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    "# Reducing depth of circuits with operator backpropagation\n",
    "\n",
    "Operator backpropagation is a technique which involves absorbing operations from the end of a quantum circuit into a Pauli operator, generally reducing the depth of the circuit at the cost of additional terms in the operator. The goal is to backpropagate as much of the circuit as possible without allowing the operator to grow too large.\n",
    "\n",
    "One way to allow for deeper backpropagation into the circuit, while preventing the operator from growing too large, is to truncate terms with small coefficients, rather than adding them to the operator. Truncating terms can result in fewer quantum circuits to execute, but doing so results in some error in the final expectation value calculation proportional to the magnitude of the truncated terms' coefficients."
   ]
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  {
   "cell_type": "markdown",
   "id": "2cbd99bb-edc8-4032-8253-2f7195080aaa",
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   "source": [
    "In this tutorial we will implement a [Qiskit pattern](https://docs.quantum.ibm.com/run/quantum-serverless#qiskit-patterns-with-quantum-serverless) for simulating the quantum dynamics of a Heisenberg spin chain using operator backpropagation:\n",
    "\n",
    "- **Step 1: Map to quantum problem**\n",
    "    - Map the time-evolved Hamiltonian onto a quantum circuit\n",
    "- **Step 2: Optimize the problem**\n",
    "    - Slice the circuit\n",
    "    - <font color=\"#0F62FE\">Backpropagate slices from the circuit onto a Pauli observable</font>\n",
    "    - Combine the remaining slices into a single circuit\n",
    "    - Transpile the circuit for the backend\n",
    "- **Step 3: Execute experiments**\n",
    "    - Calculate the expectation value using the reduced circuit and expanded observable with a [StatevectorEstimator](https://docs.quantum.ibm.com/api/qiskit/qiskit.primitives.StatevectorEstimator) for sake of simplicity in this notebook\n",
    "- **Step 4: Reconstruct results**\n",
    "    - N.A.\n",
    "\n",
    "**Note:** Qiskit loosely describes [layers](https://docs.quantum.ibm.com/api/qiskit/qiskit.dagcircuit.DAGCircuit) as being depth-1 partitions of the circuit across all qubits. This package makes use of the term **slices** to describe layers of arbitrary depth. The [qiskit_addon_obp.backpropagate](https://qiskit.github.io/qiskit-addon-obp/stubs/qiskit_addon_obp.backpropagate.html) function is designed to backpropagate entire slices at a time, so the choice of how to slice the quantum circuit can have a major impact on how well backpropagation performs for a given problem. You will lean more about **slices** below."
   ]
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   "id": "706ce970-5dd2-431a-890b-6476f232ae7f",
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   "source": [
    "## Step 1: Map to quantum problem\n",
    "### Map the time-evolution of a quantum Heisenberg model to a quantum experiment.\n",
    "\n",
    "The [qiskit_addon_utils](https://qiskit.github.io/qiskit-addon-utils/) package provides some reusable functionalities for various purposes.\n",
    "\n",
    "Its [qiskit_addon_utils.problem_generators](https://qiskit.github.io/qiskit-addon-utils/stubs/qiskit_addon_utils.problem_generators.html) module provides functions to generate Heisenberg-like Hamiltonians on a given connectivity graph.\n",
    "This graph can be either a [rustworkx.PyGraph](https://www.rustworkx.org/apiref/rustworkx.PyGraph.html) or a [CouplingMap](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.CouplingMap) making it easy to use in Qiskit-centric workflows.\n",
    "\n",
    "In the following, we first generate a heavy-hex `CouplingMap` out of which we carve a linear chain of 10 qubits. Note, that the indices of this new `reduced_coupling_map` are again zero-based."
