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MAHRahat/Grover's Algorithm.ipynb

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Created August 12, 2022 13:30
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Grover's Algorithm.ipynb
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"# IMPORTS\n",
"import qiskit\n",
"import matplotlib as mpl\n",
"from random import randint"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
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"source": [
"n = 4 #size of Query and hidden bit string\n",
"circuit = qiskit.QuantumCircuit(n+1,n) # one extra qubit for the Auxiliary,\n",
" # and a classical bit for each Query qubit"
]
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\n"
},
"metadata": {},
"execution_count": 3
}
],
"source": [
"for i in range(n):\n",
" circuit.h(i) #place Query into equal superposition\n",
"\n",
"circuit.x(n) \n",
"circuit.h(n) # bring Auxiliary into '1', then '-' state for Phase Kickback\n",
"\n",
"circuit.barrier()\n",
"circuit.draw('mpl')"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"hidden_bits = randint(0,2**n-1) #random n-digit number\n",
"hidden_bits = format(hidden_bits,'0'+str(n)+'b') #convert number to binary string"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def Oracle(circuit,n,hidden_bits):\n",
"\n",
" circuit.barrier()\n",
"\n",
" for i in range(len(hidden_bits)):\n",
" if hidden_bits[i] == '0':\n",
" circuit.x(i) #apply X Gates to any '0's in the hidden bit string so they can activate MCX\n",
"\n",
" circuit.mcx(list(range(n)),n) # check if qubit is perfectly correct\n",
"\n",
" for i in range(len(hidden_bits)):\n",
" if hidden_bits[i] == '0':\n",
" circuit.x(i) #finish wrapping X Gates around '0's to hide any\n",
"\n",
" circuit.barrier() \n",
"\n",
" return circuit"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def Diffuser(circuit,n):\n",
" \n",
" for i in range(n):\n",
" circuit.h(i) #take 's' out of superposition\n",
" circuit.x(i) #flip to |11..> to activate MCX\n",
"\n",
" circuit.mcx(list(range(n)),n) # apply Phase Kickback\n",
"\n",
" for i in range(n):\n",
" circuit.x(i)\n",
" circuit.h(i) #undo X Gate and place back into superposition\n",
" \n",
" circuit.barrier()\n",
" return circuit"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<qiskit.circuit.instructionset.InstructionSet at 0x2232e6312e0>"
]
},
