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    "# Controlled\n",
    "\n",
    "The controlled protocol lets you request a *controlled* version of a bloq: a bloq that is only active based on the status of another quantum bit or register.\n",
    "\n",
    "A key feature of any program is the ability to do branching. That is, choosing what operations to do based on input. Controlled bloqs give the quantum programmer access to branching.\n",
    "\n",
    "In its simplest form, a control bit is specified as an (additional) input to a bloq and the bloq is active when the control input is in the $|1\\rangle$ state. Otherwise, the bloq's operation is not performed. Equivalently, the control bit toggles between the bloq and the `Identity` operation.\n",
    "\n",
    "Control bits can be in quantum superposition. The result is a wavefunction containaing simultaneous branches where the controlled operation was performed and not performed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "344b415f",
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "from qualtran.drawing import show_bloq\n",
    "from qualtran.bloqs.basic_gates import XGate\n",
    "\n",
    "x = XGate()\n",
    "\n",
    "show_bloq(x)\n",
    "show_bloq(x.controlled())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "455f4c8a",
   "metadata": {},
   "source": [
    "## Interface\n",
    "\n",
    "The method for accessing the controlled version of a bloq is calling `Bloq.controlled(ctrl_spec)`. `ctrl_spec` is an instance of `qualtran.CtrlSpec` which specifies the condition under which the bloq is active. \n",
    "\n",
    "`CtrlSpec` supports $|1\\rangle$-state individual control bits, as well as:\n",
    " 1. 'negative' controls where the bloq is active if the input is |0>.\n",
    " 2. integer-equality controls where an input of an arbitrary `QCDType` must match a compile-time control value.\n",
    " 3. ndarrays of control values, where the bloq is active if **all** inputs are active.\n",
    " 4. Multiple control registers, control values for each of which can be specified\n",
    "    using 1-3 above.\n",
    "\n",
    "For example:\n",
    " \n",
    " 1. `CtrlSpec(qdtypes=QUInt(4), cvs=0b0110)`: Ctrl for a single register, of type `QUInt(4)` and shape `()`, is active when the soquet of the input register takes value 6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7f55acb5",
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   "outputs": [