   ]
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  {
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   "id": "de8ce35e-a2c5-474f-adb9-88c9afb2bd76",
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   "outputs": [],
   "source": [
    "from qiskit.transpiler import CouplingMap\n",
    "\n",
    "coupling_map = CouplingMap.from_heavy_hex(3, bidirectional=False)\n",
    "\n",
    "# Choose a 10-qubit linear chain on this coupling map\n",
    "reduced_coupling_map = coupling_map.reduce([0, 13, 1, 14, 10, 16, 5, 12, 8, 18])"
   ]
  },
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   "id": "c79b8484-7de0-47cb-be7b-147b502ad1e5",
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    "slideshow": {
     "slide_type": ""
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    "tags": [
     "skip-execution"
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   "outputs": [
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W+PpqAp9smPzgIdkbgmRvCF87dW2sj08enmrFihU0YcIEOvHEE2n06NEkExbJHyRq6CoeCxBLMAVM4ZPj6l64i3b79u2JuznrXOrjU6ddcas77vmzNp+sv3zajvj9o3Opj0/kz/AjY0r+dDzlz8t169ZpH9LVsac+Pp1j8NqwAnHPnw17qOeI+vhE/gw/JibkT/49IW/oEA8HJB9oC9/pLGqoj88sLpP4Q+OePxcuXJgWw5kzZ5LsiURNmjRJ2xfVhvr4RP4MPwom5E/+jc45lH8PuRe+Z8Pbdf6Gr49Pt61Yr1+BOOfPt99+WzlXUlLicZKHW+P79v/6178826Ms1Mdn2pwdsruUGjdbdueL0kZPXe+//74qy14cnu2nnXaaKjv7PTsjKvA4+PIJgIhqS041zjwoPBYcj93ep08fkq10dPvtt6vGN0cJE/h0bDHx1Y/Pd955RzUgdejQgQYOHKgaaQ4cOKDe547uJvoSR5tM5nP37t3UpUsXrbL68anVIEsqd97Hcc2fPIcTf67y3DI6Fz8+kT+ji4hJ+VN211Zzcekci7a28n581j4G5ewViHv+zN7jcM7w4xP5Mxyt/a5qQv6UPfTp4MGDahxvPxt1bvPjU6c9ttQd9/zJ88s8++yz2h9q8OMT+TO6d4kJ+ZMfSmzbtq26cez2XPbkVNvlCA3uzZGu+/EZqQGWVhan/Ok0BvM8Ge6F5+Ti5cMPP1SvOv7Vx2daE7bzZKUcWkiHrapOOU6dem3durXHhuOPP16VdbZssi6sUXl5ucc2FDJXwGkZrOsMbr3mZcOGDfTb3/6W7rjjDnUT7JprrlE9EnifTj65flMX1oV7ynCDoBwHn2bPnq0+NDkxObrKbpD1mj9//nwqLCys9xjs9Ffgo48+UjtM45O/KHGvOH5ySeeC/BlcfZvyJze6VlZW0t13361y+4wZM4ILFOAKyJ8BxMvDqSblT+5hOmXKFDrllFPy4Fl+LoH8GVxHW/InPznPv5H4+54cepQuvvhikvN4qB6cwVXK7QrIn7nplq+zTMiffMOQF77pceWVV9K///1v4ocw5PAw9Pvf/56GDBmi9uv4h/wZXHVb8qdbiT/96U9qtIba95zcx0SxjvwZhcp112FC/uSbyb/73e/o5ptvJjmnrRplZ+nSpfTCCy/Qvffeq7XnEfJn3exkuifu+dPpCMGf6+7fRk5PJG441rU4+dO3/tpja8kbnWo8LnljtPauyMq/+tWvlA3vvvuup04uSyfEtGnTPNujLDz55JM1c02wLfjLTQPZjStr7XjybDm0mTpPJ59u3njsTGbAlDk7mE/5YSl69uyZtb5gOTeW3brxpGJcNoVPh9VbbrlFdO3atWZCKWd71K/In8EZY75syJ/ypog455xzhOxxpuaSmTt3rtb5uPi9gPyZHz7dOTGbdVPy54IFC8RVV11Vkx7lwy0qr+ucoNzh05nrLBtdcayX67jnTzmkSQ2bvPKf//xHfeeTT7aJqqoqz74oC8ifXs6ift+ZkD95smf2Wz6oJvbs2aPwYyZHjhypxpz/5JNPokTSUxe+f+aHz7jnTzcUPEclz2dowhxIyJ/54TPXvGtC/mQ2mcmhQ4eKVq1aCf5Mb9GihZAPM4gvvvjCjW7k68if+eEzzvlz7969Qg6pJi644AIhOx4oBnmicvmgovrc/8Mf/hA5l06FzCfPd+OzpM/Zwd2neJFfUtSrjn/yja2qrf0EuvNkus6nzvkpKm49kmLiL0cNeDxXnkOgocUZ75W7JvETQfx0+qxZs9RpOvlsyG6d+5lPHtuRn6qqqKig2267jTp16qRMqt3trC47+SlB8J3b+9vp8WUSnytXrqTHHnuMnnvuOZJfnuoKeyTbkT9z48r9frQlf/KwlPIBBvXU57x589SQhXLiXar9uR8JmP+vBPkzOJ9uVrNdNyF/7ty5k2699VZ68MEHo0Qvo7qQP4PzaUP+lD+WPbzwEAK//OUv6eOPPybZUOfZF2UB+TM4n9nmTPfxJuTP5s2bK+SKi4vJGY2Bt8mHGFXvcp7rUNeC/BmcTxvyp5s/HjZ72LBhNb+T3fuiXkf+DM6nOx9mu25C/uT7nNz7jXMmfxflJ+h5tBvefuGFF9aM0BE1m1wf8mdwPuOeP9u0aUOvvPKK6mHE3zt5uoHvf//7ilVm5LjjjuMXLQvz6fQwqW1A2jBWfCOfF+6KomtsOJ5bgBe+6epenBuIzn73vqjWWRdHo6jqTFI9znBL3OX56quvVn/8ZnIWhpkXnXw6tpj46uaTJxDiP75x88Ybb6ih12TLJ/HcDdyQ5IwTaKIfcbXJyQ2m8Pnee+8RD//GE0KXlpZql9XNp3ZjLDQgrvmTb4xww+yYMWPU2MnyqXot0XHzifwZfQhMyJ881F///v3ptddeqxFg1apVav31118nnsvjiiuuqNkX5YqbzyjrTUpdcc2fHJ9u3bqpMPHNEV2Lm0/kz+ijYEL+7Nixo3LcGRLbUUH2LFarsmeHsynyVzefkVeegArjlj95rjgeGoh/H5mwuPlE/ow+IibkT37wix8CW7x4cc1w4nyDmR9muOSSS9Tvox/+8IfRiyNrdPOpxQDLK41L/uQ5lZcsWeKJxpw5c1T5jDPO8GyPslAfn2mNHXxjmXtWrFmzRt0ojdJQpy7nptyWLVucTerVGQu0d+/enu1RFjgJ6aw/Sl+jqst5g/PETHyTa/To