{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "14a471c8-ca37-41a4-b5ca-1d849e34477b",
   "metadata": {},
   "source": [
    "# 02 - Converters for Quadratic Programs\n",
    "### Modified for use with Quantum Rings toolkit for Qiskit 2.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9b76902b-00bd-4071-9042-92e98f595a53",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This code is from:\n",
    "# https://qiskit-community.github.io/qiskit-optimization/tutorials/02_converters_for_quadratic_programs.html\n",
    "\n",
    "# Modified for use with Quantum Rings SDK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "402d3603-e283-4094-aa86-52880a7736c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# Setup your account\n",
    "# You can also save your account locally using the class method QrRuntimeService.save_account(...) and\n",
    "# invoke the QrRuntimeService class constructor without any arguments.\n",
    "#\n",
    "\n",
    "import os\n",
    "my_token = os.environ[\"QR_TOKEN\"]\n",
    "my_name = os.environ[\"QR_ACCOUNT\"]\n",
    "\n",
    "#\n",
    "# Set the backend of your choice, depending upon the task and your hardware configuration.\n",
    "# See SDK documentation for additional help.\n",
    "#\n",
    "\n",
    "my_backend = \"scarlet_quantum_rings\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f0a7b4ab-ee4c-4468-ba27-a031bd13b39a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import from Quantum Rings Toolkit\n",
    "from quantumrings.toolkit.qiskit import QrRuntimeService\n",
    "\n",
    "# Acquire Quantum Rings backend\n",
    "qr_services = QrRuntimeService(name = my_name, token = my_token)\n",
    "qr_backend = qr_services.backend(name = my_backend, precision = \"single\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f01f7911-8fcb-4622-9e9d-8aa941f6c10a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_optimization import QuadraticProgram\n",
    "from qiskit_optimization.translators.docplex_mp import to_docplex_mp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bda8f072-a304-470e-a299-532bac0253d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem name: \n",
      "\n",
      "Maximize\n",
      "  3*x + 2*y + z\n",
      "\n",
      "Subject to\n",
      "  Linear constraints (2)\n",
      "    x + y + z <= 5.5  'xyz_leq'\n",
      "    x + y + z >= 2.5  'xyz_geq'\n",
      "\n",
      "  Integer variables (1)\n",
      "    0 <= z <= 7\n",
      "\n",
      "  Binary variables (2)\n",
      "    x y\n",
      "\n"
     ]
    }
   ],
   "source": [
    "qp = QuadraticProgram()\n",
    "qp.binary_var(\"x\")\n",
    "qp.binary_var(\"y\")\n",
    "qp.integer_var(lowerbound=0, upperbound=7, name=\"z\")\n",
    "\n",
    "qp.maximize(linear={\"x\": 3, \"y\": 2, \"z\": 1})\n",
    "qp.linear_constraint(linear={\"x\": 1, \"y\": 1, \"z\": 1}, sense=\"LE\", rhs=5.5, name=\"xyz_leq\")\n",
    "qp.linear_constraint(linear={\"x\": 1, \"y\": 1, \"z\": 1}, sense=\"GE\", rhs=2.5, name=\"xyz_geq\")\n",
    "print(qp.prettyprint())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "60f5246d-9582-4f30-8503-17e64421c9be",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_optimization.converters import InequalityToEquality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6b109355-afc7-4eea-abe1-1ca8f487082d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem name: \n",
      "\n",
      "Maximize\n",
      "  3*x + 2*y + z\n",
      "\n",
      "Subject to\n",
      "  Linear constraints (2)\n",
      "    x + xyz_leq@int_slack + y + z == 5  'xyz_leq'\n",
      "    x - xyz_geq@int_slack + y + z == 3  'xyz_geq'\n",
      "\n",
      "  Integer variables (3)\n",
      "    0 <= z <= 7\n",
      "    0 <= xyz_leq@int_slack <= 5\n",
      "    0 <= xyz_geq@int_slack <= 6\n",
      "\n",
      "  Binary variables (2)\n",
      "    x y\n",
      "\n"
     ]
    }
   ],
   "source": [
    "ineq2eq = InequalityToEquality()\n",
    "qp_eq = ineq2eq.convert(qp)\n",