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",
      "text/plain": [
       "<Figure size 320x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qualtran import CtrlSpec, QUInt, QBit\n",
    "\n",
    "ctrl_spec = CtrlSpec(qdtypes=QUInt(4), cvs=0b0110)\n",
    "assert ctrl_spec.is_active(6)\n",
    "cx = x.controlled(ctrl_spec=ctrl_spec)\n",
    "show_bloq(cx, type='musical_score')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95a4c968-dea5-4f8e-9752-68e13224bf4c",
   "metadata": {},
   "source": [
    " 2. `CtrlSpec(cvs=[0, 1, 1, 0])`: Ctrl for a single register, of type `QBit()` and shape `(4,)`, is active when soquets of input register take values `[0, 1, 1, 0]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4e2b1bb0-2e68-4f3e-a05c-0bfe7c822ab2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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T5ORk65jy8nJJS0uTzMxMad++faN+xrJlyyQuLk4sFouEhYVJTEyMVFZWiohIZmamdOnSRVJSUkREJD09XQwGg3VuXl6euLq6yt27d2v8nJkzZ8rq1att9n344YcSGxtr3c7MzJTw8PDaX4xm8tFHH4mzs7MAaNKXs7OzfPzxxy1ae23YQ62XS8vEqX1lZGRg6dKlKCkpgYhgypQpuHbtGqZOnQp3d3ds3rwZRqMR2dnZMJlMyMvLQ2pqar1rPvPMMxgxYgSuXLnS6Dp27dqF1NRUpKWl4erVq0hPT4eLS/VLrGka3nvvPXzwwQeIiIioMffu3bvw8PBAmzZtAFT/9l+4cCFcXV2t627evBlvvvkmoqOjER8fj3379lnna5qGmzdvIicnB3379q21vtLS0kafy6PYvHlzk96tPWCxWJCQkIC5c+c6oKofeXh41HmMPdS4HmotWn2wFRYWIioqCjt27EB4eDgsFguKioqQkJCAxMREaJoGoPqteEZGBjIzM9G5c2e715GbmwtPT094e3tj69atCAkJqXFBPDQ0FEuWLLFunz9/HpqmoaKiApcuXcJnn31W4w5hREQEIiMjoWkaFi5cCADIy8tDcXExevfuXWP9tLS0OpuyXbt2djhTxzh79qzD65M67pOxh2zXr6+HWotWH2wZGRnQ6/UIDw8HUH2nrWPHjrWOjYiIcEhDAkBycjKioqIaHOfu7m79Xq/XW6+v5OfnY8iQIRg4cCCCg4PrXSM/P7/W8/D29kZ+fn6T6ib20D9SpYdafbA1hSPfERiNRmzZsgUAEBwcjDVr1qCystL6sQCo/gcUFhZW6/zu3btj0KBBSEtLa7Ap27Zti/Ly8hr7y8vL0b59+zrnmUymxpzKI+vfvz8uX778SHN9fX1x6tQpO1dkf097D7UWrf6uaFhYGHJzc3Hw4EEA1ddrCgsL4enpieLi4mapoaCgACaTCX5+fgCAESNGwMfHB4sWLbI+nJqVlYXVq1dj1apVta5RXFyMEydOQK/X1zj28Lno9XrcuHEDZWVlNuNycnJgMBjqrNPDw8OhX1OnToVOp2vy66fT6TB16lSH11cX9tCPGuqh1qLVB5uXlxeSk5Px7rvvIigoCMHBwTh06BAWLFiA2bNnQ9M0m9vpTREUFITQ0FDcvXsX3bt3x4wZM2odt3PnTkRGRlq3nZ2dsXv3bty/fx99+vSBr68vQkNDkZSUZNM0D66PaJqGwYMHY/r06TbrPDBjxgxs27YNAwYMwMaNG+Hm5obRo0dj//791jGlpaXIzs7GyJEjH+lc7WH27Nkwm81NnmexWDB79mwHVNQ47KFqT0IP2U0L35V9Yjx8q74xHtyqHzNmjBw7dqzOcWVlZTJt2jQZNWqUlJWVPWal1Y4ePSrjx4+3bq9bt06WL19ul7Ufx4QJE0Sn0zX6UQ+dTicTJkxo6bLtgj305GCw/d2kSZPE399fVq5c2eDYixcvisFgkK5du8rp06ebobrabdq0yfrMUnx8vJhMphar5YFbt26Jr6+vuLi4NBhqLi4u4uvrK7dv327psu2CPfTk4N+Kkt1dv34do0ePRnZ2NnQ6XY2Ppw/29e/fH/v27YO3t3cLVUqqavXX2OjJ4+3tjZMnTyIpKanWO