0SS7SPlWbwKfvoYZstGPT34KkPXkvz/+8Y8qST3xxBPqSX85DBfxfjksgiEexNsMk/jkG3TXXXcd/e1vfzMmZ/nxGe+I67felvzJPT144bmadC1+fCJ/RhcNE/Inj6nL3zUfeuihNMd5/jB+cokbPHQsfnzqsMOmOm3Jn05MnJ7xTjnKVz8+kT+ji4AJ+ZNvhHDPfe5l5F6c3xh8407X4senLltsqTfO+ZN/B/fq1YvOPvtsI8LhxyfyZ3ShMSF/rl+/Xjnsng+BN3Tu3Fltd/arQsT//PiM2ATrqotz/nQHgx+s5Yeo+/Xr594c6Xp9fHr7QkuzuOuUHEdbPQkeqZWuyuS8DMRPh6xevdq1lWjFihVq+3nnnefZHlWBu8TxDcQBAwZEVaW19ThffHnYtAkTJhAPtcOT2PFEYXU1dLAYJvBpalAy4VPOe0JyLEjiVlhuBX3qqafou9/9rtZJr0zVMxe7TOGTJza7/vrraeHChcY0dGTCZy6aJ/GcOOfPZ599Vg2rVjtuGzduVJu4a6yOJRM+kT/DjYwJ+XPTpk1pwzg6wxvIOTu0NXRkwme40bHn6nHOn9wQx72Pai9r165Vm3T9PsmET+TP2lHLb9mE/Mk36QYOHEivvvqqxzndDytmwqfHYBTqVCDO+dNxin2Q48vTlClTnE1aXzPhE/kz3BCZkD+dh774/ox7kfMjqGKXLl3cmyNbz4TPyIyJeUU25E93CHiUGO6RNGrUqDqHkXIfH8Z6g3zKA9KW6dOnCznOv5BjZ6fti2qDHNdMyPE+hfyCpKqUX+SFTERCjvcZlQlp9SxdulTIIAm2BUvuCpSVlYmxY8eKl19+Wcg3SdYXMoFPx2iTJigPwqcc2ko88sgjQo4JqX0Sa0fbuL7q5lMOtaImNpPDlwmeLLL2nxwHVIu0QfjUYrChlcY9f7700ktixIgRQo5BW6OwvMEsevToIWSvSW0T7AbhE/mzJpSBV3TnTz8HZGOH+u6nc4LyIHz6+ZTUbXHPn/ImiJq0lHOOs8g52oQcJkhceumlzqbIX4PwifyZv3CZkD/feust9XtdPjmvHKuurhbjxo1T9xUOHjyYP2ezuFIQPrOoxvpD454/nQA988wzQg4V5RS1vwbhE/kzf+HTnT/l8H9CDtUvfvSjH9Xcg62qqhKXXXaZkA3JQg7lnj9ns7hSED6zqMb6Q+OeP2XPIiGHRq+JE/+OnzhxopA9j4Qcjalme9QrDfBZVsAG1W5l4TE1ec4EfiqYn/rWtfDEUQ8//LCa5EzOAE833HADjR8/Xpc5auz7jz76iOQXOW02oGIiE/h8/vnn6YUXXqCtW7eq9wm3xvMTddwj6fbbb6eioqLIQ8VzM4DPyGVPq1A3n3/+85/pxhtvTLPL2cA95nT0jgOfTgT0vurmk8eUnzRpksqd3LOPF34yRH6Zp5tuuklL7mQbwCeroH/RzaefAvzUEg+vyT07uGekjgV86lA9vU7dfPI48zxnDA8TxGOMc1neTFZ8Tp06VfV+Trc6/C3gM3yNM6lBN5+Ojdxbf9q0aYrNL774gvg30syZM0k+1OAcEukr+IxU7jorM4VPHsHkZz/7GV177bV12hrlDvAZpdp112UCn3wfh+cwrKysrJmovHv37nTnnXdqG6kBfNbNTJR7dPPJ9zyHDx+u5pPhnmb82d63b1/FpjNfV5R6OHU1wGe5b2MHnzxkyBD1JuNZ17EQ8fwhnGx4MisedgmLXgXAp1d/8OnVQ3cJfHojAD69eugugU9vBMCnVw/dJfDpjQD49OqhuwQ+vREAn149dJfApzcC4NOrh+4S+PRGAHx69dBdAp/eCIBPrx66S+DTG4EM+Ky7sWP58uU0ePBg4saOYcOGea+cwBK3/stuMurJeR7XD4teBcCnV3/w6dVDdwl8eiMAPr166C6BT28EwKdXD90l8OmNAPj06qG7BD69EQCfXj10l8CnNwLg06uH7hL49EYAfHr10F0Cn94IgE+vHrpL4NMbgQz4rLuxgy91+eWXqyGD3n77bWrRooX36gkq8aTkPGn27NmzSY6jlyDPzXYVfH4dH/BpJqfgE3yaSebXVoFP8Ak+TVYAfJocHeRP8Ak+TVYAfJocHeRP8Ak+TVYAfJocHeTPrPisv7Fj8+bNVFpaSmPGjKH77rvP5LiHZtuXX35Jffr0ITn5H8mJVamgoCC0unDh7BQAn0TgMztmojwafILPKHnLti7wCT6zZSbK48En+IySt2zrAp/gM1tmojwefILPKHnLti7wCT6zZSbK48En+IySt2zrAp9Z8VlODc2Y/vTTTwt5g18888wzDR1q3f5jx46JkSNHig4dOojt27db558NDoFP8Gkyx+ATfIJPMxXA57uZcXFbhfyJ/OnmwbR18Ak+TWPSbQ/4BJ9uHkxbB5/g0zQm3faAT/Dp5sG0dfCZMZ9lDTZ2cHAnT54s5DwVYvHixabFOlR7Jk2aJOTwXUKOjxZqPbh4MAXAJ/gMRlC4Z4NP8BkuYcGuDj7BZzCCwj0bfILPcAkLdnXwCT6DERTu2eATfIZLWLCrg0/wGYygcM8Gn+AzXMKCXR18ZsRnZo0d/ATk1VdfLVq3bi1ee+21YJGJwdnV1dXi5ptvFo0bNxbz58+PgcXJNhF8Jjv+pnsPPk2PULLtA5/Jjr/p3oNP0yOUbPvAZ7Ljb7r34NP0CCXbPvCZ7Pib7j34ND1CybYPfGYU/8waO/hSR44cET/4wQ9UDw/uOmPrcvjwYSEnIRfNmjUTc+fOtdVN6/wCn9aF1CqHwKdV4bTOGfBpXUitcgh8WhVO65wBn9aF1CqHwKdV4bTOGfBpXUitcgh8WhVO65wBnw2GNPPGDr4UtyDddNNNag6PqVOnqgaQBquI0QGbNm0S559/vigqKhKLFi2KkeUwlRUAn+DAZAXAp8nRgW3gEwyYrAD4NDk6sA18ggGTFQCfJkcHtoFPMGCyAuDT5OjANvBZLwPZNXY4l3r00UfFcccdJ/r37y82bNjgbI71a3l5uWjbtq0oKSkRFRUVsfYl6caDz6QTYLb/4NPs+CTdOvCZdALM9h98mh2fpFsHPpNOgNn+g0+z45N068Bn0gkw23/waXZ8km4d+PQlILfGDr7UBx98IEpLS0VhYaG44447RFVVlW8Npm/85JNPxPDhwwURiQkTJoiDBw+abjLsy0AB8JmBSDhEmwLgU5v0qDgDBcBnBiLhEG0KgE9t0qPiDBQAnxmIhEO0KQA+tUmPijNQAHxmIBIO0aYA+NQmPSrOQAHwmSZS7o0dfCkeJ2zGjBmiVatW4swzzxRz5swRR48eTavFxA07d+4UPBQXN9YUFxeLJUuWmGgmbAqgAPgMIB5ODV0B8Bm6xKgggALgM4B4ODV0BcBn6BKjggAKgM8A4uHU0BUAn6FLjAoCKAA+A4iHU0NXAHyGLjEqCKAA+PSIF6yxw7nU5s2bxdixY0WTJk1Ejx49xOOPPy4OHTrk7DbqtbKyUtxyyy2qgebkk08W99xzj3VzjxgluAHGgE8DggAT6lQAfNYpDXYYoAD4NCAIMKFOBcBnndJghwEKgE8DggAT6lQAfNYpDXYYoAD4NCAIMKFOBcBnndJghwEKgE8VhPw0djjxXL9+vRg3bpxo1qyZaNeunZg8ebIR819wC9ff//53cdlll4nGjRuLDh06iJkzZ4oDBw44puM1AQqAzwQEOcYugs8YBy8BpoPPBAQ5xi6CzxgHLwGmg88EBDnGLoLPGAcvAaaDzwQEOcYugs8YBy8Bpiecz/w2dji8bN++Xdx1113ijDPOUHNh9OzZU0ybNk2sXr06smGu9u3bJxYsWKB6nHDDS0FBgbjoootEWVmZOHz4sGMqXhOoAPhMYNBj5DL4jFGwEmgq+Exg0GPkMviMUbASaCr4TGDQY+Qy+IxRsBJoKvhMYNBj5DL4jFGwEmhqQvksK+BYy8m5Q1mqq6tp5cqV9Nxzz9H8+fPp008/pTZt2tAFF1yg/vr06UNnnXUWdezYMVD9cp4Qkq1WVFFRQatWraLXX3+d1qxZQ1z/gAEDaOTIkerv9NNPD1QPTrZLAfBpVzxt8wZ82hZRu/wBn3bF0zZvwKdtEbXLH/BpVzxt8wZ82hZRu/wBn3bF0zZvwKdtEbXLn4TxWR5qY0dtNLgxYtmyZbR8+XJasWIFbdu2TR0ie15Q9+7dSQ4vRZ07dyY5l4ZqFGnevDm1bNmS+HX//v3EjRr8KnttkByHjHbs2EFyDg76+OOPSQ5VRXLOEOrVqxcNHjyYBg0apP7at29f2wyUoYCvAuDTVxZsNEQB8GlIIGCGrwLg01cWbDREAfBpSCBghq8C4NNXFmw0RAHwaUggYIavAuDTVxZsNEQB8GlIIGCGrwKW8xltY0dthXft2kVr166ldevW0YYNG0h2r6GtW7eqRgxu0JDDTZGcV0M1ZLRq1YqaNm1KrVu3pqKiIjr11FNV40inTp1IDpNFJSUlVFxcrBpGateDMhTIRQHwmYtqOCcqBcBnVEqjnlwUAJ+5qIZzolIAfEalNOrJRQHwmYtqOCcqBcBnVEqjnlwUAJ+5qIZzolIAfEalNOrJRQHL+NTb2JFLAHAOFIACUAAKQAEoAAWgABSAAlAACkABKAAFoAAUgAJQAApAASgABVwKlDdyFbAKBaAAFIACUAAKQAEoAAWgABSAAlAACkABKAAFoAAUgAJQAApAgdgpgMaO2IUMBkMBKAAFoAAUgAJQAApAASgABaAAFIACUAAKQAEoAAWgABSAAm4F0NjhVgPrUAAKQAEoAAWgABSAAlAACkABKAAFoAAUgAJQAApAASgABaBA7BRoIi0uj53VMBgKQAEoAAWgABSAAlAACkABKAAFoAAUgAJQAApAASgABaAAFIACXyuw6n/Epl6dejGgRAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<PIL.PngImagePlugin.PngImageFile image mode=RGBA size=1595x59>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from rustworkx.visualization import graphviz_draw\n",
    "\n",
    "graphviz_draw(reduced_coupling_map.graph, method=\"circo\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f95ba561-f211-4935-bde6-989c0d364ec8",
   "metadata": {},
   "source": [
    "Next, we generate a Pauli operator modeling a Heisenberg XYZ Hamiltonian.\n",
    "\n",
    "$$\\hat{H} = \\sum_{(j,k)\\in E} (J_{x} \\sigma_j^{x} \\sigma_{k}^{x} +\n",
    "    J_{y} \\sigma_j^{y} \\sigma_{k}^{y} + J_{z} \\sigma_j^{z} \\sigma_{k}^{z}) +\n",
    "    \\sum_{j\\in V} (h_{x} \\sigma_j^{x} + h_{y} \\sigma_j^{y} + h_{z} \\sigma_j^{z})$$\n",
    "\n",
    "Where $G(V,E)$ is the graph of the coupling map provided."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "056df48a-0f8d-4a42-9c47-784343a5d6d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SparsePauliOp(['IIIIIIIXXI', 'IIIIIIIYYI', 'IIIIIIIZZI', 'IIIIIXXIII', 'IIIIIYYIII', 'IIIIIZZIII', 'IIIXXIIIII', 'IIIYYIIIII', 'IIIZZIIIII', 'IXXIIIIIII', 'IYYIIIIIII', 'IZZIIIIIII', 'IIIIIIIIXX', 'IIIIIIIIYY', 'IIIIIIIIZZ', 'IIIIIIXXII', 'IIIIIIYYII', 'IIIIIIZZII', 'IIIIXXIIII', 'IIIIYYIIII', 'IIIIZZIIII', 'IIXXIIIIII', 'IIYYIIIIII', 'IIZZIIIIII', 'XXIIIIIIII', 'YYIIIIIIII', 'ZZIIIIIIII', 'IIIIIIIIIX', 'IIIIIIIIIY', 'IIIIIIIIIZ', 'IIIIIIIIXI', 'IIIIIIIIYI', 'IIIIIIIIZI', 'IIIIIIIXII', 'IIIIIIIYII', 'IIIIIIIZII', 'IIIIIIXIII', 'IIIIIIYIII', 'IIIIIIZIII', 'IIIIIXIIII', 'IIIIIYIIII', 'IIIIIZIIII', 'IIIIXIIIII', 'IIIIYIIIII', 'IIIIZIIIII', 'IIIXIIIIII', 'IIIYIIIIII', 'IIIZIIIIII', 'IIXIIIIIII', 'IIYIIIIIII', 'IIZIIIIIII', 'IXIIIIIIII', 'IYIIIIIIII', 'IZIIIIIIII', 'XIIIIIIIII', 'YIIIIIIIII', 'ZIIIIIIIII'],\n",
      "              coeffs=[0.39269908+0.j, 0.78539816+0.j, 1.57079633+0.j, 0.39269908+0.j,\n",
      " 0.78539816+0.j, 1.57079633+0.j, 0.39269908+0.j, 0.78539816+0.j,\n",
      " 1.57079633+0.j, 0.39269908+0.j, 0.78539816+0.j, 1.57079633+0.j,\n",
      " 0.39269908+0.j, 0.78539816+0.j, 1.57079633+0.j, 0.39269908+0.j,\n",
      " 0.78539816+0.j, 1.57079633+0.j, 0.39269908+0.j, 0.78539816+0.j,\n",
      " 1.57079633+0.j, 0.39269908+0.j, 0.78539816+0.j, 1.57079633+0.j,\n",
      " 0.39269908+0.j, 0.78539816+0.j, 1.57079633+0.j, 1.04719755+0.j,\n",
      " 0.52359878+0.j, 0.34906585+0.j, 1.04719755+0.j, 0.52359878+0.j,\n",