    "print(qp_eq.prettyprint())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d3ed6cd7-b425-4b90-a468-2218a6c2f681",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_optimization.algorithms import CplexOptimizer\n",
    "\n",
    "cplex_optimizer = CplexOptimizer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dd82976f-e5b8-43b4-a0c0-4cd8e63ad591",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fval=8.0, x=1.0, y=1.0, z=3.0, status=SUCCESS\n"
     ]
    }
   ],
   "source": [
    "result_orig = cplex_optimizer.solve(qp)\n",
    "print(result_orig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ccd9e8b8-dff8-4aaa-a24f-efc9ef376bab",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fval=8.0, x=1.0, y=1.0, z=3.0, xyz_leq@int_slack=0.0, xyz_geq@int_slack=2.0, status=SUCCESS\n"
     ]
    }
   ],
   "source": [
    "result_eq = cplex_optimizer.solve(qp_eq)\n",
    "print(result_eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "904444d0-af26-416d-9959-ae0f97e0609c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "interpreting values of result_eq: [1. 1. 3.]\n",
      "values of result_orig: [1. 1. 3.]\n"
     ]
    }
   ],
   "source": [
    "print(\"interpreting values of result_eq:\", ineq2eq.interpret(result_eq.x))\n",
    "print(\"values of result_orig:\", result_orig.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c6d654d7-657e-4227-874d-703d43fdb6b6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem name: \n",
      "\n",
      "Maximize\n",
      "  3*x + 2*y + z\n",
      "\n",
      "Subject to\n",
      "  Linear constraints (2)\n",
      "    x + xyz_leq@int_slack + y + z == 5  'xyz_leq'\n",
      "    x - xyz_geq@int_slack + y + z == 3  'xyz_geq'\n",
      "\n",
      "  Integer variables (3)\n",
      "    0 <= z <= 7\n",
      "    0 <= xyz_leq@int_slack <= 5\n",
      "    0 <= xyz_geq@int_slack <= 6\n",
      "\n",
      "  Binary variables (2)\n",
      "    x y\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(qp_eq.prettyprint())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "facf2aa4-da0b-4f6a-af4d-735ca02c6f77",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_optimization.converters import IntegerToBinary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2caf3011-e077-4152-abe0-a1dcd82fe614",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem name: \n",
      "\n",
      "Maximize\n",
      "  3*x + 2*y + z@0 + 2*z@1 + 4*z@2\n",
      "\n",
      "Subject to\n",
      "  Linear constraints (2)\n",
      "    x + xyz_leq@int_slack@0 + 2*xyz_leq@int_slack@1 + 2*xyz_leq@int_slack@2 + y\n",
      "    + z@0 + 2*z@1 + 4*z@2 == 5  'xyz_leq'\n",
      "    x - xyz_geq@int_slack@0 - 2*xyz_geq@int_slack@1 - 3*xyz_geq@int_slack@2 + y\n",
      "    + z@0 + 2*z@1 + 4*z@2 == 3  'xyz_geq'\n",
      "\n",
      "  Binary variables (11)\n",
      "    x y z@0 z@1 z@2 xyz_leq@int_slack@0 xyz_leq@int_slack@1 xyz_leq@int_slack@2\n",
      "    xyz_geq@int_slack@0 xyz_geq@int_slack@1 xyz_geq@int_slack@2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "int2bin = IntegerToBinary()\n",
    "qp_eq_bin = int2bin.convert(qp_eq)\n",
    "print(qp_eq_bin.prettyprint())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "90a98fc7-5a6f-43a9-9995-468766c09953",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fval=8.0, x=1.0, y=1.0, z=3.0, xyz_leq@int_slack=0.0, xyz_geq@int_slack=2.0, status=SUCCESS\n"
     ]
    }
   ],
   "source": [
    "result_eq = cplex_optimizer.solve(qp_eq)\n",
    "print(result_eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ab1c326f-9af2-4aeb-ba48-9a1676a9ff9e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fval=8.0, x=1.0, y=1.0, z@0=1.0, z@1=1.0, z@2=0.0, xyz_leq@int_slack@0=0.0, xyz_leq@int_slack@1=0.0, xyz_leq@int_slack@2=0.0, xyz_geq@int_slack@0=0.0, xyz_geq@int_slack@1=1.0, xyz_geq@int_slack@2=0.0, status=SUCCESS\n"
     ]
    }
   ],
   "source": [
    "result_eq_bin = cplex_optimizer.solve(qp_eq_bin)\n",
