pi / 2, np.pi / 2]  # Now we homodyne the p-quadratures by setting thr angle to pi/2\n",
    "samplesEPRpp = singleloop(r, alpha, phi, theta, shots)\n",
    "\n",
    "samplespp = samplesEPRpp.T\n",
    "p0 = samplespp[0]\n",
    "p1 = samplespp[1]\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "plt.plot(p0, p1, \".\")\n",
    "plt.xlabel(r\"$p_0$\")\n",
    "plt.ylabel(r\"$p_{1}$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now calculate the sample variance and the expected variance,\n",
    "except for the effect of finite size statistics, they are almost identical\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.03548400449860628, 0.03663127777746836)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(p0 + p1), 2 * np.exp(-2 * r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generating GHZ states\n",
    "-----------------------\n",
    "\n",
    "The GHZ states (named after Greenberger, Horne and Zeilinger) [6] can be\n",
    "thought as an $n$-partite generalization of the EPR states [7]. We\n",
    "will prepare these states using the single loop architecture\n",
    "encapsulated in the function ``singleloop`` defined before.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.52220534, -1.23988693, -1.26801579, -1.23267925, -1.26416284,\n",
       "        -1.2843186 , -1.26506774, -1.28691118, -1.24585304, -1.23932062,\n",
       "        -1.2995661 ]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 10\n",
    "vac_modes = 1  # This is an ancilla mode that is used at the beginning of the protocol\n",
    "shots = 1\n",
    "r = 4\n",
    "alpha = [np.arccos(np.sqrt(1 / (n - i + 1))) if i != n + 1 else 0 for i in range(n + vac_modes)]\n",
    "alpha[0] = 0.0\n",
    "phi = [0] * (n + vac_modes)\n",
    "phi[0] = np.pi / 2\n",
    "theta = [0] * (n + vac_modes)  # We will measure first all the states in the X quadrature\n",
    "\n",
    "singleloop(r, alpha, phi, theta, shots)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that all the *sampled* positions are the\n",
    "same. We can also sample our state in the $p$ basis\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -0.52960821,  29.02743432, -93.3646886 ,  32.95431112,\n",
       "        -39.99464345,  45.80328279, -52.37852011,  59.10381464,\n",
       "         -8.2737421 ,   7.31907984,  19.76999235]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = [np.pi / 2] * (n + vac_modes)  # Now we measure in p quadrature\n",
    "\n",
    "samplep = singleloop(r, alpha, phi, theta, shots)\n",
    "samplep"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There does not seem to be anything interesting going on when we look at\n",
    "the $p$ quadratures, yet if we consider the sum of the sampled\n",
    "values of the momenta we find that the momenta add up to approximately\n",
    "zero:\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(samplep[1:])  # Note that we exclude the first element, the \"vacuum mode\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, like for the EPR state defined before, one can introduce\n",
    "nullifiers for the GHZ states such as\n",
    "$N_k = x_k - x_n$ for $1 \\leq k < n$,\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now generate many samples and statistically verify that the variances\n",
    "of the nullifier decay exponentially with the amount of squeezing\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Collect x-samples\n",
    "shots = 1000\n",
    "theta = [0] * (n + vac_modes)\n",
    "samplesGHZx = singleloop(r, alpha, phi, theta, shots)\n",
    "\n",
    "nullifier_X = lambda sample: (sample - sample[-1])[vac_modes:-1]\n",
    "val_nullifier_X = np.var([nullifier_X(x) for x in samplesGHZx], axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sample variances of the X nullifiers are\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00068616, 0.00066431, 0.00066148, 0.00068736, 0.00064939,\n",
       "       0.00071838, 0.00067035, 0.00068083, 0.00066421])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val_nullifier_X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While their expected value is\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0006709252558050237"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * np.exp(-2 * r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conclusion and final remarks\n",
    "----------------------------\n",
    "We have introduced the basic ideas of time-domain circuits by gradually\n",
    "transforming a simple one-loop ``n``-mode optical setup from a brute\n",
    "force simulator to a time-domain simulator using the [``TDMProgram``](https://strawberryfields.readthedocs.io/en/stable/code/api/strawberryfields.TDMProgram.html).\n",
    "Using the later class we achieve significant computational savings: a brute force\n",
    "Gaussian simulator requires resources scaling quadratically with the number of modes,\n",
    "a time-domain approach requires only constant (and very modest) resources.\n",
    "We have used this highly efficient implementation to study the correlations\n",
    "of EPR and GHZ states, the canonical bipartite and multipartite entangled\n",
    "states in the continuous-variable domain.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "References\n",
    "----------\n",
    "\n",
    "[1]    S. Takeda, T. Kan and A. Furusawa. On-demand photonic entanglement synthesizer.\n",
    "    Science Advances, 2019. doi:10.1126/sciadv.aaw4530 .\n",
    "\n",
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  }
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