      " 0.34906585+0.j, 1.04719755+0.j, 0.52359878+0.j, 0.34906585+0.j,\n",
      " 1.04719755+0.j, 0.52359878+0.j, 0.34906585+0.j, 1.04719755+0.j,\n",
      " 0.52359878+0.j, 0.34906585+0.j, 1.04719755+0.j, 0.52359878+0.j,\n",
      " 0.34906585+0.j, 1.04719755+0.j, 0.52359878+0.j, 0.34906585+0.j,\n",
      " 1.04719755+0.j, 0.52359878+0.j, 0.34906585+0.j, 1.04719755+0.j,\n",
      " 0.52359878+0.j, 0.34906585+0.j, 1.04719755+0.j, 0.52359878+0.j,\n",
      " 0.34906585+0.j])\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from qiskit_addon_utils.problem_generators import generate_xyz_hamiltonian\n",
    "\n",
    "# Get a qubit operator describing the Heisenberg XYZ model\n",
    "hamiltonian = generate_xyz_hamiltonian(\n",
    "    reduced_coupling_map,\n",
    "    coupling_constants=(np.pi / 8, np.pi / 4, np.pi / 2),\n",
    "    ext_magnetic_field=(np.pi / 3, np.pi / 6, np.pi / 9),\n",
    ")\n",
    "print(hamiltonian)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a858a3f-fc3d-4e09-9db9-8d064e036045",
   "metadata": {},
   "source": [
    "From the qubit operator, we can generate a quantum circuit which models its time evolution.\n",
    "Once again, the [qiskit_addon_utils.problem_generators](https://qiskit.github.io/qiskit-addon-utils/stubs/qiskit_addon_utils.problem_generators.html) module comes to the resuce with a handy function do just that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1d68f197-ffa4-49de-9fe8-243b1facbd00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1175.83x521.733 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.synthesis import LieTrotter\n",
    "from qiskit_addon_utils.problem_generators import generate_time_evolution_circuit\n",
    "\n",
    "circuit = generate_time_evolution_circuit(\n",
    "    hamiltonian,\n",
    "    time=0.2,\n",
    "    synthesis=LieTrotter(reps=2),\n",
    ")\n",
    "circuit.draw(\"mpl\", style=\"iqp\", scale=0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddc43a7d-6558-4f82-90a6-7ec5370a7fd5",
   "metadata": {},
   "source": [
    "## Step 2: Optimize the problem\n",
    "### Create circuit slices to backpropagate\n",
    "\n",
    "Remember, the ``backpropagate`` function will backpropagate entire circuit slices at a time, so the choice of how to slice can have an impact on how well backpropagation performs for a given problem. Here, we will group gates of the same type into slices using the [slice_by_gate_types](https://qiskit.github.io/qiskit-addon-utils/stubs/qiskit_addon_utils.slicing.slice_by_gate_types.html) function.\n",
    "\n",
    "For a more detailed discussion on circuit slicing, check out this [how-to guide](https://qiskit.github.io/qiskit-addon-utils/how_tos/create_circuit_slices.html) of the [qiskit-addon-utils](https://qiskit.github.io/qiskit-addon-utils/index.html) package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5d7f0d4e-ce4a-4f11-976b-437a74244b08",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Separated the circuit into 18 slices.\n"
     ]
    }
   ],
   "source": [
    "from qiskit_addon_utils.slicing import slice_by_gate_types\n",
    "\n",
    "slices = slice_by_gate_types(circuit)\n",
    "print(f\"Separated the circuit into {len(slices)} slices.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7e3ef27-8c58-4790-9269-26dacfafa0a1",
   "metadata": {},
   "source": [
    "### Constrain how large the operator may grow during backpropagation\n",
    "\n",
    "During backpropagation, the number of terms in the operator will generally approach $4^N$ quickly, where $N$ is the number of qubits. The size of the operator can be bounded by specifying the ``operator_budget`` kwarg of the ``backpropagate`` function, which accepts an [OperatorBudget](https://qiskit.github.io/qiskit-addon-obp/stubs/qiskit_addon_obp.utils.simplify.OperatorBudget.html) instance.\n",