3hhYWFISkrCyZMnGWrkEHzHRg53/vx5+Pv7AwDOnTtX6107IntisJHDlZaWWp//MplM9T56QWQP/ChKRMphsBGRchhsRKQcBhsRKYfBRkTKYbARkXIYbESkHAYbESmHwUZEymGwEZFyGGxEpBwGGxEph8FGRMphsBGRchhsRKQcBhsRKYfBRkTKYbARkXIYbESkHAYbESmHwUZEymGwEZFyGGxEpBwGGxEph8FGRMphsBGRchhsRKQcBhsRKYfBRkTKYbARkXIYbESkHAYbESmHwUZEymGwEZFyGGxEpBwGGxEph8FGRMphsBGRchhsRKQcBhsRKYfBRkTKYbARkXIYbESkHAYbESmHwUZEymGwEZFyGGxEpBwGGxEph8FGRMphsBGRchhsRKQcBhsRKYfBRkTKYbARkXIYbESkHAYbESmHwUYOdefOHWzZssW6vWXLFty5c6cFK6KngZOISEsXQeq5cOECPvnkE2zduhXl5eU2x9zc3PDLX/4SS5YsQZ8+fVqoQlIZg43sLi0tDZGRkaioqEBVVVWtY1xcXODq6oo//elPGDFiRDNXSKpjsJFdnThxAkOGDEFlZSUsFku9Y52dneHq6opDhw4hODi4mSqkpwGDjexGRNC3b19cvHgRZrO5UXN0Oh38/Pxw9uxZODk5ObhCelooe/Pg008/xfXr1+sd07NnT2RlZQEAhg8fjl69eiE2NhYAkJ2djaFDh8Lf3x+BgYGYNWsWysrKAABlZWXQNA3t2rWD0Wi0rnfjxg0EBAQAACoqKvDOO+/g+eefR9++fREYGIhNmzZZx165cgU6nQ6apkHTNPj7++O3v/2t9fj777+P3//+9wCAAwcOYM+ePTa1iwjCw8Nx9epVAMBbb72FP/zhD4/wStnPoUOHcP78+UaHGgCYzWacO3cOhw8fdmBlj4Y91IqJonr06CGZmZm1HjObzWI2m23GDBs2TJKTk61jLly4IH/9619FRKSqqkp+/vOfy4oVK2zWeXjO+vXr5d133xURkX/913+VyZMni8lkEhGRy5cvi7+/v3zxxRfW7fbt21vnFhUVSefOneX06dM16l2xYoX827/9m82+xMREmTVrlnX7hx9+ED8/P6mqqqrrJXG4adOmiYuLiwBo0peLi4tMnz69xequC3uo9XJpmTi1r4yMDCxduhQlJSUQEUyZMgXXrl3D1KlT4e7ujs2bN8NoNCI7Oxsmkwl5eXlITU2td00/Pz/r9zqdDi+88AJOnz5d7xyj0YgVK1YgNzcXRqMReXl58PDwAFD9m/2TTz5BdHQ05s6dW2NuaWkpRASenp4AgNdeew2apmH48OGIi4uD2WzGgQMHMHnyZLz//vuIj4/HsmXLrPOfe+459O7dG/v27cO4ceNqra+0tLTe+h/X/v3767xZUJ+qqiqkpaU5vL4H/y1qwx5qXA+1Fq0+2AoLCxEVFYUdO3YgPDwcFosFRUVFSEhIQGJiIjRNA1DdMBkZGcjMzETnzp2b9DNKS0uxceNG/Nd//VedY0pKSnDu3Dm88MIL2L59O/z8/NCpUyebMaGhoSgoKMAPP/xgnaNpGsxmMy5cuIC3334bPj4+NnM0TcOvf/1rFBUV4dNPPwUAVFZW4tChQxg0aFCN9dPS0upsynbt2jXpvJtTQUGBw+uTOi4ns4ds16+vh1qLVn+NLSMjA3q9HuHh4QCq77R17Nix1rERERFNbsiKigpMnToVo0ePxqRJk+oct3v3bowdO7ZRF8Dd3d0BAM8++yyysrKQnZ2NgoICfP3119i1a1eD82/dugWdTlcjCLy9vZGfn9/gfLLFHvqRKj3U6t+xNUVT3xFUVlZi6tSp6NKlC/77v/+73rHJycmYNWsWAGDAgAHIzc3F7du3bX7jZmRkICAgAJ6enigsLLSZ37FjR4waNQp79+5FZGRkvT+rbdu2uH//PkTE5h9BeXm5teFrYzKZ6l33cY0dOxYZGRlNunkAVH9MCwsLw+7dux1Umf087T3UWrT6d2xhYWHIzc3FwYMHAQAWiwWFhYXw9PREcXHxI69bVVWFX/ziF+jYsSPWr19f72/RiooKZGRkYPjw4QCqr61MnDgRv/rVr3Dv3j0A1Xew3nnnHXzyySe1rnH//n0cOnQIer2+xrGHz6V9+/bo1q0bLl26ZDMuJycHBoOhzjo9PDwc+hUTE9PkUAOq74zGxMQ4vL66sId+1FAPtRatPti8vLyQnJyMd999F0FBQQgODsahQ4ewYMECzJ49G5qmWW/HN0ViYiL++Mc/4vjx4xgwYAA0TUNMTEytY/fv349//ud/Rps2baz7tm7dit69e6N///7w8/PD888/j48//hhjxoyxjnlwfeTBl8FgqPWi8KRJk5CVlQVN06yPErz88svYu3evdYyIIC0trd6POo42adIkdOjQocnzvLy8WrRu9lC1J6GH7KbF7sc+YR6+7d6UOXPmzJHt27fXOc5sNsvSpUtF0zS5ffv2Y1Za7erVq