nonogram-ising-model.ipynb

{
 "cells": [
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     "data": {
      "text/plain": [
       "BinaryQuadraticModel({'q00': 4.0, 'q01': -2.0, 'q02': -2.0, 'q03': 0.0, 'q10': -2.0, 'q11': 0.0, 'q12': 0.0, 'q13': -2.0, 'q20': -2.0, 'q21': 0.0, 'q22': 0.0, 'q23': -2.0, 'q30': 4.0, 'q31': -2.0, 'q32': -2.0, 'q33': 0.0}, {('q01', 'q00'): -4.0, ('q02', 'q00'): 4.0, ('q02', 'q01'): -2.0, ('q03', 'q00'): -2.0, ('q03', 'q01'): 4.0, ('q03', 'q02'): -2.0, ('q11', 'q10'): 4.0, ('q12', 'q10'): -2.0, ('q12', 'q11'): -2.0, ('q13', 'q10'): 0.0, ('q13', 'q11'): -2.0, ('q13', 'q12'): 4.0, ('q21', 'q20'): 4.0, ('q22', 'q20'): -2.0, ('q22', 'q21'): -2.0, ('q23', 'q20'): 0.0, ('q23', 'q21'): -2.0, ('q23', 'q22'): 4.0, ('q31', 'q30'): -8.0, ('q32', 'q30'): 8.0, ('q32', 'q31'): -4.0, ('q33', 'q30'): -4.0, ('q33', 'q31'): 8.0, ('q33', 'q32'): -4.0, ('q10', 'q00'): -4.0, ('q20', 'q00'): 4.0, ('q20', 'q10'): -2.0, ('q30', 'q00'): -2.0, ('q30', 'q10'): 4.0, ('q30', 'q20'): -2.0, ('q11', 'q01'): 4.0, ('q21', 'q01'): -2.0, ('q21', 'q11'): -2.0, ('q31', 'q01'): 0.0, ('q31', 'q11'): -2.0, ('q31', 'q21'): 4.0, ('q12', 'q02'): 4.0, ('q22', 'q02'): -2.0, ('q22', 'q12'): -2.0, ('q32', 'q02'): 0.0, ('q32', 'q12'): -2.0, ('q32', 'q22'): 4.0}, 4.0, Vartype.BINARY)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import dwavebinarycsp as dbc\n",
    "\n",
    "csp = dbc.ConstraintSatisfactionProblem(dbc.BINARY)\n",
    "csp.add_constraint([(0,0,1,1),(0,1,1,0),(1,1,0,0)], ['q00', 'q01', 'q02', 'q03']) # 2\n",
    "csp.add_constraint([(0,1,0,1),(1,0,0,1),(1,0,1,0)], ['q10', 'q11', 'q12', 'q13']) # 1,1\n",
    "csp.add_constraint([(0,1,0,1),(1,0,0,1),(1,0,1,0)], ['q20', 'q21', 'q22', 'q23']) # 1,1\n",
    "csp.add_constraint([(0,0,1,1),(0,1,1,0),(1,1,0,0)], ['q30', 'q31', 'q32', 'q33']) # 2\n",
    "csp.add_constraint([(0,0,1,1),(0,1,1,0),(1,1,0,0)], ['q00', 'q10', 'q20', 'q30']) # 2\n",
    "csp.add_constraint([(0,1,0,1),(1,0,0,1),(1,0,1,0)], ['q01', 'q11', 'q21', 'q31']) # 1,1\n",
    "csp.add_constraint([(0,1,0,1),(1,0,0,1),(1,0,1,0)], ['q02', 'q12', 'q22', 'q32']) # 1,1\n",
    "csp.add_constraint([(0,0,1,1),(0,1,1,0),(1,1,0,0)], ['q30', 'q31', 'q32', 'q33']) # 2\n",
    "bqm = dbc.stitch(csp)\n",
    "\n",
    "bqm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$- 4.0 q_{00} q_{01} + 4.0 q_{00} q_{02} - 2.0 q_{00} q_{03} - 4.0 q_{00} q_{10} + 4.0 q_{00} q_{20} - 2.0 q_{00} q_{30} + 4.0 q_{00} - 2.0 q_{01} q_{02} + 4.0 q_{01} q_{03} + 4.0 q_{01} q_{11} - 2.0 q_{01} q_{21} - 2.0 q_{01} - 2.0 q_{02} q_{03} + 4.0 q_{02} q_{12} - 2.0 q_{02} q_{22} - 2.0 q_{02} + 4.0 q_{10} q_{11} - 2.0 q_{10} q_{12} - 2.0 q_{10} q_{20} + 