time-loops.ipynb

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   "source": [
    "# Coding a quantum time-machine: testing the power of closed-timelike-curves using quantum circuits in Qiskit"
   ]
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   "source": [
    "Welcome to the code tutorial for the “quantum time-loops” installment of the Paradoxes series on the Qiskit YouTube channel. In this tutorial, we’ll explain how to simulate closed-timelike-curves with quantum circuits. Along the way, we will see how we can resolve classic time-travel paradoxes such as the Grandfather Paradox, and how time-loops could give us vast computational power — allowing us to violate the no-cloning theorem and store large amounts of classical information in a single qubit. By using Qiskit to simulate having access to time-loops using Qiskit, we will see how time-loops let us get around the usual constraints of quantum mechanics, and even break quantum cryptographic protocols.\n",
    "\n",
    "If you haven't already, I recommend you first watch [our video](https://youtu.be/jcC1Ck45Ykw) on the Qiskit YouTube channel, which explains the context of the thought experiment and provides a useful overview of the Qiskit code we’ll use to simulate it in this tutorial. I also suggest reading the blog post (link coming soon) for a deeper look at the background of the thought experiment.\n",
    "\n",
    "Now, let's start by considering a classic time-travel paradox and seeing how to resolve this in quantum mechanics. \n",
    "\n",
    "### The Grandfather Paradox \n",
    "\n",
    "The Grandfather Paradox is a typical time-travel paradox: A time traveler travels to the past and kills their own grandfather, doing so before the grandfather has had the child that will become the time traveler's parent. If the grandfather never creates the human being that will be the time traveler's parent, it means the time traveler was never born in the first place, and therefore never went back in time to kill their grandfather... a paradox!  \n",
    "\n",
    "A solution to the grandfather paradox in quantum mechanics was proposed by David Deutsch in 1991, using a consistency condition. This condition imposes that a system coming out of a time-machine must be identical to the one that went in. It holds whether the system in the time-loop is a qubit, or any other kind of quantum system. \n",
    "\n",
    "### Strange consequences \n",
    "\n",
    "However, the consistency condition leads to a lot of powerful phenomena beyond standard quantum mechanics. For example, with access to a quantum time-loop, you can: \n",
    "1) Violate Heisenberg's uncertainty principle by simultaneously measuring a quantum state in the X basis and the Z basis\n",
    "2) Violate the no-cloning theorem, you can clone as many quantum states as you like\n",
    "3) Store unbounded amounts of classical information, like the complete works of Shakespeare or your entire music collection, in a single qubit\n",
    "4) Break the security of quantum cryptographic protocols like BB84 \n",
    "\n",
    "Let's simulate a time-loop with a quantum circuit to see how we can simulate some of these extra computational powers using Qiskit. "
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    "**A time-loop as a quantum circuit**\n",
    "\n",
    "In the [Qiskit video](https://youtu.be/jcC1Ck45Ykw), I enter a \"time-machine\", and appear in the past. Then I have a conversation with my past self. My past self then goes into the time-machine, and I carry on with the video. Let's model this situation using quantum circuits. \n",
    "\n",