/LCCy+IxWIREZHdu3fLtGnT7LL249i0aVOTH/f48ssvW7psu2APPTkYbH83adIk8ff3l5UrVzY49t69e2IwGMTHx0d2797dDNXVbseOHZKXlyciIv/7v/8r33//fYvV8o9WrlzZ6FCLjY1t6XLthj305OCfVJFDbN26Fe+//z6uXr0KnU5nvfb24PsePXrggw8+wIwZM1q4UlIRg40cxmKxYPfu3UhISEBSUhIAYMqUKXj99dcxbtw4ODu3+ku89IRisJHDlZaWWh+TMJlM9d6hJLIH/sokIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYiEg5DDYiUg6DjYiUw2AjIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYiEg5DDYiUg6DjYiUw2AjIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYiEg5DDYiUg6DjYiUw2AjIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYiEg5DDYiUg6DjYiUw2AjIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYyGFu3LiBVatWISQkBDqdDjqdDiEhIVi1ahVu3rzZ0uWRwpxERFq6CFKL2WzG22+/jc8//xzOzs6YOnUqAgICAABnzpxBYmIiLBYL3nzzTXz00UfQ6XQtXDGphsFGdmU2m/Hqq68iKSkJK1aswLx589CpUyebMbdv38YXX3yBlStXYsqUKfjqq6/g7MwPD2Q/Li1dAKllxYoV2LFjB3bs2IFJkybVOqZTp074j//4DwQGBuLll1+Gn58ffvvb3zZzpaQ0UdTq1auloKCg3jE9evSQzMxMEREZNmyY9OzZU1auXCkiIt99950EBweLwWCQgIAAefnll6WwsFBERC5evCgGg0HatGljnS8icuzYMRk7dqyIiBQVFcmvfvUr6dWrl/Tp00eCg4PFaDRax6anp4ubm5sYDAYxGAzSr18/Wb9+vfX4G2+8Ifv37xcRkeTkZMnIyLCpvbS0VEJCQuTu3bsiIvLyyy/LoUOHHuGVsp+ioiJp27atLFu2rNFzli1bJm3btpWioiIHVvZo2EOtl7LB9o8N9zCz2Sxms7lGUyYnJ1vHlJeXy71796zbCxYskAULFtT7M5YtWyZxcXFisVgkLCxMYmJipLKyUkREMjMzpUuXLpKSkiIi1U1pMBisc/Py8sTV1dXaZP9o5syZsnr1apt9H374ocTGxlq3MzMzJTw8vK6Xo1l8/vnnotPp5Pvvv2/0nO+//150Op2sXbvWgZU9GvZQ66XER9GMjAwsXboUJSUlEBFMmTIF165dw9SpU+Hu7o7NmzfDaDQiOzsbJpMJeXl5SE1NrXfNZ555xvq92WxGaWkp2rVrV++cXbt2ITU1FWlpabh69SrS09Ph4lL9Emuahvfeew8ffPABIiIiasy9e/cuPDw80KZNGwDA8OHDsXDhQri6ulrX3bx5M958801ER0cjPj4e+/bts87XNA03b95ETk4O+vbtW2t9paWl9db/uDZv3oyJEyeia9eujZ7TtWtXTJw4EQkJCZg5c6YDqwM8PDzqPMYealwPtRatPtgKCwsRFRWFHTt2IDw8HBaLBUVFRUhISEBiYiI0TQMAGI1GZGRkIDMzE507d27U2hUVFXjxxRdx9epVBAUFYdeuXXWOzc3NhaenJ7y9vbF161aEhITA1dXVZkxoaCiWLFli3T5//jw0TUNFRQUuXbqEzz77DG5ubjZzIiIiEBkZCU3TsHDhQgBAXl4eiouL0bt37xrrp6Wl1dmUDf2jelxt2rRBZGRkk+cNGDAAKSkpDq9P6rhPxh6yXb++HmotWv2tqIyMDOj1eoSHhwMAnJ2d0bFjx1rHRkRENLohAcDV1RVZWVn44Ycf4O/vj/j4+DrHJicnIyoqqsE13d3drd/r9XpkZWXh7NmzuHTpElatWoWTJ082uEZ+fn6t5+Ht7Y38/PwG5zuKiFjfLTRFmzZt6gyd5sAe+lFL95C9tPpga4pHfUfg6uqK119/Hf/zP/9T5xij0WhtyuDgYJw4cQKVlZU2YzIyMhAWFlbr/O7du2PQoEFIS0trsJ62bduivLy8xv7y8nKbpn+YyWRy6FePHj3w/fffN1j/w65du4YePXo4vD57eNp7qLVo9cEWFhaG3NxcHDx4EABgsVhQWFgIT09PFBcXP/K6V69exb1796xrbt++HUFBQbWOLSgogMlkgp+fHwBgxIgR8PHxwaJFi1BVVQUAyMrKwurVq7Fq1apa1yguLsaJEyeg1+trHHv4XPR6PW7cuIGysjKbcTk5OTAYDHWek4eHh0O/xo8fj8TERFRUVNTzytq6f/8+EhMTMWHCBIfXVxf20I8a6qHWotUHm5eXF5KTk/Huu+8iKCgIwcHBOHToEBYsWIDZs2dD0zRkZWU1ed1Tp05h8ODBCAoKQlBQEG7evIk1a9bUOnbnzp0215acnZ2xe/du3L9/H3369IGvry9CQ0ORlJRk0zQPro9omobBgwdj+vTptV6jmjFjBrZt24YBAwZg48aNcHNzw+jRo7F//37rmNLSUmRnZ2PkyJFNPld7mTNnDm7evInk5ORGz0lOTsbNmzcxZ84cB1ZWP/ZQtSehh+ymRe/JPkEevlXfGA9u1Y8ZM0aOHTtW57iysjKZNm2ajBo1SsrKyh6z0mpHjx6V8ePHW7fXrVsny5cvt8vaj2PEiBHi4+Mj165da3DstWvXxMfHR0aMGNEMlTkee+jJwWD7u0mTJom/v7/14cr6PHi4smvXrnL69OlmqK52mzZtsj6zFB8fLyaTqcVqeSAvL0+6du0qer1ecnNz6xyXm5srer1eunbtKvn5+c1YoeOwh54c/FtRsruLFy9izJgxuHLlCqKiojBv3jz069cPAHD27Fl88cUXMBqN6NmzJ/bu3Yvnn3++hSsm1TDYyCFMJhO2bt2Kzz//HDk5OTbH+vbtizfffBO//OUvHf7sGj2dGGzkUCKCv/zlLxg6dCgA4ODBgxgyZAicnJxauDJSGYONHO4f/5TIZDLV++gFkT20+sc9iIgexmAjIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYiEg5DDYiUg6DjYiUw2AjIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYiEg5DDYiUg6DjYiUw2AjIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYiEg5DDYiUg6DjYiUw2AjIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYiEg5DDYiUg6DjYiUw2AjIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONHKa0tBRr1qzB+PHjrft8fX3xs5/9DGvWrMG9e/dasDpSmZOISEsXQepJSUlBdHQ0rl+/brO/ffv2KC4uBgB4e3tj48aNNsFHZA98x0Z2t379ekRGRuLmzZuIjo7GkSNHrMdOnDiBU6dOYfbs2bh58yYiIyOxfv36FqyWlCREdpSWliY6nU6effZZSU1NFRERk8kkAASALF682Do2NTVV2rVrJzqdzjqWyB74jq0Wx48fx7hx4wAAxcXFmDNnDnx9faHX6xESEoKdO3daxx44cADu7u7QNA2apiEgIAAbNmywHo+OjkZ6ejoAwGg02rx7AYB79+5h4MCBKCkpAQC88sorOHz4sKNP0SGqqqoQExMDs9mM3//+9xg5cmS940eOHImvvvoKZrMZ8+fPR1VVVTNV6njsoRbW0sn6JFq2bJnExcWJxWKRsLAwiYmJkcrKShERyczMlC5dukhKSoqIiKSnp4vBYLDOzcvLE1dXV7l7926NdWfOnCmrV6+22ffhhx9KbGysdTszM1PCw8Ptf1LNYM+ePQJAJk6caLO/rndsD0ycOFEAyN69e5urVIdjD7WspzbYdu7cKf7+/tK/f39ZunSpdOrUSS5fviwiIoGBgVJQUCCpqanSrVs3uX//vs3ctWvXyuDBg0WkZlOeOXNGvLy8pKysTEREhg0bJsnJyZKSkiJeXl7StWtXMRgMsmHDBhER8fX1lYsXL9qs7+/vL2fPnnXQmTvOW2+9JQBk27ZtNvsbCrbExEQBIG+99VZzlWoX7KEnl0vLvVdsOTdu3MDrr7+OgwcPol+/fli/fj1u374NAMjNzYWnpye8vb2xdetWhISEwNXV1WZ+aGgolixZYt0+f/48NE1DRUUFLl26hM8++wxubm42cyIiIhAZGQlN07Bw4UIAQF5eHoqLi9G7d+8a66elpaFv3751nkNpaenjvAQOcfnyZQBAjx490K1bN1y7dq3GmN/97nf43e9+Z93+6U9/im3btlnnP2nn5eHhUet+FXpIZU9lsB05cgRBQUHo168fAOCNN97A/PnzAQDJycmIiopqcA13d3fr93q9HllZWQCA/Px8DBkyBAMHDkRwcHC9a+Tn56Nz58419nt7eyM/P7/eue3atWuwxpYyaNCgRo/929/+hsGDBwMAkpKSkJSU5KiyHonU8TSUCj2kMt48AODk5GT93mg0WpsyODgYJ06cQGVlpc34jIwMhIWF1bpW9+7dMWjQIKSlpTX4c9u2bYvy8vIa+8vLy22anp587KEny1MZbKGhoTh16hTOnTsHAPjyyy9RUVGBgoICmEwm+Pn5AQBGjBgBHx8fLFq0yHrHLisrC6tXr8aqVatqXbu4uBgnTpyAXq+vcczT09P6cCpQ/Vv6xo0bKCsrsxmXk5MDg8FQ7zmYTKYn7stoNAIAJkyYUOPYggULAACLFy+ucWzChAkAgJ07d7b4OTz8pXIPKa2lL/K1FKPRKP7+/hIUFCRvv