    "\n",
    "Here we specify that backpropagation should stop when the number of qubit-wise commuting Pauli groups in the operator grows past 8."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1279b567-ba19-4542-9dc1-c57a91118a20",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_addon_obp.utils.simplify import OperatorBudget\n",
    "\n",
    "op_budget = OperatorBudget(max_qwc_groups=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6306e6a1-56fb-432d-80aa-5277233c9ed9",
   "metadata": {},
   "source": [
    "### Backpropagate slices from the circuit\n",
    "\n",
    "First, we will specify the Pauli-Z observable on qubit 0, and we will backpropagate slices from the time-evolution circuit until the terms in the observable can no longer be combined into 8 or fewer qubit-wise commuting Pauli groups.\n",
    "\n",
    "Below you will see that we backpropagated 7 slices but only used 6 of the 8 allotted Pauli groups. This implies that backpropagating one more slice would cause the number of Pauli groups to exceed 8. We can verify that this is the case by inspecting the returned metadata."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "65ec9cb1-a4ed-497b-a616-180e9659956f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Backpropagated 7 slices.\n",
      "New observable has 18 terms, which can be combined into 8 groups.\n",
      "Note that backpropagating one more slice would result in 27 terms across 12 groups.\n",
      "The remaining circuit after backpropagation looks as follows:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1226x521.733 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.quantum_info import SparsePauliOp\n",
    "from qiskit_addon_obp import backpropagate\n",
    "from qiskit_addon_utils.slicing import combine_slices\n",
    "\n",
    "# Specify a single-qubit observable\n",
    "observable = SparsePauliOp(\"IIIIIIIIIZ\")\n",
    "\n",
    "# Backpropagate slices onto the observable\n",
    "bp_obs, remaining_slices, metadata = backpropagate(observable, slices, operator_budget=op_budget)\n",
    "# Recombine the slices remaining after backpropagation\n",
    "bp_circuit = combine_slices(remaining_slices, include_barriers=True)\n",
    "\n",
    "print(f\"Backpropagated {metadata.num_backpropagated_slices} slices.\")\n",
    "print(\n",
    "    f\"New observable has {len(bp_obs.paulis)} terms, which can be combined into {len(bp_obs.group_commuting(qubit_wise=True))} groups.\"\n",
    ")\n",
    "print(\n",
    "    f\"Note that backpropagating one more slice would result in {metadata.backpropagation_history[-1].num_paulis[0]} terms \"\n",
    "    f\"across {metadata.backpropagation_history[-1].num_qwc_groups} groups.\"\n",
    ")\n",
    "print(\"The remaining circuit after backpropagation looks as follows:\")\n",
    "bp_circuit.draw(\"mpl\", scale=0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d25b9701-f1b1-4230-9dcc-554b85e91cf7",
   "metadata": {},
   "source": [
    "Next, we will specify the same problem with the same constraints on the size of the output observable. However, this time, we allot an error budget to each slice using the [setup_budet](https://qiskit.github.io/qiskit-addon-obp/stubs/qiskit_addon_obp.utils.truncating.setup_budget.html) function. Pauli terms with small coefficients will be truncated from each slice until the error budget is filled, and leftover budget will be added to the following slice's budget.\n",
    "\n",