    "I'm going to be using reduced density matrices to describe the states of quantum systems. If you are not familiar with the formalism of density matrices, I recommend reading [the section on density matrices on the Qiskit Learning Platform](https://learn.qiskit.org/course/quantum-hardware/density-matrix). \n",
    "\n",
    "Now I'm going to model myself going into and out of the time-machine as a quantum system. If you want to find out more about the validity of treating macroscopic observers as quantum systems, take a look at my videos on [Schrödinger's cat](https://youtu.be/sBtAe8BsOhA?si=udkFiIvEFTlz7Gvz) and [Wigner's friend](https://youtu.be/TMBK88Mpg5U?si=DMmnqFeNjDZ206Wk). Here I'm going to assume that quantum theory is universal, and we can describe any system as a quantum state. \n",
    "\n",
    "Here is the overall circuit:"
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    "![Screenshot 2023-03-04 at 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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Let's say that my original self that started the video was in the state $\\psi_{in}$, represented by the statevector $|{\\psi_{in}}\\rangle$. \n",
    "\n",
    "Then my future self comes out of the time-machine. I will describe the state of my future self by the density matrix $\\rho_{CTC}$, where CTC stands for closed-timelike-curve, which is the technical term for time-loops in physics. \n",
    "\n",
    "Next, my two selves interact. Since they are quantum systems, they must interact via a unitary interaction, which I have labelled U'. \n",
    "\n",
    "After that, my original self enters the time-machine. To avoid paradoxes, I must enter the time-machine in the same state that I leave the time-machine, so my state as I enter the time-machine must also be $\\rho_{CTC}$. \n",
    "\n",
    "My other self stays and continues with the video, and I have labelled her final state as $\\rho_{out}$.\n",
    "\n",
    "It is helpful to rewrite this circuit in an equivalent form. Let's add a SWAP gate between my two selves before the end of the circuit. This is a valid unitary gate, which swaps the states of two systems. \n",
    "\n",
    "Then I can write my circuit using a unitary U, which is the same as U' but with a SWAP gate at the end. Now the first quantum system begins in psi_in and comes out in $\\rho_{out}$ after the unitary U, and the second quantum system comes out of the time machine in the state $\\rho_{CTC}$, then goes back in to the time-machine in the state $\\rho_{CTC}$, after the unitary U. \n",
    "\n",
    "So in our rewritten circuit, the consistency condition for avoiding \"grandfather paradoxes\" is that the qubit that goes into the time-loop must be in the same state as the qubit that comes out of the time-loop. \n",
    "\n",
    "Mathematically, the reduced state of the system that goes in to the time-loop, $\\rho_{CTC}$, must be equal to the state we get when we let the input state $\\psi_{in}$ and the input state $\\rho_{CTC}$ interact via the unitary U, and then trace out the first system, so the reduced state of the second system remains as $\\rho_{CTC}$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NOtxuMbBOKmX",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "![Screenshot 2023-03-04 at 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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Now, famously, standard quantum mechanics is linear. The consistency condition introduces non-linearity, because the consistent state imposed on the qubit in the time-loop depends on the state of the qubit it interacts with. This non-linearity makes lots of strange things happen that can't occur in standard quantum mechanics without time-loops, which we will now demonstrate using Qiskit!\n",