/22dOrUSdatWyfLly+3GXfnzh2Jjo6WXr16Sa9evcTNzU3++te/Wo+np6eLm5ubGAwGMRgM4u/vL++//771+IMLvyIi3377rfTr1080TbNe+J08ebJ8/fXX1vEmk0m6desmJSUlDjx7x6isrBR/f38BYHNOIiJLliwRAPLOO+/Y7E9JSREA4u/vb71r2Fqwh55cT22wPaxTp04yZswYOXbsWJ1jysrKZNq0aTJq1CjrHavHdfToURk/frx1u7Z/GK3JN998Y31A95tvvrHury3YvvnmG3n22WeVeUCXPfTkYLD93T/eqm9umzZtsj6zFB8fLyaTqUXqsJe4uDhxdnYWnU4nc+fOldOnT8t3330nBw8elMuXL8uZM2dk3rx5otPpxNnZWeLi4lq6ZLtgDz05+Efw5BApKSl444038MMPPwAAOnTogI4dO6KwsBBFRUUAgM6dO2PTpk38I3iyOwYbOUxpaSk2btyIXbt24fTp07hz5w68vLwQGBiIf/mXf8Ebb7xR53NiRI+DwUZEynkqH/cgIrUx2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYiEg5DDYiUg6DjYiUw2AjIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYiEg5DDYiUg6DjYiUw2AjIuUw2IhIOQw2IlIOg42IlMNgIyLlMNiISDkMNiJSDoONiJTDYCMi5TDYiEg5DDYiUg6DjYiUw2AjIuUw2IhIOQw2IlLO/wPTj4Fi9dTMzwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 320x440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ctrl_spec = CtrlSpec(cvs=[0, 1, 1, 0])\n",
    "assert ctrl_spec.is_active([0, 1, 1, 0])\n",
    "cx = x.controlled(ctrl_spec=ctrl_spec)\n",
    "show_bloq(cx, type='musical_score')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0c79e8f-991d-45a5-a628-6928b615bfc0",
   "metadata": {},
   "source": [
    " 3. `CtrlSpec(qdtypes=[QBit(), QBit()], cvs=[[0, 1], [1, 0]]).is_active([0, 1], [1, 0])`:\n",
    "    Ctrl for 2 registers, each of type `QBit()` and shape `(2,)`, is active when the soquet for\n",
    "    each register takes values `[0, 1]` and  `[1, 0]` respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dbbc994a-5a2d-42b7-998c-70a8b8b52f16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 320x440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "ctrl_spec = CtrlSpec(qdtypes=[QBit(), QBit()], cvs=[[0, 1], [1, 0]])\n",
    "assert ctrl_spec.is_active([0, 1], [1, 0])\n",
    "cx = x.controlled(ctrl_spec=ctrl_spec)\n",
    "show_bloq(cx, type='musical_score')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76350f9c",
   "metadata": {},
   "source": [
    "The controlled bloq is defined by its decomposition in addition to its classical and quantum simulation protocols. For a general bloq, we can provide a decomposition of its controlled version by controlling each of the