"metadata": {},
"execution_count": 7
}
],
"source": [
"from math import pi,sqrt,floor\n",
"\n",
"iterations = floor((pi/4)*sqrt(n)) #formula for number of iterations\n",
"\n",
"for i in range(iterations):\n",
" circuit = Oracle(circuit,n,hidden_bits)\n",
" circuit = Diffuser(circuit,n) #Amplitude Amplification\n",
"\n",
"circuit.barrier()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<Figure size 1230.4x385.28 with 1 Axes>"
],
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Eje7du7sdIWIWMwNOqGsA0bA4h1jMDFhE84q48fHHH7sdIWIWMwNOqGsA0bA4h1jMDFhE8woAAAAA8DyaVwAAAACA59G8Im7k5OS4HSFiFjMDTqhrANGwOIdYzAxYRPMKAAAAAPA8mlfEjUGDBrkdIWIWMwNOqGsA0bA4h1jMDFiU4HYAr3tuubRznzv7blJfGniBO/tGfLvj03VaVVDgyr7Tk5P1UPsUV/btBsa66rg1X0czV1MfVcfqWFusa6Ait99+u/Lz813Zd0ZGhmbNmuXKvhEbNK8Odu6TNn/ldgogtlYVFOitfXvdjlEtMNZVx+J8TX1UHatjbbGugYrk5+crLy/P7RgwitOGETfGjh3rdoSIWcwMOKGuAUTD4hxiMTNgEc0r4sa4cePcjhAxi5kBJ9Q1gGhYnEMsZgYsonlF3Ojdu7fbESJmMTPghLoGEA2Lc4jFzIBFNK+IG3v27HE7QsQsZgacUNcAomFxDrGYGbCI5hUAAAAA4Hk0r4gbKSn2bvlgMTPghLoGEA2Lc4jFzIBFNK+IG4sWLXI7QsQsZgacUNcAomFxDrGY2ZpatWqpQ4cO6tSpk5o2beq4fnZ2thISuCtovKF5Rdy455573I4QMYuZASfUNYBoWJxDLGa2oGXLlvrDH/6g1atXq6CgQOvXr9fq1av1+eef6+uvv9ZLL72kgQMHntKkTpo0Sf/4xz/0zDPPuJQclcXTzWswGNT06dPVtm1b1axZU+np6crLy1P79u01cuRIt+PBYxYuXOh2hIhZzGzNocLjX+/ZLAWD7mWpLqhrlKX4sPTl+uPfFx1yLwu8zeIcYjGzlyUnJ+uxxx7T5s2bNWHCBHXq1EmhUEgbN27UmjVrtGfPHp111lm66qqrtGjRIm3atEmXX365pJLG9Z577lFRUZEWL17s8m+CWPN08zpixAhNnjxZo0aN0ssvv6zs7GzdeOON2rJli7p16+Z2vDLlTMnSR89PCXs5YEHoyBEduW2cih97otTy4sXP68jNwxQqLCznke4pPiytWSq9/djxZasWS+/8Sfpyg3u5nFgca6ssztcW6yMUkrZ9JL01R1rzf8eXvzVb+uxtKeTRN5QsjrVks66BE6WlpWnNmjUaOXKkioqK9MwzzygrK0vJyclq3769OnfurEaNGql58+b6xS9+oU8//VQtW7bUq6++qvfff/9Y43rTTTdpwYIFbv86iDHPNq/z58/X008/rSVLlujOO+9Unz59NHHiRPXq1UtFRUXq2rWr2xGBasOXmKiECb9W8KWlCq7MlySFtm5V8Mm/KvCbO+WrU8fdgCcJFkv5i6Uv10kKlf7Z4f3Smpe828BaG2tULYv1seU96bO3pOIjpZcHi6VtH0ob3nAnlxOLYw1Y17lzZ+Xm5qp58+b6+OOP1aVLF/30pz9VXl6eDh48WGrdzz//XH/84x+VmpqqCRMmqKioSD179lQwGKRxjWOebV6nTp2qfv36KTMzs9TyNm3aKDExUWlpaZJKPmPQrl07+f1+5eTkuBEVHpGXl+d2hIhZyuxr2UL+W4epePpMhfbuVdG0B+W/9hr50zq7He0UX22S9n1e8Tob3yx58exFlsa6LJbq2iJL9XGwQNr6QcXr7FwlFXr0FpmWxjqeWJxDLGb2mtq1a2vx4sWqX7++XnjhBV188cVat26d4+OKi4tVu3ZtJSQkKBQKye/3q27dulWQGG7wZPO6Y8cOrVmzRoMHDz7lZ9u3b1dqaqpq1KghSerXr59eeeUV9e7du6pjwmPWrl3rdoSIWcvsH3CtfM2bqWjUWCkQkH/YULcjlWnnKkm+itc5vF/6ekuVxDktVsa6LNbq2iIr9bFrrU45+6EsO1dXepTTZmWs44nFOcRiZq+ZOnWqWrdurfz8fA0ZMkSHDx8O63Enfsb14YcfliQ99NBDatasWWXGhUs8ef3oHTt2SJIaN25cavmBAweUl5en/v37H1t24YUXntY+fD6HV7b/cf3EZWraMSuibX/0wu+1Yun0UsuOHCxU8059I9pOXl6ufnFFn4geE6/Gjx/vuM7MmTMd15s5c2asIoUlnDxuZA48OE3+9LSIH+fz+eRL66zQik/kvyFbvsTEiLeRm5srX/eeET8uEvPv/lwN6zpfRn/sz+5UTt5DlZol3sbay89Ft+braObqeKuPk/16yFO6rMvNCgTKf7kRDBYr59lXdPdlV1dqFqtjbbGuK+LlOaQ8FjNX5K5pJReD8Pl8pb52U6NGjTR69GgVFxdr+PDhOnQovCu6ndi4Hj1VuFmzZho4cKDGjx+vX/3qV6XWz8vLc/13RdlCoTDe6ZRHm9eGDRtKkjZu3Kgrr7zy2PIHHnhAu3bt8uzFmo7qce1E9Rhwd6llOVOy3AkDxFBo61YF//Z3+YcMVnDe3+S/5CL5GjVyO9YpDhz6QaFQyPEP1KHD+6soUeSsjLV1VudrK/Vx8PAPksPzMKQQz8UYs1rXqL5GjBihpKQkvfDCC8rPzw/rMWU1rpI0ZcoUDRw4UMOHD9fEiRN14MCBSkyOqubJ5rVVq1ZKS0vT1KlT1aBBAzVp0kQ5OTlaunSpJMWkeQ23u//ja9Lmr6Le3WnJzMxSzpTwcsa7DRucr64zc+ZMx1sozZgxI1aRwuKU263MfZd/qLf27Y3oMaHDR0o+7zVwgALDhym0b5+KH5yhwP1T5fOH/wmErKwsvR7m8+90ffZ2yYVgnCx4ZbZqnjm7UrPE21h7+bno1nwdzVwdb/Vxsm+2SSsdLkcR8Cdo9P8M1n3PVG4Wq2Ntsa4r4uU5pDwWM1dkwv2PSyp5LXzi11UlKyvrlM8I//jHP5YkPfXUU2Fto7zGVZJWrlyp/Px8ZWRkqEePHqX2lZmZqdzc3Oh/CbjGk5959fv9WrhwoVJTUzV69GgNHz5cDRs21NixYxUIBI5drAk40aRJk9yOEDFLmYNPPiVfQoL8Q2+SJAXG3KbQl7sVXOS9e6g1SZP8gYrXOae9VPPMqskTKUtjXRZLdW2Rpfpo0EI64yyV/xl0n1SjjnROu6pMFT5LYx1PLM4hFjN7hc/nU5cuXSRJH3zgcIU3Vdy4HnV0O14/WxOR82TzKknt2rXTsmXL9MMPP2j79u2aPHmyVq9erZSUFNWqVcvtePCg7OxstyNEzErm4Mp8BZe+osCE38iXUHLChq92bQXuulPBufMU2rrV5YSl1aorpQ8oo4H9zwvouk2kjj+u6lThsTbWZbFS1xZZqw+fT8oYWP4bRUm1pC7XS34PngdmbazjicU5xGJmr6hXr57OPPNMffvtt9q9e3eF64bTuErSp59+Kklq0aJFzPPCXR78c1G+5cuXq2fP0hc8+O1vf6unnnpKe/bs0erVq3X77bcrLy9PrVu3diXjoLtzI1qO2OnYsaPWr1/vdoyIWMns75Ih/5LnTl3eKVX+F715BOKs86Vet0o7Vkn//qhkWb3zpCbpJUddnY7MusXiWJ/MSl1bnK8t1ketulLPn0pfrJW+WCMV/ucU2Da9pfM6lzSwXmRxrCWbdX0yK3PIiSxm9orvvvtObdu2VaLDxdCSkpJ02WWXOTaukvTMM8/olVde0ddffx3ruHCZmea1sLBQGzdu1JgxY0otnzx5siZPnuxSKgBeVquu1Lb38eb1ghvdzQNUVwk1pOZdS/69/p+L4Lbs4W4mAN4QDAb12WefOa53+PBh9e/fX7169dKrr75a4brffPONvvnmm1hFhIeYaV7r1Kmj4uJit2MAAAAAcEFBQYFj44r45tnPvAKRysrKcjtCxCxmBpxQ1wCiYXEOsZgZsIjmFXFjzpw5bkeImMXMgBPqGkA0LM4hFjMDFtG8Im6MHj3a7QgRs5gZcEJdA4iGxTnEYmbAIppXxA2LN522mBlwQl0DiIbFOcRiZsAimlcAAAAAgOfRvAIAAAAAPI/mFXHD4s3BLWYGnFDXAKJhcQ6xmBmwyMx9Xt3SpH713LdFCxYsUHZ2ttsxIuJW5vTk5Crfpxf27YbqONZu1bVbc2Y0+62O9eEWq2Ntsa6jxd/z+JaRkXFaj9uyfZckqVXzc0t9XRX7hnf4QqFQyO0QgJMNGzY4rtOxY0fHdz47dOgQq0hhccrtxczx6PXpJf/te6e7OeKB1ecivIPnY/VmcQ6xmLkiE+5/XJI07a6Rpb72Oqu5EVucNgwAAAAA8DyaVwAAAACA59G8Im7Mnj3b7QgRs5gZcEJdA4iGxTnEYmbAIppXxI3U1FS3I0TMYmbACXUNIBoW5xCLmQGLaF4RNzIzM92OEDGLmQEn1DWAaFicQyxmBiyieQUAAAAAeB7NK+JG9+7d3Y4QMYuZASfUNYBoWJxDLGYGLKJ5Rdz4+OOP3Y4QMYuZASfUNYBoWJxDLGYGLKJ5BQAAAAB4Hs0rAAAAAMDzaF4RN3JyctyOEDGLmQEn1DWAaFicQyxmBiyieQUAAAAAeB7NK+LGoEGD3I4QMYuZASfUNYBoWJxDLGYGLEpwO4DXPbdc2rnPnX03qS8NvMCdfSO+3fHpOq0qKHBl3+nJyXqofYor+3YDY1113Jqvo5mrqY+qY3WsLdY1EI9uv/125efnV/l+MzIyNGvWrCrfr1fRvDrYuU/a/JXbKYDYWlVQoLf27XU7RrXAWFcdi/M19VF1rI61xboG4lF+fr7y8vLcjlHtcdow4sbYsWPdjhAxi5kBJ9Q1gGhYnEMsZgYsonlF3Bg3bpzbESJmMTPghLoGEA2Lc4jFzIBFNK+IG71793Y7QsQsZgacUNcAomFxDrGYGbCI5hVxY8+ePW5HiJjFzIAT6hpANCzOIRYzAxbRvAIAAAAAPI/mFXEjJcXeLR8sZgacUNcAomFxDrGYGbCI5hVxY9GiRW5HiJjFzIAT6hpANCzOIRYzw3t8Pp8SEriTaUVoXhE37rnnHrcjRMxiZsAJdQ0gGhbnEIuZUXn8fr8uu+wyTZw4UQsWLNA///lPvfTSS5o1a5aGDh2qs88++5TH+Hw+zZkzR/Pnz6eBrYCnm9dgMKjp06erbdu2qlmzptLT05WXl6f27dtr5MiRbseDxyxcuNDtCBGzmBlwQl0DiIbFOcRiZsReUlKSfv3rX2vLli16/fXXNWXKFA0ePFhXXHGFrrrqKv3yl7/U3LlztWPHDs2bN0/t2rWTdLxxHTVqlK666ip16tTJ5d/EuzzdvI4YMUKTJ0/WqFGj9PLLLys7O1s33nijtmzZom7durkdr0w5U7L00fNTwl4OWBA6ckRHbhun4seeKLW8ePHzOnLzMIUKC11KVrHvv5TWLD3+/btPSNs+kooOuZfJidWxtsjifG21Pg4VSp+9Jb01+/iyT9+U9n/rWiRHVsfaYl0D8SAjI0PLly/XAw88oBYtWmjTpk2aMWOGbr75ZvXr10/XXnut/vd//1dLly5VIBDQTTfdpPz8fN1xxx3HGtcDBw7ommuuUX5+vtu/jmd59pj0/Pnz9fTTTys3N1eZmZmSpD59+uiTTz7Rc889p65du7qcEKg+fImJSpjwaxX9/Hb5enSXv0uGQlu3KvjkXxX4/X3y1anjdsRTfLm+dOMqSQe+K3kB/cUa6YIhUtIZ7mSriMWxRtWxWB+Fe6QV/5COHCy9/PNPpC9WS10GSfWauJOtIhbHGoA7+vTpoxdffFFnnHGGNm3apF/+8pd65ZVXFAqFSq23ZMkSSVLz5s01adIk3XLLLZo+fbokHWtc33jjjSrPb4lnj7xOnTpV/fr1O9a4HtWmTRslJiYqLS1N+/bt09VXX6127dopPT1dV1xxhT777DOXEsNteXl5bkeImKXMvpYt5L91mIqnz1Ro714VTXtQ/muvkT+ts9vRTvHD3v80rqH//DvJ/r3S2leqOlX4LI11WSzVtUWW6iMYlPIXS0fKOduhuEjKf04qOly1ucJlaazjicU5xGJmxEanTp20ZMkSnXHGGZo7d67S09P18ssvn9K4nmj79u269dZb9corx1+MPP/88zSuYfBk87pjxw6tWbNGgwcPPuVn27dvV2pqqmrUqCGfz6fbb79dGzdu1KpVq3T11Vdr+PDhLiSGF6xdu9btCBGzltk/4Fr5mjdT0aixUiAg/7Chbkcq0458ldm0nuibrSVNrldZGeuyWKtri6zUx9ebpYPfq/znY6jkNP7dG6oyVWSsjHU8sTiHWMyM6CUkJOivf/2r6tSpo2effVa33HKLDhw44Pi4o59x7devnw4dOqTi4mINGTJEF154YRWkts2Tpw3v2LFDktS4ceNSyw8cOKC8vDz1799fklSvXj317dv32M8vvPBCPfDAA2Htw+fzhbXe9ROXqWnHrLDWPeqjF36vFUunl1p25GChmnfqW84jypaXl6tfXNEnosfEq/HjxzuuM3PmTMf1Zs6cGatIYQknjxuZAw9Okz89LeLH+Xw++dI6K7TiE/lvyJYvMTHibeTm5srXvWfEj4vE03dtUpOGbRzXu+m/fq4X3n2kUrPE21h7+bno1nwdzVwdb/Vxsl8OnKP+P/qZAv5AuesUB4v0xENLNGnu9ZWaxepYW6zrinh5DimPxcwVuWvaY5JKavvEr73Oi7l/9rOfqWvXrtq2bZtuu+22Co+2HnXixZmOnircp08fTZw4UbNnz1ZGRkap9fPy8lz/PatCOGMnebR5bdiwoSRp48aNuvLKK48tf+CBB7Rr165yL9Y0a9YsDRgwoCoiVqjHtRPVY8DdpZblTMlyJwwQQ6GtWxX829/lHzJYwXl/k/+Si+Rr1MjtWKdITEgKb71AeOu5wcpYW2d1vrZSHwmBJMnhBYlPvpL1PMrKWJ/Ial0D1owbN06S9Jvf/EaFYVzErazG9Y033tDbb7+tESNGKD09XRdddJHefffdyo5ulieb11atWiktLU1Tp05VgwYN1KRJE+Xk5Gjp0pKrr5TVvE6aNEmfffaZ3nzzzbD2EW53/8fXpM1fhZ89ljIzs5QzJbyc8W7DBudzymbOnOl4C6UZM2bEKlJYnHK7lbnv8g/11r7IzpkNHT5S8nmvgQMUGD5MoX37VPzgDAXunyqfP/xPIGRlZen1MJ9/p2vlIumbbXI8dXjO0w9p4fkPVWqWeBtrLz8X3Zqvo5mr460+Tvbvj6VNDh8F9PsDGjLsat39ZOVmsTrWFuu6Il6eQ8pjMXNFJtz/uKSS18Infu11bufOysoq9dnmrl27KiUlRV988YUWL17s+PjyGldJOnz4sP785z/r7rvv1k9/+tNSzWtmZqZyc3Nj/vtY5cnPvPr9fi1cuFCpqakaPXq0hg8froYNG2rs2LEKBAJKSyt92s+UKVP00ksv6ZVXXlHt2rVdSg23TZo0ye0IEbOUOfjkU/IlJMg/9CZJUmDMbQp9uVvBRc4TdlVrmqGKG1efVDNZOqtl1eSJlKWxLoulurbIUn2cmyr5wnil0SS98rOcDktjHU8sziEWMyM6PXr0kCS99tprKioqqnDdihrXo15++WVJUvfu3SsncJzwZPMqSe3atdOyZcv0ww8/aPv27Zo8ebJWr16tlJQU1apV69h6kyZN0osvvqjXXntN9erVcy8wXJedne12hIhZyRxcma/g0lcUmPAb+RJKTtjw1a6twF13Kjh3nkJbt7qcsLSGraRG7cr5oU/y+aSOPy75r9dYG+uyWKlri6zVR1JtqZ3DxybP7ynVrlclcSJibazjicU5xGJmRKdz55Krjq9cubLC9cJpXCUdu7drp06dqsVnXE+XJ08bLs/y5cvVs+fxCx6sXbtWv/vd79S6dWtlZWUdW+7mjX0H3Z0b0XLETseOHbV+/Xq3Y0TESmZ/lwz5lzx36vJOqfK/6L0jED6f1OkqaXM9acdKqfjI8Z/VOUtqd6nUoLlr8SpkbazLYqWuLc7XFuujWRcpIUn67B3pUMHx5Um1pZY9S37uRRbHWrJZ1yezMoecyGJmROfDDz9UUlKSli9fXuF648ePd2xcJWn//v164oknVFRUpEAg4Hg0t7oy07wWFhZq48aNGjNmzLFlqampJs7RB1D1/AGpbe+Sozq5D5cs63GzlHyON4+4AvHs3FSpcUfp253Sin+ULLt4VMnzFAAsmjt3rubOneu43hNPPKH+/ftr2rRpjvdxdfrcNAw1r3Xq1FFxcbHbMQAYc+KFh89sXP56ACqXzy/Vb3b8expXANVBQUGBLr/8crdjxA3PfuYViNSJp45bYTEz4IS6BhANi3OIxcyARTSviBtz5sxxO0LELGYGnFDXAKJhcQ6xmBmwiOYVcWP06NFuR4iYxcyAE+oaQDQsziEWMwMW0bwibli8gbPFzIAT6hpANCzOIRYzAxbRvAIAAAAAPI/mFQAAAADgeTSviBsWbw5uMTPghLoGEA2Lc4jFzIBFNK+IGwsWLHA7QsQsZgacUNcAomFxDrGYGbAowe0AXtekfvXct0X33nuvsrOz3Y4REbcypycnV/k+vbBvN1THsXarrt2aM6PZb3WsD7dYHWuLdR0t/p7DizIyMiJ+zJbtuyRJrZqfW+rryt5vPKN5dTDwArcTALH3UPsUtyNUG4x11bE4X1MfVcfqWFusayAezZo1K+LHTLj/cUnStLtGlvoap4/ThgEAAAAAnkfzirgxe/ZstyNEzGJmwAl1DSAaFucQi5kBi2heETdSU1PdjhAxi5kBJ9Q1gGhYnEMsZgYsonlF3MjMzHQ7QsQsZgacUNcAomFxDrGYGbCI5hUAAAAA4Hk0rwAAAAAAz6N5Rdzo3r272xEiZjEz4IS6BhANi3OIxcyARTSviBsff/yx2xEiZjEz4IS6BhANi3OIxcyARTSvAAAAAADPo3kFAAAAAHgezSviRk5OjtsRImYxM+CEugYQDYtziMXMgEU0rwAAAAAAz6N5RdwYNGiQ2xEiZjEz4IS6BhANi3OIxcyARQluB/C655ZLO/e5s+8m9aWBF7izb8S3Oz5dp1UFBa7sOz05WQ+1T3Fl325grKuOW/N1NHM19VF1rI61xboG4A2333678vPzXdl3RkaGZs2aFfPt0rw62LlP