    "print(result_eq_bin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "79b4343a-eb71-46cd-9381-de7e28424bb7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "interpreting values of result_eq_bin: [1. 1. 3. 0. 2.]\n",
      "values of result_eq: [1. 1. 3. 0. 2.]\n"
     ]
    }
   ],
   "source": [
    "print(\"interpreting values of result_eq_bin:\", int2bin.interpret(result_eq_bin.x))\n",
    "print(\"values of result_eq:\", result_eq.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "36b92dab-a2f9-469e-a791-2c90ce7375e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem name: \n",
      "\n",
      "Maximize\n",
      "  3*x + 2*y + z@0 + 2*z@1 + 4*z@2\n",
      "\n",
      "Subject to\n",
      "  Linear constraints (2)\n",
      "    x + xyz_leq@int_slack@0 + 2*xyz_leq@int_slack@1 + 2*xyz_leq@int_slack@2 + y\n",
      "    + z@0 + 2*z@1 + 4*z@2 == 5  'xyz_leq'\n",
      "    x - xyz_geq@int_slack@0 - 2*xyz_geq@int_slack@1 - 3*xyz_geq@int_slack@2 + y\n",
      "    + z@0 + 2*z@1 + 4*z@2 == 3  'xyz_geq'\n",
      "\n",
      "  Binary variables (11)\n",
      "    x y z@0 z@1 z@2 xyz_leq@int_slack@0 xyz_leq@int_slack@1 xyz_leq@int_slack@2\n",
      "    xyz_geq@int_slack@0 xyz_geq@int_slack@1 xyz_geq@int_slack@2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(qp_eq_bin.prettyprint())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "db60ee2a-0057-412a-aae2-e262938f2efc",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_optimization.converters import LinearEqualityToPenalty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6bce425b-1111-42ef-96e0-5bacb42ac617",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem name: \n",
      "\n",
      "Maximize\n",
      "  -26*x^2 + 26*x*xyz_geq@int_slack@0 + 52*x*xyz_geq@int_slack@1\n",
      "  + 78*x*xyz_geq@int_slack@2 - 26*x*xyz_leq@int_slack@0\n",
      "  - 52*x*xyz_leq@int_slack@1 - 52*x*xyz_leq@int_slack@2 - 52*x*y - 52*x*z@0\n",
      "  - 104*x*z@1 - 208*x*z@2 - 13*xyz_geq@int_slack@0^2\n",
      "  - 52*xyz_geq@int_slack@0*xyz_geq@int_slack@1\n",
      "  - 78*xyz_geq@int_slack@0*xyz_geq@int_slack@2 - 52*xyz_geq@int_slack@1^2\n",
      "  - 156*xyz_geq@int_slack@1*xyz_geq@int_slack@2 - 117*xyz_geq@int_slack@2^2\n",
      "  - 13*xyz_leq@int_slack@0^2 - 52*xyz_leq@int_slack@0*xyz_leq@int_slack@1\n",
      "  - 52*xyz_leq@int_slack@0*xyz_leq@int_slack@2 - 52*xyz_leq@int_slack@1^2\n",
      "  - 104*xyz_leq@int_slack@1*xyz_leq@int_slack@2 - 52*xyz_leq@int_slack@2^2\n",
      "  + 26*y*xyz_geq@int_slack@0 + 52*y*xyz_geq@int_slack@1\n",
      "  + 78*y*xyz_geq@int_slack@2 - 26*y*xyz_leq@int_slack@0\n",
      "  - 52*y*xyz_leq@int_slack@1 - 52*y*xyz_leq@int_slack@2 - 26*y^2 - 52*y*z@0\n",
      "  - 104*y*z@1 - 208*y*z@2 + 26*z@0*xyz_geq@int_slack@0\n",
      "  + 52*z@0*xyz_geq@int_slack@1 + 78*z@0*xyz_geq@int_slack@2\n",
      "  - 26*z@0*xyz_leq@int_slack@0 - 52*z@0*xyz_leq@int_slack@1\n",
      "  - 52*z@0*xyz_leq@int_slack@2 - 26*z@0^2 - 104*z@0*z@1 - 208*z@0*z@2\n",
      "  + 52*z@1*xyz_geq@int_slack@0 + 104*z@1*xyz_geq@int_slack@1\n",
      "  + 156*z@1*xyz_geq@int_slack@2 - 52*z@1*xyz_leq@int_slack@0\n",
      "  - 104*z@1*xyz_leq@int_slack@1 - 104*z@1*xyz_leq@int_slack@2 - 104*z@1^2\n",
      "  - 416*z@1*z@2 + 104*z@2*xyz_geq@int_slack@0 + 208*z@2*xyz_geq@int_slack@1\n",
      "  + 312*z@2*xyz_geq@int_slack@2 - 104*z@2*xyz_leq@int_slack@0\n",
      "  - 208*z@2*xyz_leq@int_slack@1 - 208*z@2*xyz_leq@int_slack@2 - 416*z@2^2\n",
      "  + 211*x - 78*xyz_geq@int_slack@0 - 156*xyz_geq@int_slack@1\n",
      "  - 234*xyz_geq@int_slack@2 + 130*xyz_leq@int_slack@0 + 260*xyz_leq@int_slack@1\n",
      "  + 260*xyz_leq@int_slack@2 + 210*y + 209*z@0 + 418*z@1 + 836*z@2 - 442\n",
      "\n",
      "Subject to\n",
      "  No constraints\n",
      "\n",
      "  Binary variables (11)\n",
      "    x y z@0 z@1 z@2 xyz_leq@int_slack@0 xyz_leq@int_slack@1 xyz_leq@int_slack@2\n",
      "    xyz_geq@int_slack@0 xyz_geq@int_slack@1 xyz_geq@int_slack@2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "lineq2penalty = LinearEqualityToPenalty()\n",