subbloqs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ac9bf2ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ERUUhMDDwmRbR7oK1sh1rRc6OwUp2c+PGDUyfPh319fWYM2cOhg8fDg+Prj99ePjwIcrLy5GdnQ2DwYDc3Nx23zTTE7FWtmOtyNkxWMmuKisrcejQIZw6dQrV1dVWv/nYETc3NwQGBmLu3LlYvnw5Bg8e/Jxm6nisle1YK3JmDFYiIiKFePASERGRQgxWIiIihRisRERECjFYiYiIFGKwEhERKcRgJSIiUojBSkREpBCDlYiISCEGKxERkUIMViIiIoUYrERERAoxWImIiBRisBIRESnEYCUiIlKIwUpERKQQg5WIiEghBisREZFCDFYiIiKFGKxEREQKMViJiIgUYrASEREpxGAlIiJSiMFKRESkEIOViIhIIQYrERGRQgxWIiIihRisRERECv0PPU0MyP6mSp8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 480x120 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 480x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qualtran.bloqs.for_testing import TestSerialCombo\n",
    "\n",
    "serial = TestSerialCombo()\n",
    "cserial = serial.controlled()\n",
    "show_bloq(serial.decompose_bloq(), type='musical_score')\n",
    "show_bloq(cserial.decompose_bloq(), type='musical_score')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f26d386",
   "metadata": {},
   "source": [
    "## Implementation\n",
    "\n",
    "Bloq authors can override `Bloq.get_ctrl_system(...)` to provide a custom controlled version of a bloq. Please read the docstrings for this method to understand the required return values.\n",
    "\n",
    "We've already seen an example where `XGate().controlled()` will give the `CNOT` bloq. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2524c557",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CNOT\n"
     ]
    }
   ],
   "source": [
    "cx = XGate().controlled()\n",
    "print(cx)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7b490bb",
   "metadata": {},
   "source": [
    "This behavior may depend on the control spec. For example, if we want to control on the input line being in the state corresponding to the unsigned integer `255`, we wouldn't get a `CNOT` bloq."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a42248a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C[8][X]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 320x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qualtran import QInt\n",
    "c255x = XGate().controlled(CtrlSpec(QInt(8), cvs=255))\n",
    "show_bloq(c255x, type='musical_score')\n",
    "print(c255x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8603f99f",
   "metadata": {},
   "source": [
    "## Default Fallback\n",
    "\n",
    "If a bloq does not override `get_ctrl_system`, the system will use the `qualtran.Controlled` meta-bloq to wrap the original bloq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6255dcc4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Controlled(subbloq=TestAtom(), ctrl_spec=CtrlSpec(qdtypes=(QBit(),), cvs=(array(1),)))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qualtran.bloqs.for_testing import TestAtom\n",