    "In order to enable this truncation, we need to setup our error budget like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3ba04824-dbe7-4e11-80b9-ea2320a131d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_addon_obp.utils.truncating import setup_budget\n",
    "\n",
    "truncation_error_budget = setup_budget(max_error_per_slice=0.005)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6dda21f-4a28-4c4e-9727-15288973150e",
   "metadata": {},
   "source": [
    "Note that by allocating `5e-3` error per slice for truncation, we are able to remove 3 more slices from the circuit, while remaining within the original budget of 8 commuting Pauli groups in the observable. By default, `backpropagate` uses the L1 norm of the truncated coefficients to bound the total error incurred from truncation. For other options refer to the [how-to guide on specifying the p_norm](https://qiskit.github.io/qiskit-addon-obp/how_tos/bound_error_using_p_norm.html).\n",
    "\n",
    "In this particular example where we have backpropagated 10 slices, the total truncation error should not exceed ``(5e-3 error/slice) * (10 slices) = 5e-2``.\n",
    "For further discussion on distributing an error budget across your slices, check out [this how-to guide](https://qiskit.github.io/qiskit-addon-obp/how_tos/truncate_operator_terms.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5e8bae1a-ef18-4eb0-9d2a-1ac7bbdced3b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Backpropagated 10 slices.\n",
      "New observable has 19 terms, which can be combined into 8 groups.\n",
      "After truncation, the error in our observable is bounded by 4.933e-02\n",
      "Note that backpropagating one more slice would result in 27 terms across 13 groups.\n",
      "The remaining circuit after backpropagation looks as follows:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 924.998x521.733 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Run the same experiment but truncate observable terms with small coefficients\n",
    "bp_obs_trunc, remaining_slices_trunc, metadata = backpropagate(\n",
    "    observable, slices, operator_budget=op_budget, truncation_error_budget=truncation_error_budget\n",
    ")\n",
    "\n",
    "# Recombine the slices remaining after backpropagation\n",
    "bp_circuit_trunc = combine_slices(remaining_slices_trunc, include_barriers=True)\n",
    "\n",
    "print(f\"Backpropagated {metadata.num_backpropagated_slices} slices.\")\n",
    "print(\n",
    "    f\"New observable has {len(bp_obs_trunc.paulis)} terms, which can be combined into {len(bp_obs_trunc.group_commuting(qubit_wise=True))} groups.\\n\"\n",
    "    f\"After truncation, the error in our observable is bounded by {metadata.accumulated_error(0):.3e}\"\n",
    ")\n",
    "print(\n",
    "    f\"Note that backpropagating one more slice would result in {metadata.backpropagation_history[-1].num_paulis[0]} terms \"\n",
    "    f\"across {metadata.backpropagation_history[-1].num_qwc_groups} groups.\"\n",
    ")\n",
    "print(\"The remaining circuit after backpropagation looks as follows:\")\n",
    "bp_circuit_trunc.draw(\"mpl\", scale=0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e258829-af9f-43ad-8c79-9455243d7ced",
   "metadata": {},
   "source": [
    "### Now that we have our reduced ansatze and expanded observables, we can transpile our experiments to the backend.\n",
    "\n",
    "Here we will use the 14-qubit [FakeMelbourneV2](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.fake_provider.FakeMelbourneV2) from [qiskit-ibm-runtime](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime) to demonstrate how to transpile to a QPU backend."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b219035b-c5e7-4a08-a8df-cd275bdfe7a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