    "qubo = lineq2penalty.convert(qp_eq_bin)\n",
    "print(qubo.prettyprint())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b9eaabc2-8a5a-4575-91ce-36ea73a3616a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fval=8.0, x=1.0, y=1.0, z@0=1.0, z@1=1.0, z@2=0.0, xyz_leq@int_slack@0=0.0, xyz_leq@int_slack@1=0.0, xyz_leq@int_slack@2=0.0, xyz_geq@int_slack@0=0.0, xyz_geq@int_slack@1=1.0, xyz_geq@int_slack@2=0.0, status=SUCCESS\n"
     ]
    }
   ],
   "source": [
    "result_eq_bin = cplex_optimizer.solve(qp_eq_bin)\n",
    "print(result_eq_bin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "69756a70-092f-477c-b6f3-a36cf4f243a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fval=8.0, x=1.0, y=1.0, z@0=1.0, z@1=1.0, z@2=0.0, xyz_leq@int_slack@0=0.0, xyz_leq@int_slack@1=0.0, xyz_leq@int_slack@2=0.0, xyz_geq@int_slack@0=0.0, xyz_geq@int_slack@1=1.0, xyz_geq@int_slack@2=0.0, status=SUCCESS\n"
     ]
    }
   ],
   "source": [
    "result_qubo = cplex_optimizer.solve(qubo)\n",
    "print(result_qubo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "6e37c5c6-dbba-4677-a957-fe3baa88a65f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "interpreting values of result_eq_bin: [1. 1. 1. 1. 0. 0. 0. 0. 0. 1. 0.]\n",
      "values of result_eq_bin: [1. 1. 1. 1. 0. 0. 0. 0. 0. 1. 0.]\n"
     ]
    }
   ],
   "source": [
    "print(\"interpreting values of result_eq_bin:\", lineq2penalty.interpret(result_qubo.x))\n",
    "print(\"values of result_eq_bin:\", result_eq_bin.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "efa6fc69-1eda-48e0-b6aa-f798462e3a7c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result_orig.x [1. 1. 3.]\n",
      "interpreting result_qubo.x [1. 1. 3.]\n"
     ]
    }
   ],
   "source": [
    "print(\"result_orig.x\", result_orig.x)\n",
    "\n",
    "x = result_qubo.x\n",
    "for conv in [lineq2penalty, int2bin, ineq2eq]:\n",
    "    x = conv.interpret(x)\n",
    "print(\"interpreting result_qubo.x\", x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "39535c76-5c61-420a-87d5-019556e7d2df",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<h3>Version Information</h3><table><tr><th>Software</th><th>Version</th></tr><tr><td><code>qiskit</code></td><td>2.2.1</td></tr><tr><td><code>qiskit_optimization</code></td><td>0.7.0</td></tr><tr><th colspan='2'>System information</th></tr><tr><td>Python version</td><td>3.12.9</td></tr><tr><td>OS</td><td>Windows</td></tr><tr><td colspan='2'>Tue Oct 21 15:14:32 2025 Mountain Daylight Time</td></tr></table>"
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       "<h3>Quantum Rings Version Information</h3><table><tr><th>Software</th><th>Version</th></tr><tr><td><code>QuantumRingsLib</code></td><td>0.11.0</td></tr><tr><td><code>quantumrings-toolkit-qiskit</code></td><td>0.2.0</td></tr></table>"
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      "text/html": [
       "<div style='width: 100%; background-color:#d5d9e0;padding-left: 10px; padding-bottom: 10px; padding-right: 10px; padding-top: 5px'><h3>This code is a part of a Qiskit project</h3><p>&copy; Copyright IBM 2017, 2025.</p><p>This code is licensed under the Apache License, Version 2.0. You may<br>obtain a copy of this license in the LICENSE.txt file in the root directory<br> of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.<p>Any modifications or derivative works of this code must retain this<br>copyright notice, and modified files need to carry a notice indicating<br>that they have been altered from the originals.</p><p>Modifications (c) Copyright Quantum Rings Inc, 2025<br>Modified from the originals<br>Added support for Quantum Rings toolkit for Qiskit. </p></div>"
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   "source": [
    "import tutorial_magics\n",
    "\n",
    "%qiskit_version_table\n",
    "%quantumrings_version_table\n",
    "%qiskit_copyright"
   ]
  },
  {
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   "source": []
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