    "\n",
    "atom = TestAtom()\n",
    "catom = atom.controlled()\n",
    "catom"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f0452eb",
   "metadata": {},
   "source": [
    "This metabloq forms an important part of the 'controlled' protocol. It adapts the other qualtran protocols to handle controlled versions of arbitrary bloqs. It delegates its protocols to the wrapped bloq.\n",
    "\n",
    " - **Signature:** That of the wrapped bloq with new registers according to `ctrl_spec`.\n",
    " - **Decomposition:** The controlled version of a composite bloq is formed by controlling each\n",
    "   of the subbloqs.\n",
    " - **Classical simulation:** This uses the control spec’s activation method to check classical values.\n",
    "   If the gate is meant to be active, the wrapped classical simulation protocol is employed.\n",
    "   Otherwise: the input values are returned unchanged.\n",
    " - **Tensor simulation:** Currently, tensor simulation will proceed via the decomposition.\n",
    " - **Call graph:** The wrapped bloq's call graph with controlled versions of each subbloq.\n",
    " - **Wire_symbol:** Existing registers delegate to the wrapped bloq. New control registers use the\n",
    "   wire symbol information provided by the control spec.\n",
    " - **Names:** The wrapped bloq's names encased with \"C[...]\"\n",
    " - **Adjoint:** Use the default fallback. The control lines are all symmetric.\n",
    " - **Cirq**: Use the default fallback. No translation to `cirq.ControlledOperation` is done."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "12a460f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use the default fallback for `OnEach`; but the subbloqs all have custom\n",
    "# controlled behavior: \n",
    "#  C^2[X]        -> Toffoli\n",
    "#  C[Split/Join] -> Split/Join\n",
    "from qualtran.bloqs.basic_gates import OnEach\n",
    "\n",
    "ccx3 = OnEach(n=3, gate=x).controlled(CtrlSpec(cvs=(1,1)))\n",
    "show_bloq(ccx3.decompose_bloq(), type='musical_score')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24aa3d20-7803-4480-b717-5e3a2d5e6ba3",
   "metadata": {},
   "source": [
    "Only bloqs with all-THRU registers can be controlled. Otherwise, it's not clear what the equivalent \"identity\" operation is."
   ]
  }
 ],
 "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": "3.11.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}