4.0 q_{10} q_{30} - 2.0 q_{10} - 2.0 q_{11} q_{12} - 2.0 q_{11} q_{13} - 2.0 q_{11} q_{21} - 2.0 q_{11} q_{31} + 4.0 q_{12} q_{13} - 2.0 q_{12} q_{22} - 2.0 q_{12} q_{32} - 2.0 q_{13} + 4.0 q_{20} q_{21} - 2.0 q_{20} q_{22} - 2.0 q_{20} q_{30} - 2.0 q_{20} - 2.0 q_{21} q_{22} - 2.0 q_{21} q_{23} + 4.0 q_{21} q_{31} + 4.0 q_{22} q_{23} + 4.0 q_{22} q_{32} - 2.0 q_{23} - 8.0 q_{30} q_{31} + 8.0 q_{30} q_{32} - 4.0 q_{30} q_{33} + 4.0 q_{30} - 4.0 q_{31} q_{32} + 8.0 q_{31} q_{33} - 2.0 q_{31} - 4.0 q_{32} q_{33} - 2.0 q_{32} + 4.0$$"
      ],
      "text/plain": [
       "-4.0⋅q₀₀⋅q₀₁ + 4.0⋅q₀₀⋅q₀₂ - 2.0⋅q₀₀⋅q₀₃ - 4.0⋅q₀₀⋅q₁₀ + 4.0⋅q₀₀⋅q₂₀ - 2.0⋅q₀₀\n",
       "⋅q₃₀ + 4.0⋅q₀₀ - 2.0⋅q₀₁⋅q₀₂ + 4.0⋅q₀₁⋅q₀₃ + 4.0⋅q₀₁⋅q₁₁ - 2.0⋅q₀₁⋅q₂₁ - 2.0⋅q\n",
       "₀₁ - 2.0⋅q₀₂⋅q₀₃ + 4.0⋅q₀₂⋅q₁₂ - 2.0⋅q₀₂⋅q₂₂ - 2.0⋅q₀₂ + 4.0⋅q₁₀⋅q₁₁ - 2.0⋅q₁₀\n",
       "⋅q₁₂ - 2.0⋅q₁₀⋅q₂₀ + 4.0⋅q₁₀⋅q₃₀ - 2.0⋅q₁₀ - 2.0⋅q₁₁⋅q₁₂ - 2.0⋅q₁₁⋅q₁₃ - 2.0⋅q\n",
       "₁₁⋅q₂₁ - 2.0⋅q₁₁⋅q₃₁ + 4.0⋅q₁₂⋅q₁₃ - 2.0⋅q₁₂⋅q₂₂ - 2.0⋅q₁₂⋅q₃₂ - 2.0⋅q₁₃ + 4.0\n",
       "⋅q₂₀⋅q₂₁ - 2.0⋅q₂₀⋅q₂₂ - 2.0⋅q₂₀⋅q₃₀ - 2.0⋅q₂₀ - 2.0⋅q₂₁⋅q₂₂ - 2.0⋅q₂₁⋅q₂₃ + 4\n",
       ".0⋅q₂₁⋅q₃₁ + 4.0⋅q₂₂⋅q₂₃ + 4.0⋅q₂₂⋅q₃₂ - 2.0⋅q₂₃ - 8.0⋅q₃₀⋅q₃₁ + 8.0⋅q₃₀⋅q₃₂ -\n",
       " 4.0⋅q₃₀⋅q₃₃ + 4.0⋅q₃₀ - 4.0⋅q₃₁⋅q₃₂ + 8.0⋅q₃₁⋅q₃₃ - 2.0⋅q₃₁ - 4.0⋅q₃₂⋅q₃₃ - 2\n",
       ".0⋅q₃₂ + 4.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy\n",
    "expr = bqm.offset\n",
    "for symb, coef in bqm.linear.items():\n",
    "    expr += sympy.symbols(symb) * coef\n",
    "for (symb1, symb2), coef in bqm.quadratic.items():\n",
    "    expr += sympy.symbols(symb1) * sympy.symbols(symb2) * coef\n",
    "\n",
    "sympy.init_printing()\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True -20.0 {'q00': 0, 'q01': 0, 'q02': 1, 'q03': 1, 'q10': 0, 'q11': 1, 'q12': 0, 'q13': 1, 'q20': 1, 'q21': 0, 'q22': 1, 'q23': 0, 'q30': 1, 'q31': 1, 'q32': 0, 'q33': 0}\n",
      "True -20.0 {'q00': 1, 'q01': 1, 'q02': 0, 'q03': 0, 'q10': 1, 'q11': 0, 'q12': 1, 'q13': 0, 'q20': 0, 'q21': 1, 'q22': 0, 'q23': 1, 'q30': 0, 'q31': 0, 'q32': 1, 'q33': 1}\n",
      "True -20.0 {'q00': 0, 'q01': 1, 'q02': 1, 'q03': 0, 'q10': 1, 'q11': 0, 'q12': 0, 'q13': 1, 'q20': 1, 'q21': 0, 'q22': 0, 'q23': 1, 'q30': 0, 'q31': 1, 'q32': 1, 'q33': 0}\n"
     ]
    }
   ],
   "source": [
    "import dimod\n",
    "import itertools\n",
    "\n",
    "res = dimod.ExactSolver().sample(bqm)\n",
    "min_energy = next(res.data()).energy\n",
    "for sample in itertools.takewhile(lambda sample: sample.energy == min_energy, res.data()):\n",
    "    print(csp.check(sample.sample), sample.energy, sample.sample)"
   ]
  }
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