    "\n",
    "## Coding with Closed-Timelike-Curves\n",
    "\n",
    "Unfortunately, we don't currently have access to time-loops - or even know if they can really exist. My interaction with my past self in the video was artificially made by filming two separate clips and editing them on top of each other, and was pre-prepared to make the interaction self-consistent according to the consistency condition. \n",
    "\n",
    "Similarly, when coding this as a quantum circuit, we have artificially simulate the non-linearity of having access to a time-loop. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3nKL3L0H138-",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "**Distinguishing |0$\\rangle$ and |-$\\rangle$ with one measurement:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tFJR_o3cECBB",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "For our first trick with CTCs, I'll show you how they let us distinguish the quantum states |0$\\rangle$ and |-$\\rangle$ with a single measurement. This protocol was demonstrated in the paper \"Localised closed timelike curves can perfectly distinguish quantum states\" by Todd A. Brun, Jim Harrington, and Mark M. Wilde, which you can read [here](https://arxiv.org/abs/0811.1209).\n",
    "\n",
    "Here's the quantum circuit given in Fig. 1 of the paper:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FhmWrzAINYYM",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![Screenshot 2023-03-04 at 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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IoFz-76QNV6z",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Let's code this in Qiskit. In the code, I'll first ask for user input of \"0\" to prepare the |0$\\rangle$ state and \"-\" to prepare the |-$\\rangle$ state. If the user inputs \"0\", then my code leaves the system qubit as |0$\\rangle$ and the time-loop qubit as |0$\\rangle$, which is the state needed to make the time-loop qubit's input and output states the same according to the consistency condition. \n",
    "\n",
    "If the user inputs \"-\", then my code applies an H and Z gate to the system qubit to prepare it in the |-$\\rangle$ state, and an X gate to the CTC qubit to prepare it in the |1$\\rangle$ state, which is the state needed to satisfy the consistency condition when the input is |-$\\rangle$. \n",
    "\n",
    "I have artifically introduced the non-linearity into the quantum circuits by making the preparation of $\\rho_{CTC}$ depend on the input state $\\psi$, which in a real time-loop would automatically be self-consistent. \n",
    "\n",
    "Let's run this for an input of \"0\" and an input of \"-\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 139
    },
    "id": "PwJEGhES_FIG",
    "outputId": "71a329e8-0fd6-4704-c1e1-1580e643d085",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter '0' to prepare |0> or '-' to prepare |->0\n"
     ]
    },
    {
     "data": {
      "image/png": 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XFNj1MUOvbzVtGpKk2u0obYjadAHa6BnQkgXQNRJQmn6lRS/qW9iWlZXh+PHjtapb2zBXU38fWFpawsfHp1Z91rVGt+Ry+PBhHDhwAGPGjIGFhQW8vb3RtGlTZGVlITMzE+Xl5bC2tsaiRYsqXR+u5urqCg8PD1y4cAGWlpZYunSpzvMSEhLw1VdfYcmSJWjRogXatm2LgoICnD17FiqVCm5ubti0aZPWzN7Pz0/TtoeHB3x9fWFhYYEJEyZgwoQJAIDp06dj586d+Ouvv/Dkk0/CyckJ7dq1Q1lZGS5cuIDr168DAF555RWt8Rw9ehRA45mh67sD1NB7vzQUkgR0HARY2QIXDgKiiotGlPZAlwjAsQG95pycHFy4cAFlZWUoKSnRu9748eMNCnOg4hLlzMzMWi951odGt/X/0qVL2Lx5MxISEpCeno7s7GzcuHEDDg4O8PHxQVhYGCZNmoR27dpV286gQYOwc+dOTJkyBZ9++qnOc5KSkvDzzz9jz549yMjIwNWrV6FUKtGhQwdERkZi2rRpVX74OGvWLCQlJWmWiDZu3Ignn3xSc05xcTG++OILfP/990hNTUVRURFcXFzg5uaGRx99FMOHD0e/fv20XvdDDz0EZ2dnXLt2rVKfGRkZaNeuHVq1aqXzskJ1fRcXF1y9erXar405qCnMozYDtwqBZrbA/FEVx/S5TUBDp8oDLh+ruNtifi4AUTEr7zwUaOFdcfdFc/Mgt8+tSlBQEHbu3ImmTZvWyb1ZTLX1v9EFujFkZGTA19cX9vb2OHPmDJydnU09JLqHPjNzXYEONI5QV0v8X0XAWzcBHn3Z1KOpWl0EOlAR6kOHDkVUVJTR2+b90BuQ6dOno6SkBHPnzmWYmyGre2aZtd0Bev/yi0ICLM1w1koPbt++fdi3b5+ph2FUDPRa+t///odNmzbB398fU6dONfVwSIdH/r1A6GYBMLhL7bfzq0Pd0gLo6gF0bGP8MRLVBQa6HpKSkjBz5kxkZ2fj1KlTsLe3x9q1a832Bj10N9QNpVAAzwQbZyxE9aXRXbZoiISEBCQkJCArKwvh4eHYvXs3unTpYuphERFp4RRTDzNmzNBsICIiMlecoRMRyQQDnYhIJhjoREQywUAnIpIJBjoRkUww0ImIZIKBTkQkEwx0IiKZYKATEckEd4oSkVmzs7Or9NvFHsTSFetxO78ATe3tMP2lZyo9NwY7OzujtFNbDHQiMmuSJBn13uJKaxsoS8qgtLaBvb19pecNGZdciIhkgoFORCQTDHQiIplgoBMRyQQDnYhIJhjoREQywUAnIpIJBjoRkUww0ImIZIKBTkQkEwx0IiKZYKATEckEA52ISCYY6EREMsFAJyKSCQY6EZFMMNCJiGSCv7GIyMwJAZSX1E276j/Lio3btsIKkCTjtkk1Y6ATmbnyEmD3/9Vd+8X5xm+/3zTAQmncNqlmXHIhIpIJBjoRkUww0ImIZIKBTkQkEwx0IiKZYKATEckEA52ISCYY6EREMsFAJyKSCQY6EZFMMNBJllSlQF7Rg7VxswAoLzfOeIjqAwPdzGVkZGDhwoUICQmBu7s7rK2t0bx5c/Ts2RMzZ85Eeno6AOCRRx6BJEm1fpw+fdrgPs2VqhRYFQ98HgfcMTDUc24DH+0Avv2boU4NB2/OZaZKS0vxwQcf4MMPP4RKpYJCoYCbmxv8/f2Rk5OD5ORkJCcnY/ny5Vi+fDkcHBwQEhKi1cadO3dw9OhRAKhUBgBKpRI+Pj4G9zlt2rS6/SIYaMM+IP1Kxd+/iANeDQccbPSvn3Mb+CwOuF0IJGcAzg7AEP86GSqRUTHQzVBpaSmeffZZbNq0CTY2NoiKisKrr76Kli1bas45c+YMli9fjpiYGFy/fh07d+6s1M7333+PZ555Bm5ubti7d6/R+zRXg/2BszkVSyZZt2oX6veGOQC0cQQe9a3b8RIZC5dczNCUKVOwadMmODk54ffff8e8efO0ghUAvL29ER0dje3bt6Nv374620lJSQEAdO3atd76NActHIDJ4UBzu4rn6lCvaflFV5i/2h9oUovZvTk7cjYeA6ZLWP/Hh1WeM3x2E7wZHVp/gyKj4gzdzPz6669YsWIFAGDNmjXo3bt3tecPGDCgyrIjR44AALp161ZvfZoLdah/HqffTF3uYU6NA2foZkQIgbfffhsAMHbsWAwfPvyB2tNnhm7sPs2JvjN1hjnJBQPdjOzcuROpqakAgDlz5jxQW1evXkVWVhaA6mfoxuzTHFUV6uX//vq1snKGOckHl1zMyJYtWwAAPXv2RIcOHR6oLfXs3N7eHt7e3vXSp7nStfyi+Pf3XeargH+zvdGEeVFJAW7lXzP1MKgOMNDNSEJCAgCgf//+D9yWev28S5cuUCiqfiNmzD7N2f2hrp6hN7YwB4B1ce9jXdz7ph4G1QEGuhm5cOECAKBjx44P3Ja+V7gYs099BAYGIjs7u1760sXe2ROhL/8A26atNMduZZ/Ez/Ofwv8V3DDZuKqjtLTFyinG28w1uNd/0K/rMzrL3v3KOJ+h+Pj6oLi00ChtGdvI8a/DvklTZGVnwd3dvdJzU3N1dUVycrJBdRnoZqK4uBgFBQUAgGbNmj1we/pc4WLsPvWRnZ2Ny5cv10tfujQvs9PMztVKy8qRfeUKCm9fNc2gamBjZWfU9tycvdHDN1xnmUJhYZQ+sjIzUVRSYJS2jK28rEzz5+XLlys9b8gY6GZCqVTC2toaKpUKeXl5D9SWSqXCyZMnAVQ/Qzdmn/pydXWtl350aeLSDn1f2qiZnQshIEkSnN06YfS7e7AnZjRU+bkmG19VlJa2ph5CrbVu08ZsZ+gKCwvNn25ubpWem9qDfI8w0M1I586dcfDgQezbtw9jx441uJ3U1FSUlpZCoVDA37/6PevG6lNfhr6VfFC6Lk0c3UvCV4kVa+rNWj+M/y4/UuvbBNSHsmJg9/+ZehS1k346HRZKU49Ct4Wfr8PtvHy0dm2NS5cuVXrekPGyRTPy1FNPAQBiY2ORmZlZ7bkZGRlITEzUWaZeP/fy8oK9vX299GnOqrrOvK2LYTtKicwVA92MTJ48Gd7e3rh16xb69+9fKTyFEDh69CimTZsGPz8/FBXpTh59d4gas09zVdOmIUNvE0BkjrjkYkaaNGmC7du3Y8SIEThx4gQee+wxtGrVCh4eHlCpVLh48SJu3Ki4EkOpVKJHjx4626nNPVyM1ac50ncHaG1vE0BkrjhDNzPe3t44dOgQoqOjER4ejvLychw+fBhnzpyBi4sLnn76aaxbtw45OTlwdnbW2Yb6lrn6zNCN1ae5qe12/sYwU+/qFYpdSwWe6T+zynO2LsjD8lfi629QZFScoZshGxsbvPzyy3j55ZcNqq+eUddnn+bE0HuzcKZODR1n6CQ7O48bfm8WXTP1Pyv/Uicis8RAJ9l5uhfg62r4dv57Q71Xe2Bgl7oZJ5GxccmFZEdpCUzsC5SUAfbWhrXRwgF4Y3DFUov6Rl5E5o6BTrKktKx4PIhmDW+DJjVyXHIhIpIJBjoRkUww0ImIZIKBTkQkEwx0IiKZYKATEckEA52ISCYY6EREMsFAJyKSCQY6EZFMcOs/kZlTWAH9ppl6FLWjsDL1CBonBjqRmZMkmO0vXCbzwiUXIiKZYKATEckEA52ISCYY6EREMsFAJyKSCQY6EZFMMNCJiGSCgU5EJBMMdCIimWCgExHJBAOdiEgmGOhERDLBQCcikgkGOhGRTDDQiYhkgoFORCQTDHQiIplgoBMRyQQDnYhIJhjoREQywUAnIpIJBjoRkUww0Mns7NmzB5GRkWjbti0kScK8efNMPSSiav3666/o1q0brK2t4enpiWXLlplkHAx0Mjt5eXno1KkTlixZAldXV1MPh6haycnJiIyMxMCBA5GSkoJ58+Zhzpw5+Oyzz+p9LJb13iNRDYYOHYqhQ4cCAGbMmGHi0RBV76OPPkL37t2xZMkSAEDHjh2RmpqKxYsXY/LkyZAkqd7GwkAnIlkqLS3DPxezKh8vK9P8efrcpUrP7+Xi2BROzZtW28+ff/6JF154QevY4MGDsWzZMpw/fx6enp4P8Cpqh4FORLJkaWmBQ8dPIyXtjM7ygsIifLnh1yqf29lY4/UJT9bYT1ZWVqWlQfXzrKyseg10rqETkWyNGBCCpk3sDar7+KBH0dTBsLpq9bncAjDQiUjG7Gys8dSwvrWu193PG/4Pt9fr3NatWyM7O1vr2JUrVwCg3j/UZ6ATkaz5eLqjd0Bnvc9v5mCPEeEhep8fEhKC3377TevYjh074O7ujrZt2+rdjjEw0Mns5OXlISUlBSkpKSguLkZ2djZSUlJw5ozutVCimgzp2wstnJrrde5Tw0Jha2Otd9tvvPEGDh06hJkzZ+LkyZP45ptv8Omnn2LGjBlccjFUaGgoJEmCJEkYNGhQtecePHhQc64kSYiLi6unUZI+kpOT0b17d3Tv3h1ZWVlYsWIFunfvjokTJ5p6aNRAWVlZYvTwflAoqg/YkMDO8G7rVqu2e/bsiR9//BHbt29H165d8e677+K9997DlClTHmTIBpHlVS5xcXHIyspC69atdZZ/88039Twiqo3Q0FAIIWo87/zlK3B1cYS1tbIeRkUNnbtrC4SFBGBXYrLO8pbOjhj8WC+D2h42bBiGDRv2IMMzCtnM0NU6dOiA8vJyfPvttzrLS0tLsX79ejRr1gytWrWq59GRsahUxfh60w4sXvEdrly7YerhUAMRGtwNHm1aVjquUEgYPbwfrKwa9hxXdoE+ZswYKBQKxMbG6izfsWMHcnJy8PTTT8PGxqaeR0fG8tehVBQUqWBnawMXp2amHg41EBYKBZ4eVjm4B/QJhFsrFxONynhkF+ht2rRBWFgYjhw5gmPHjlUqVy+3jBs3rtp20tPT8d///hft27eHjY0NHB0dER4ejh9//FHn+Tdv3sSXX36JkSNHwsfHB3Z2dnBwcEBAQAAWL16MwsLCKuvNmjULfn5+sLOzg62tLTw8PNCvXz8sWrQIxcXFmnPj4+MhSRJCQ0OrHLenpyckSUJGRkaVxxMSEjBs2DC0aNECCoVC6zUVFhZi+fLl6NWrF5o1awZbW1v4+fkhKioKd+7cqfZrVl9UqmIk7j8KAAjr3QMWCtn9N6Y65OLUDMP6BWuee7RphceCuppwREYkZKJv374CgIiJiRHffPONACCmT5+udc7NmzeFjY2NaNeunSgvLxdt27YVAMSuXbu0ztu0aZOwtrYWAIS9vb3w9/cXbm5uAoAAIGbMmFGp/9jYWAFAKJVK0bZtW9GzZ0/h7e0tLC0tBQARHBwsCgsLtercunVL+Pr6CgBCoVCIDh06iMDAQNGmTRuhUCgEAHH16lXN+bt37xYARN++fav8Oqhf07lz53QeX7RokVAoFKJ58+YiMDBQuLm5iS1btgghhMjMzBRdunTRjKddu3bCz89PWFlZCQCic+fOWuMxlT/+OiRmfLhCLF25XpSWlZl6ONQAlZeXiy83/CreXb5aXL1+09TDMZqGvWBUhVGjRuGVV17BunXr8OGHH0Lx7wxuw4YNKCoqwtixY6u8nOj48eMYO3YsysrK8PHHH2PKlCmwtKz4MiUkJOCZZ57B4sWL0bdvXwwZMkRTz9/fH1u3bkV4eLjWUk5mZiamTp2KzZs3Y/ny5Zg9e7ambPXq1Th9+jS6du2Kbdu2wd3dXVN27do1fPvtt0ZfFpozZw7eeecdzJ07F1ZWVgCAoqIiCCEwevRoHDt2DMOHD8fnn3+Ohx56SDOW8ePHY9u2bZg8eTK+//57g/v/9OvNuJOn+92KPoQQyMsvAADk5RdhcfR3BrdFjZsQAhYWFlj57TZTD0WLQxNbTH1hlEF1ZRno9vb2GDVqFGJjY/HHH38gPDwcADTr6mPHjq2y7rx581BUVIQFCxbg9ddf1yrr27cvoqOjMXLkSHz00UeVAt3f379Se23atMHatWvRvHlzxMbGagX6yZMnAQDjx4/XCnMAcHFxwbRp02r3wvUwePBgvP/++1rHbGxssG3bNiQmJqJLly7YuHEjrK3vXofr4uKC7777Dg8//DA2bdqECxcuwMPDw6D+7+QV4nZe/gO9BrUilQpFKpVR2qLGqxDy+T8ky0AHKtbIY2NjERsbi/DwcJw7dw579+5FUFAQfH19ddYpLi7GL7/8AkmSMGnSJJ3nREREwMrKCnv37kVpaalm9g4AJSUl+OmnnxAXF4eMjAzk5+drLr+TJAmnT59GQUEB7OzsAEAzA962bRv+85//oEmTJsb8Euj04osv6jy+efNmAMALL7ygFeZqTZo0wYABA7BmzRokJibiueeeM6h/hya2BtUD7s7OBQAba2soG/gVCUS6PMj3iGy/I8LCwuDm5obNmzcjOjoasbGxEELg+eefr7JOeno6ioqKYGlpiZEjR1Z5niRJKCoqQm5urubSx8zMTAwdOhRHjhypdlw3btzQBPqECROwbNkyxMXFwc3NDYMHD0ZISAhCQ0N1zvaNoWPHjjqPqz9A/vLLL7Flyxad55w/fx4AcOnSJZ3l+jD0rSQAxCelYEfCfrg4NcMb/3mKH4YS3Ue2ga5QKDBmzBgsXboUmzdvxtq1a2FlZYXRo0dXWefmzZsAKq5V//PPP2vs494rV8aPH48jR44gICAA8+fPR0BAAJydnTXr1B4eHrh48SJKSko0ddq0aYOkpCTMnTsX27Ztw4YNG7BhwwYA0PzGHmNvVrC31333OPVrT0tLq7GNqq7Y0Yeha+hcO6fGgmvoVRg3bhyWLl2KOXPm4Pz584iMjISzs3OV56uXPJydnXHt2jW9+8nOzsbOnTtha2uL3377rVIfQghcv35dZ92HH34YGzZsQHFxMfbv34/4+Hhs2LABx44dw4gRI5CYmIjevXsDuHsrTlHNLsr8fMPWp9WvfevWrYiIiDCoDX0YYw2da+dEusk60Lt06YJu3bohJSUFAKpdbgEAHx8fKJVK5ObmIjs7W+9bX547dw5AxXKGrh8Yx44dqzFolUol+vTpgz59+mD27Nl44oknsGXLFqxevVoT6OrZtfrWnPe7efNmrX4Q3cvPzw8pKSlITU2t00A3ZH2Qa+fUmHANvRpvvvkm1qxZA6VSWePyhZ2dHQYPHoyff/4Zn3zyCRYtWqRXH7a2Ff8A2dnZEEJUuiSytr8BXJIkhISEYMuWLcjKuvsrtLy8vABU/ADJyclBy5baW5ijo6Nr1c+9nnjiCaxbtw4xMTGYOnWqZp3f2Ax5K8m1cyL9yP47Y+zYsYiLi8Ovv/6q8+qN+73//vuwtbXFkiVLMH/+fOTl5WmV5+bmYvXq1fjggw80x/z8/ODk5ITMzExERUWhvLwcQMVVL1FRUVi7di2Uyso3kHrnnXewcuXKSssx586dw+rVqwEAPXr00Bx3dHRE7969UVxcjGnTpqGoqEhT9sMPP2DBggWaNfvaevzxx9GnTx+cPXsWQ4YM0VxSqVZaWordu3djzJgxUNXjcodKVYw9+ys+aOauUKIamGhDk9Hdu1NUX1XtFN22bZtwcHAQAIS1tbXw9/cXvXr1Ep6enkKSJAFAjB49WqtOdHS0Zidpy5YtRWBgoHB0dBQARFRUlM4dnJGRkQKAkCRJtG/fXgQFBYkOHTpodon6+fmJGzduaPWzd+9eoVQqBQDh4OAgAgICNLtY586dW+NO0fuP3+vKlSsiKChI8zratWsngoODRefOnYWNjY3m+P07XuvS7r8Pc1cokZ443dFh2LBhSEtLw1tvvQVvb2+cPXsWx48fh5WVFYYMGYLo6Gh88sknWnVefvllrF+/HgEBAbh16xbS09Ph5+eH9evXY968eTr7mTNnDmbNmoXg4GAUFhbi0KFDyMzMRPfu3bFw4ULs27cPzZs316oTEhKCP/74A2FhYRBC4OTJk3B3d8f69esxf/78B3rdLVu2RGJiIlatWoWwsDDcvn0bBw8exPXr19GtWzfMnDkTBw4cqNebmtnaKGFvZ8PZOZEeJCH0uPE0kQkVF5fAwtKCgU5UAwY6EZFMcMpDRCQTDHQiIplgoBMRyQQDnYhIJhjoREQywUAnIpIJBjoRkUww0ImIZIKBTkQkEwx0IiKZYKATEckEA52ISCYY6EREMsFAJyKSCQY6EZFMMNCJiGSCgU5EJBMMdCIimWCgExHJBAOdiEgmGOhERDLBQCcikgkGOhGRTDDQiYhkgoFORCQTDHQiIplgoBMRyQQDnYhIJhjoREQywUAnIpIJBjoRkUww0ImIZIKBTkQkEwx0IiKZYKATEckEA52ISCYY6EREMsFAJyKSCQY6EZFM/D9tfWcRjfN3IAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 458.03x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "\n",
    "user_input = input(\"Enter '0' to prepare |0> or '-' to prepare |->\")\n",
    "\n",
    "sys = QuantumRegister(1, \"System\")\n",
    "ctc = QuantumRegister(1, \"CTC\")\n",
    "cr = ClassicalRegister(1, \"Measure\")\n",
    "\n",
    "qc = QuantumCircuit(sys, ctc, cr)\n",
    "\n",
    "if user_input == \"-\":\n",
    "    qc.h(sys)\n",
    "    qc.z(sys)\n",
    "    qc.barrier()\n",
    "    qc.x(ctc)\n",
    "    qc.barrier()\n",
    "\n",
    "qc.swap(sys, ctc)\n",
    "qc.ch(sys, ctc)\n",
    "qc.measure(sys, cr)\n",
    "\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "I3-M97hlAAc9",
    "outputId": "0413a6b0-d712-44b7-bcf1-0a2f1f8b8090",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Measurement results:\n",
      "{'0': 1024}\n"
     ]
    }
   ],
   "source": [
    "from qiskit_aer import AerSimulator \n",
    "from qiskit import transpile\n",
    "\n",
    "backend = AerSimulator()\n",
    "transpiled_circuit = transpile(qc, backend)\n",
    "result = backend.run(transpiled_circuit).result()\n",
    "counts = result.get_counts(transpiled_circuit)\n",
    "\n",
    "print(\"Measurement results:\")\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Try the different inputs for yourself! You will see that when the input state is \"0\", the output is always 0, and when the input state is \"-\", the output is always 1. So time-loops allow us to perfectly distinguish the \"0\" state from the \"-\" state with a single measurement!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5NvIS8H8DwOU",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "**Distinguishing states for BB84 protocol, |0$\\rangle$, |1$\\rangle$, |+$\\rangle$ and |-$\\rangle$, in one shot**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "b_VrPIaq6-Sc",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Using the same idea, we can create a quantum circuit that can distinguish between the four states |0$\\rangle$, |1$\\rangle$, |+$\\rangle$ and |-$\\rangle$ in a single shot. This means that someone with access to a time-loop could cheat the BB84 protocol, which is meant to provide a fool-proof way of protecting information from eavesdroppers using quantum cryptography. The protocol relies on the ability to check if someone intercepted a message, but with a time-loop, the eavedropper could intercept the message, measure its state, and then prepare an exact copy of the state, covering their tracks. \n",
    "\n",
    "Here's the circuit for distinguishing the four BB84 states, from Fig. 2 of the paper: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RNRe5-PvNi3v",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![Screenshot 2023-03-04 at 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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with the definitions of the unitary gates given in equation (3) of the paper:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3pt0HwS8Nn5A"
   },
   "source": [
