steinhaus-triangle-ising-model.ipynb

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    {
     "data": {
      "text/plain": [
       "BinaryQuadraticModel({'aux0': -1.0, 'q0': -0.5, 'q1': 0.0, 'q3': 0.0, 'aux1': -1.0, 'q2': 0.5, 'q4': 1.0, 'aux2': -1.0, 'q5': 0.5}, {('q0', 'aux0'): 1.0, ('q1', 'aux0'): -1.0, ('q1', 'q0'): 0.5, ('q3', 'aux0'): -1.0, ('q3', 'q0'): 0.5, ('q3', 'q1'): 1.5, ('q1', 'aux1'): 1.0, ('q2', 'aux1'): -1.0, ('q2', 'q1'): 0.5, ('q4', 'aux1'): -1.0, ('q4', 'q1'): 0.5, ('q4', 'q2'): 1.5, ('q3', 'aux2'): 1.0, ('q4', 'aux2'): -1.0, ('q4', 'q3'): 0.5, ('q5', 'aux2'): -1.0, ('q5', 'q3'): 0.5, ('q5', 'q4'): 1.5, ('q2', 'q0'): 1.0, ('q3', 'q2'): 1.0, ('q4', 'q0'): 1.0, ('q5', 'q0'): 1.0, ('q5', 'q1'): 1.0, ('q5', 'q2'): 1.0}, 0.0, Vartype.SPIN)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import dwavebinarycsp as dbc\n",
    "\n",
    "csp = dbc.ConstraintSatisfactionProblem(dbc.SPIN)\n",
    "tri_constraint = lambda x, y, z: x*y*z == 1\n",
    "csp.add_constraint(tri_constraint, ['q0', 'q1', 'q3'])\n",
    "csp.add_constraint(tri_constraint, ['q1', 'q2', 'q4'])\n",
    "csp.add_constraint(tri_constraint, ['q3', 'q4', 'q5'])\n",
    "csp.add_constraint(lambda *xs: sum(xs) == 0, ['q0', 'q1', 'q2', 'q3', 'q4', 'q5'])\n",
    "bqm = dbc.stitch(csp, min_classical_gap=.1)\n",
    "\n",
    "bqm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$1.0 aux_{0} q_{0} - 1.0 aux_{0} q_{1} - 1.0 aux_{0} q_{3} - 1.0 aux_{0} + 1.0 aux_{1} q_{1} - 1.0 aux_{1} q_{2} - 1.0 aux_{1} q_{4} - 1.0 aux_{1} + 1.0 aux_{2} q_{3} - 1.0 aux_{2} q_{4} - 1.0 aux_{2} q_{5} - 1.0 aux_{2} + 0.5 q_{0} q_{1} + 1.0 q_{0} q_{2} + 0.5 q_{0} q_{3} + 1.0 q_{0} q_{4} + 1.0 q_{0} q_{5} - 0.5 q_{0} + 0.5 q_{1} q_{2} + 1.5 q_{1} q_{3} + 0.5 q_{1} q_{4} + 1.0 q_{1} q_{5} + 1.0 q_{2} q_{3} + 1.5 q_{2} q_{4} + 1.0 q_{2} q_{5} + 0.5 q_{2} + 0.5 q_{3} q_{4} + 0.5 q_{3} q_{5} + 1.5 q_{4} q_{5} + 1.0 q_{4} + 0.5 q_{5}$$"
      ],
      "text/plain": [
       "1.0⋅aux₀⋅q₀ - 1.0⋅aux₀⋅q₁ - 1.0⋅aux₀⋅q₃ - 1.0⋅aux₀ + 1.0⋅aux₁⋅q₁ - 1.0⋅aux₁⋅q₂\n",
       " - 1.0⋅aux₁⋅q₄ - 1.0⋅aux₁ + 1.0⋅aux₂⋅q₃ - 1.0⋅aux₂⋅q₄ - 1.0⋅aux₂⋅q₅ - 1.0⋅aux₂\n",
       " + 0.5⋅q₀⋅q₁ + 1.0⋅q₀⋅q₂ + 0.5⋅q₀⋅q₃ + 1.0⋅q₀⋅q₄ + 1.0⋅q₀⋅q₅ - 0.5⋅q₀ + 0.5⋅q₁\n",
       "⋅q₂ + 1.5⋅q₁⋅q₃ + 0.5⋅q₁⋅q₄ + 1.0⋅q₁⋅q₅ + 1.0⋅q₂⋅q₃ + 1.5⋅q₂⋅q₄ + 1.0⋅q₂⋅q₅ + \n",
       "0.5⋅q₂ + 0.5⋅q₃⋅q₄ + 0.5⋅q₃⋅q₅ + 1.5⋅q₄⋅q₅ + 1.0⋅q₄ + 0.5⋅q₅"
      ]
     },
     "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 -9.0 {'aux0': 1, 'aux1': 1, 'aux2': 1, 'q0': -1, 'q1': 1, 'q2': 1, 'q3': -1, 'q4': 1, 'q5': -1}\n",
      "True -9.0 {'aux0': 1, 'aux1': 1, 'aux2': 1, 'q0': -1, 'q1': -1, 'q2': -1, 'q3': 1, 'q4': 1, 'q5': 1}\n",
      "True -9.0 {'aux0': -1, 'aux1': 1, 'aux2': 1, 'q0': 1, 'q1': -1, 'q2': 1, 'q3': -1, 'q4': -1, 'q5': 1}\n",
      "True -9.0 {'aux0': 1, 'aux1': -1, 'aux2': -1, 'q0': 1, 'q1': 1, 'q2': -1, 'q3': 1, 'q4': -1, 'q5': -1}\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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