    "from qiskit_ibm_runtime.fake_provider import FakeMelbourneV2\n",
    "\n",
    "# Specify a backend and a pass manager for transpilation\n",
    "backend = FakeMelbourneV2()\n",
    "pm = generate_preset_pass_manager(backend=backend, optimization_level=1)\n",
    "\n",
    "# Transpile original experiment\n",
    "circuit_isa = pm.run(circuit)\n",
    "observable_isa = observable.apply_layout(circuit_isa.layout)\n",
    "\n",
    "# Transpile backpropagated experiment\n",
    "bp_circuit_isa = pm.run(bp_circuit)\n",
    "bp_obs_isa = bp_obs.apply_layout(bp_circuit_isa.layout)\n",
    "\n",
    "# Transpile the backpropagated experiment with truncated observable terms\n",
    "bp_circuit_trunc_isa = pm.run(bp_circuit_trunc)\n",
    "bp_obs_trunc_isa = bp_obs_trunc.apply_layout(bp_circuit_trunc_isa.layout)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "966bcc9b-48a4-4a6a-8b03-e5aded1ab9df",
   "metadata": {},
   "source": [
    "## Step 3: Execute quantum experiments\n",
    "### Calculate expectation value\n",
    "\n",
    "Finally, we can run the backpropagated experiments and compare them with the full experiment using the noiseless [StatevectorEstimator](https://docs.quantum.ibm.com/api/qiskit/qiskit.primitives.StatevectorEstimator). We can see that the backpropagated expectation value without truncation is equivalent to the exact value within the limits of numerical precision.\n",
    "\n",
    "The expectation value on the operator with truncated terms has some error on the order of ``1e-4``, which is within the expected tolerance.\n",
    "\n",
    "**Note:** We use a statevector-based ``Estimator`` primitive to illustrate the effect of truncation on the output. To run on the backend to which the experiments were transpiled in Step 2, one would import the [EstimatorV2](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.EstimatorV2) from ``qiskit-ibm-runtime`` and pass the backend instance into the constructor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ae47b4e1-f40e-4308-a32d-2ad7ecc56c03",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact expectation value: 0.8854160687717507\n",
      "Backpropagated expectation value: 0.8854160687717532\n",
      "Backpropagated expectation value with truncation: 0.8850236647156059\n",
      "    - Expected Error for truncated observable: 4.933e-02\n",
      "    - Observed Error for truncated observable: 3.924e-04\n"
     ]
    }
   ],
   "source": [
    "from qiskit.primitives import StatevectorEstimator as Estimator\n",
    "\n",
    "estimator = Estimator()\n",
    "\n",
    "# Run the experiments using Estimator primitive\n",
    "result_exact = estimator.run([(circuit_isa, observable_isa)]).result()[0].data.evs.item()\n",
    "result_bp = estimator.run([(bp_circuit_isa, bp_obs_isa)]).result()[0].data.evs.item()\n",
    "result_bp_trunc = (\n",
    "    estimator.run([(bp_circuit_trunc_isa, bp_obs_trunc_isa)]).result()[0].data.evs.item()\n",
    ")\n",
    "\n",
    "print(f\"Exact expectation value: {result_exact}\")\n",
    "print(f\"Backpropagated expectation value: {result_bp}\")\n",
    "print(f\"Backpropagated expectation value with truncation: {result_bp_trunc}\")\n",
    "print(f\"    - Expected Error for truncated observable: {metadata.accumulated_error(0):.3e}\")\n",
    "print(f\"    - Observed Error for truncated observable: {abs(result_exact - result_bp_trunc):.3e}\")"
   ]
  }
 ],
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  "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",
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