    "![Screenshot 2023-03-04 at 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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's how to code this circuit in Qiskit: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "from qiskit.circuit.library import CSwapGate\n",
    "#Define custom gates \n",
    "ccswap = CSwapGate(ctrl_state=0).control(1, ctrl_state=0)\n",
    "#custom ccXX gate\n",
    "qc_X2 = QuantumCircuit(2)\n",
    "qc_X2.x(0)\n",
    "qc_X2.x(1)\n",
    "X2 = qc_X2.to_gate()\n",
    "X2.name = \"X2\"\n",
    "ccxx = X2.control(2, ctrl_state='10')\n",
    "#custom ccXH gate \n",
    "qc_xh = QuantumCircuit(1)\n",
    "qc_xh.h(0)\n",
    "qc_xh.x(0)\n",
    "XH = qc_xh.to_gate()\n",
    "XH.name = \"XH\"\n",
    "ccxh = XH.control(2, ctrl_state='01')\n",
    "#custom cc,SWAP, X1 H2 gate \n",
    "qc_4 = QuantumCircuit(2)\n",
    "qc_4.swap(0,1)\n",
    "qc_4.x(0)\n",
    "qc_4.h(1)\n",
    "X1_H2_SWAP = qc_4.to_gate()\n",
    "X1_H2_SWAP.name = \"X1_H2_SWAP\"\n",
    "xhs = X1_H2_SWAP.control(2, ctrl_state='11')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter '0', '1', '+', or '-' to prepare corresponding state on first qubit: 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1045.33x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "user_input = input(\"Enter '0', '1', '+', or '-' to prepare corresponding state on first qubit: \")\n",
    "sys, ctc, cr = QuantumRegister(2, \"System\"), QuantumRegister(2, \"CTC\"), ClassicalRegister(2, \"Measure\")\n",
    "qc = QuantumCircuit(sys, ctc, cr)\n",
    "\n",
    "if user_input == \"1\":\n",
    "    qc.x(sys[0]); qc.x(ctc[1])\n",
    "elif user_input == \"+\":\n",
    "    qc.h(sys[0]); qc.x(ctc[0])\n",
    "elif user_input == \"-\":\n",
    "    qc.x(sys[0]); qc.h(sys[0]); qc.x(ctc)\n",
    "elif user_input != \"0\":\n",
    "    print(\"Invalid input. Please enter '0', '1', '+', or '-'.\")\n",
    "    \n",
    "qc.swap(sys[0], ctc[0]); qc.swap(sys[1], ctc[1])\n",
    "qc.append(ccswap, [sys[0], sys[1], ctc[0], ctc[1]])\n",
    "qc.append(ccxx, [sys[0], sys[1], ctc[0], ctc[1]])\n",
    "qc.append(ccxh, [sys[0], sys[1], ctc[0]])\n",
    "qc.append(xhs, [sys[0], sys[1], ctc[0], ctc[1]])\n",
    "qc.measure(sys[0], cr[0]); qc.measure(sys[1], cr[1])\n",
    "\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 0
    },
    "id": "D-IfTd0FAz6L",
    "outputId": "8c3f42ff-9ed1-4f98-9f42-5ab0b77424cc",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Measurement results:\n",
      "{'00': 1024}\n"
     ]
    }
   ],
   "source": [
    "transpiled_circuit = transpile(qc, backend)\n",
    "result = backend.run(transpiled_circuit).result()\n",
    "counts = result.get_counts(transpiled_circuit)\n",
    "\n",
    "print(\"Measurement results:\")\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "If you try running this with different inputs, you will see that when we input \"0\", the output is 00; when we input \"1\", the output is 10; when we input \"+\", the output is 01; and when we input \"-\", the output is 11. So, we can distinguish any of the four possible input states with a single measurement. "
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    "**The strange powers given by CTCs**\n",
    "\n",
    "From an information-theory perspective, we would achieve something extremely surprising if we could really implement this circuit. We would gain two bits of classical information by measuring a single input qubit, even though a qubit can normally only store 1 bit of information. \n",
    "\n",
    "Even worse, we could construct a similar circuit to distinguish between any number of non-orthogonal states! This means we could store an unbounded amount of classical information in a single qubit! You could try making this circuit yourself, or even making one that violates the no-cloning theorem. \n",
    "\n",
    "Access to time-loops make us much more powerful than if we just had access to a universal quantum computer. Exactly how powerful was worked out by quantum scientists Scott Aaronson and John Watrous in 2008 (see [this paper](https://arxiv.org/abs/0808.2669) for details). \n",
    "\n",
    "The power of computers is defined by complexity classes. Aaronson and Watrous showed that the complexity class for a computer with access to time-loops is PSPACE: all problems solvable by a conventional computer using a polynomial amount of memory! (However, it is worth nothing that these problems may still require exponential time.) PSPACE is a huge space, much bigger than the complexity class of quantum computers without time-loops. Strangely, given access to time-loops, the complexity classes of classical and quantum computers become the same."
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    "## Paradoxes remain...\n",
    "\n",
    "While the remarkable computational power of time-loops makes their existence surprising and counter-intuitive, it does not rule them out. However, some problems remain in making time-loops fully consistent with the laws of physics. \n",
    "\n",
    "One is the \"Knowledge paradox.\"\n",
    "\n",
    "In the video, I explain how time-loops work to my past self. Armed with this knowledge, my past self goes through the time-machine and explains time-loops to another past version of me. There is no logical inconsistency here, but where did my knowledge about time-loops come from? \n",
    "\n",
    "If I was taught about time-loops from my past self, then there is no mechanism by which that knowledge could have been created.\n",
    "\n",
    "Another problem is with locality. \n",
    "\n",
    "Einstein proposed a criterion for locality of quantum theory, which says that one system can only be affected by another system if they directly interact. Even though some accounts of entanglement make it appear that measuring one quantum system instantaneously affects the other, there is a local formulation of quantum theory, explained in my previous videos on the [EPR paradox](https://youtu.be/eoPX4WJlOM8?si=xWcyxEP-T2tp4KQ7) and [quantum teleportation](https://youtu.be/KsvNsY4cVvE?si=DxN5-7wpiW6l5kDW). Einstein's locality is important for making quantum theory consistent with a theory of gravity. \n",
    "\n",
    "With time-loops, Einstein's principle of locality is violated! Observables of a qubit going into a time-loop could in principle be different from those coming out of the closed-timelike-curve, even though the density matrix is the same, violating Einstein's locality. Some attempts have been made to restore locality by modifying quantum theory, but the challenge remains of ensuring that there are no time-travel paradoxes emerging in these alternative formulations.\n",
    "\n",
    "The unsolved problems with time-loops might be hints that they are fundamentally incompatible with our universe. Then again: the idea of efficiently factorizing large numbers seemed impossible before the discovery of quantum computing and [Shor's algorithm](https://youtu.be/6qD9XElTpCE?si=kDNljxY5yq5FnlFs). So, perhaps one day, the discovery that time-loops are possible will bring another revolution in computing. \n",
    "\n",
    "That's all on Quantum Paradoxes for now - hope you enjoyed this series of videos, blogs and code tutorials, and have fun coding your own thought experiments with Qiskit!"
   ]
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