2vyV2ymA2FpVUKC39u11O0a1wFhXHYvzNfVRdayOtcW6BuAN+fn5ysvLcztGTHHaMOLG2LFj3Y4QMYuZASfUNYBoWJxDLGYGLKJ5RdwYN26c2xEiZjEz4IS6BhANi3OIxcyARTSviBu9e/d2O0LELGYGnFDXAKJhcQ6xmBmwiOYVcWPPnj1uR4iYxcyAE+oaQDQsziEWMwMW0bwCAAAAADyP5hVxIyXF3i0fLGYGnFDXAKJhcQ6xmBmwiOYVcWPRokVuR4iYxcyAE+oaQDQsziEWMwNl8fl8atOmjS699FL17dtXXbt2VVJSUrnrJyYmavz48UpIqJo7sNK8Im7cc889bkeImMXMgBPqGkA0LM4hFjMDJ+rTp48WLFigffv2adOmTXrjjTf02muvacWKFSosLNR7772n4cOHq1atWscek5iYqH/84x+aMWOG5syZUyU5Pd28BoNBTZ8+XW3btlXNmjWVnp6uvLw8tW/fXiNHjnQ7XplypmTpo+enhL0csbNw4UK3I0TMSubQkSM6cts4FT/2RKnlxYuf15GbhylUWOhSMmcFXx3/escqqeiQe1nCYXmsj7JS1xbna8v1cahQ+vfy498f+M69LOGwOtYW6/pkVuaQE1nMDEhS69atlZeXpzfffFODBw9W3bp19cUXX2jZsmV6/fXXtX79egUCAfXq1UtPPvmkNm/erKuvvvpY43rddddp7969mj17dpXk9XTzOmLECE2ePFmjRo3Syy+/rOzsbN14443asmWLunXr5nY8oNrwJSYqYcKvFXxpqYIr8yVJoa1bFXzyrwr85k756tRxN2AZDu+XViyQPpx7fNmG16S35kjbV7iXy4nFsUbVsVgfwaD06TLp7cekTbnHl7/7hLT2Zam4yLVoFbI41gAQieuuu07/+te/1Lt3b3311Ve699571aJFCzVp0kSXXnqpLr/8cqWkpKhu3boaNmyYPvnkE5177rl68cUXtX79+mONa9++fbVy5coqyezZ5nX+/Pl6+umntWTJEt15553q06ePJk6cqF69eqmoqEhdu3Z1OyJQrfhatpD/1mEqnj5Tob17VTTtQfmvvUb+tM5uRztF8RHpk4XSvu2n/ixYJG1cJu3Ir/JYYbM01qh61upj45vS5yskhU792a610tqlUqiMn3mBtbEGgHBde+21WrhwoWrXrq1nn31WHTp00H333aft20998VRYWKi5c+eqe/fuuuOOO1RcXKzWrVvr4MGDVdq4Sh5uXqdOnap+/fopMzOz1PI2bdooMTFRaWlpkqQBAwYoLS1NXbp0UY8ePfT666+7ERcekJeX53aEiFnL7B9wrXzNm6lo1FgpEJB/2FC3I5Vp9wap0OGWe5+9XdLkepWVsS6Ltbq2yEp97P/W+Y2irzZK339ZFWlOj5WxjicW5xCLmVF9NW/eXM8884wCgYB+//vf6+abb9a+ffscHxcIBHTxxRcrEAgoFAqpZs2a6tSpUxUkPq5qLgsVoR07dmjNmjUaP378KT/bvn27UlNTVaNGDUnS008/rXr16kmSVq5cqaysLO3du1eBQKAqI5fy0Qu/14ql00stO3KwUM079XUpUfWwdu1aNWrUyO0YEbGW2efzyZfWWaEVn8h/Q7Z8iYluRyrTztWSfCrzSM9RRYekPZulxh2qKlVkrIx1WSzVtdX52kp97FoTxko+6Ys1Ut1zKz3OabEy1ieyWtdHWZpDjrKYGdXX448/ruTkZOXk5Ojuu+8O6zEnf8Z11qxZuu+++/T//t//06uvvqrdu3dXcuoSnm1eJalx48allh84cEB5eXnq37//sWVHG1dJ+u677+Tz+RQK4/wjn88XVpbrJy5T045ZYa17VI9rJ6rHgNKFkDMlsm1IUl5ern5xRZ+IHxePynoj42QzZ850XG/mzJmxihSWcPK4kTnw4DT509Miflxo61YF//Z3+YcMVnDe3+S/5CL5IvxjnZubK1/3nhHvOxLz7/5cDes2dVzvF7f9WgvzpjuuF414G2svPxfdmq+jmavjrT5O9ushT+myLjcrECj/5UawuFiL//5PpVxxVaVmsTrWFuu6Il6eQ8pjMXNF7pr2mKSS18Infu11FnN7MXO3bt304x//WN9++63GjBkT1mNOblyPnip84YUXql+/frrttts0adKkUo/Jy8uL6HcNp3+TPHracMOGDSVJGzduLLX8gQce0K5du065WNPYsWPVqlUrXX/99Vq0aFGV3WcIqE5Ch4+UfN5r4AAFRgyX76JeKn5whkLBoNvRTlF44FsFQ865fjjozcudWhprVD1L9fHDge8cX7yEFOK5CABV5LbbbpMk/eUvf9GePQ6fsVL5jaskTZs2TZI0cuTIKjvr1ZNdXqtWrZSWlqapU6eqQYMGatKkiXJycrR06VJJOqV5ffTRRyWVdPjjx4/XW2+9pToOVwEMt7v/42vS5q+c16sMmZlZypni0atYVLENGzY4rjNz5kzHWyjNmDEjVpHC4pTbrcx9l3+ot/btjegxwSefki8hQf6hN0mSAmNuU9GosQouWqzA4OvD3k5WVpZer+Srs2x5X9rybsXr+PzS4jceV9IZj1dqlngbay8/F92ar6OZq+OtPk727U5p+fyK1wn4E/TL392o3z97Y6VmsTrWFuu6Il6eQ8pjMXNFJtxf8ncvFAqV+trrLOZ2O3NWVtYpn8e+7LLLJEnPPPOM4+Mralylkt5r+/btat68uTp06KC1a9ce+1lmZqZyc3Nj84ucwJNHXv1+vxYuXKjU1FSNHj1aw4cPV8OGDTV27FgFAoFjF2s6WWZmpvx+v9591+FVK+LSyacrWGAlc3BlvoJLX1Fgwm/k+8+ZDb7atRW4604F585TaOtWlxOW1iRNSqihks+9luO8zlLSGVUWKWzWxrosVuraImv1Ufe8kn/l8km1G0gNW1dZpLBZG+t4YnEOsZgZ1U/9+vV1/vnna//+/VqzpuKLEjg1rkd99NFHkk49uFhZPHnkVZLatWunZcuWlVo2dOhQpaSkqFatWpJKLtv8zTffqEWLFpJKLti0efNmdezYscrzHjXo7tyIliN2srOz3Y4QMSuZ/V0y5F/y3KnLO6XK/+JiFxJVrMYZUpdB0sqckgszHfOfizid3UZq79GPk1sb67JYqWuL87W1+vD5pPQBJc/Fgq90yoXUatWVulwv+T34Vrq1sT7KYl2fzMocciKLmVH9nHdeybuJ27ZtU3Fxcbnrhdu4StJnn31WatuVzbPNa1mWL1+unj2PX/Dghx9+0JAhQ1RYWKiEhATVrFlT8+bNU/PmzV1MCbd07NhR69evdztGRCxmtqLuudJFPyu5j+TG/7wPdk47qUm6VL9ZyYtqVA7qGidKqi11v0na81nJ8/HrLSXLU/tLjdpLFVzLCdWUxTnEYmZUP+vWrVNycrLj9YFq1KihRo0aOTaukjR58mT94Q9/0P79+2Mdt0xm/mQUFhZq48aNpa6Kdc455+iDDz5wMRUAL0usKTXvdrx57XyNu3mA6sofkM5pX/Lv9f9c4PvcVHczAUB1EwqFVFhY6LheYWGh+vfvrxYtWjieXlxVTetRZprXOnXqVHh4GwAAAAAQvYKCAsfG1Q0e/JQJcHqysrLcjhAxi5kBJ9Q1gGhYnEMsZgYsonlF3JgzZ47bESJmMTPghLoGEA2Lc4jFzIBFNK+IG6NHj3Y7QsQsZgacUNcAomFxDrGYGbCI5hVxozJuhFzZLGYGnFDXAKJhcQ6xmBmwiOYVAAAAAOB5NK8AAAAAAM+jeUXcsHhzcIuZASfUNYBoWJxDLGYGLDJzn1e3NKlfPfdt0YIFC5Sdne12jIi4lTk9ObnK9+mFfbuhOo61W3Xt1pwZzX6rY324xepYW6zraPH3HIiNjIyM03rclu27JEmtmp9b6uuq2LcTmlcHAy9wOwHCde+995r7w+FW5ofap1T5Pqur6jjWbtW1xfm6OtaHW6yOtcW6jhZ/z4HYmDVr1mk9bsL9j0uSpt01stTXXsBpwwAAAAAAz6N5BQAAAAB4Hs0r4sbs2bPdjhAxi5kBJ9Q1gGhYnEMsZgYsonlF3EhNTXU7QsQsZgacUNcAomFxDrGYGbCI5hVxIzMz0+0IEbOYGXBCXQOIhsU5xGJmwCKaVwAAAACA59G8Im50797d7QgRs5gZcEJdA4iGxTnEYmbAIppXxI2PP/7Y7QgRs5gZcEJdA4iGxTnEYmbAIppXAAAAAIDn0bwCAAAAADyP5hVxIycnx+0IEbOYGXBCXQOIhsU5xGJmwCKaVwAAAACA59G8Im4MGjTI7QgRs5gZcEJdA4iGxTnEYmbAogS3A3jdHZ+u06qCAlf2nZ6crIfap5zWY59bLu3cF+NAYWhSXxp4QdXvFwAAAEB8o3l1sKqgQG/t2+t2jIjt3Cdt/srtFAAAAAAQG5w2jLgxduxYtyNEzGJmwAl1DSAaFucQi5kBi2heETfGjRvndoSIWcwMOKGuAUTD4hxiMTNgEc0r4kbv3r3djhAxi5mtOVR4/Ovvd0vFRe5lqS6oa5Sl6JD03a7j3x856F4WeJvFOcRiZsAiPvOKuLFnzx63I0TMYmYLCr6SdqyS9nwmHf7h+PKPnpF8PqlOI+m8TtK5KVJCDfdyxivqGkcdKpR2rpa+XC/tP+nyEXmPSLXqSud0kJqklXwNSDbnEIuZAYtoXgHEjcP7pU/flHZvKH+dUEgq2C19ulva/I7Uro90bmpJUwsgNoLF0raPpK3vS6Fg+esd+E7a9mHJui26Sa0ukgKJVZcTAGALzSviRkrK6d1WyE0WM3vVd7uk/MXSkf3hP6bokLTuFenrLVLqlVKAGTEmqOvq7fD+kufi97uc1z0mJP17ufT1VqnL9VLNMystHgywOIdYzAxYxGdeETcWLVrkdoSIWczsRd9/KX2yMLLG9URfbZT+9ULJ0SJEj7quvo4ckFYsiLBxPcEP30jL/y4ddOf26vAIi3OIxcyARTSviBv33HOP2xEiZjGz1xQdlv61RCo+XP46fe8s+VeRb7aWnL6I6FHX1df616Qfvq54Hafn48HvpbVLS07xR/VkcQ6xmBmwyNPNazAY1PTp09W2bVvVrFlT6enpysvLU/v27TVy5Ei348FjFi5c6HaEiFnM7DWfvV3yYjcWtn4gFXLNjahR19XTVxtL/sXCvs+lnatisy3YY3EOsZgZsMjTzeuIESM0efJkjRo1Si+//LKys7N14403asuWLerWrZvb8coUOnJER24bp+LHnii1vHjx8zpy8zCFCgvLeaS7cqZk6aPnp4S9HPCCwz9IO/8Vu+2FgtK/P47d9oDqIhQqefMnlrZ9VPHFngAA1Y9nL08yf/58Pf3008rNzVVmZqYkqU+fPvrkk0/03HPPqWvXri4nLJsvMVEJE36top/fLl+P7vJ3yVBo61YFn/yrAr+/T746ddyOCMSNL9ZIoRh/TnX3p1LbPlJSrdhuF4hn339ZcouqWDr4fckFnM5uHdvtAgDs8uyR16lTp6pfv37HGtej2rRpo8TERKWlpZVa/vjjj8vn8yknJ6cqY5bJ17KF/LcOU/H0mQrt3auiaQ/Kf+018qd1djtaXMvLy3M7QsQsZvaSvdtjv81gsfTdzthvtzqhrqufynguVuZ24W0W5xCLmQGLPNm87tixQ2vWrNHgwYNP+dn27duVmpqqGjVqHFu2adMmPfXUU+rZs2dVxqyQf8C18jVvpqJRY6VAQP5hQ92OFPfWrl3rdoSIWczsFUfv11oZvv+ycrZbXVDX1U9BJT1nKmu78DaLc4jFzIBFnjxteMeOHZKkxo0bl1p+4MAB5eXlqX///seWFRUV6dZbb9WcOXN0++23h70Pn88X1nqBB6fJn57mvGIZ2/eldVZoxSfy35AtX2Lkd13Pzc2Vr/vpNeTXT1ymph2zInrMRy/8XiuWTi+17MjBQjXv1DfsbeTl5eoXV/SJaL/hGD9+vOM6M2fOdFxv5syZsYoUlnDyeC2zFUkJNfV/fzhQapnTFYXL+/nrpctes//fnzXjkp9FkS5+WX0uonI9PO59dWxR+u/V6TwfT34urv/XFnX/CecNxxOLc4jFzBW5a9pjkkpeq574tddZzG0xs+RO7lCYl5j3ZPPasGFDSdLGjRt15ZVXHlv+wAMPaNeuXaUu1jR58mT1799fGRkZVR2zQqGtWxX829/lHzJYwXl/k/+Si+Rr1MjtWBXqce1E9Rhwd6llOVOy3AkDOKjMSdTn8+RJKYB3Vdbz0cCLPABA1fFk89qqVSulpaVp6tSpatCggZo0aaKcnBwtXbpUko41rx9++KHefPNN5ebmRryPcLv7vss/1Fv79ka27cNHSj7nOnCAAsOHKbRvn4ofnKHA/VPl84f/ojgrK0uvn+aN7v74mrQ5xhfPCEdmZpZypsT+5nwbNmxwXGfmzJmOt1CaMWNGrCKFxSm3FzNbEQpJuQ9LxUeOLzv5qM1RR4/wlPfzk40ae6umL7g1uoBxyupzEZUr/znp6y2ll8Xi+dg+5fyw/17DBotziMXMFZlw/+OSSl4Ln/i111nMbTGz5O3cnjy84Pf7tXDhQqWmpmr06NEaPny4GjZsqLFjxyoQCBy7WNOyZcu0efNmtW7dWi1bttQHH3ygMWPG6KGHHnI1f/DJp+RLSJB/6E2SpMCY2xT6creCixa7miveTZo0ye0IEbOY2St8Pim5kk5mOPOcytludUFdVz/JlfScqaztwtssziEWMwMWefLIqyS1a9dOy5YtK7Vs6NChSklJUa1aJfewmDBhgiZMmHDs51lZWRo3bpwGDRpUpVlPFFyZr+DSV5Tw6MPyJZQMr692bQXuulPF/3O3/Bd0le/8813LF8+ys7PdjhAxi5m9pF5T6dtKuDJw3Sax32Z1Ql1XP/WbSlsrabuofizOIRYzAxZ58shreZYvX17q865e5O+SocQlz8nXrPRfXH+nVCW+uNizjeugu3NP+bxrRcu9qGPHjm5HiJjFzF5yXiXcfapha6lmcuy3W51Q19VP/eZSrXqx3WZiTenstrHdJmywOIdYzAxYZKZ5LSws1MaNG9W1a9dy18nNzXX1qCuAqlW7ntSoXWy32eKC2G4PqA58Pql5jN9bbtZVCnj2/DAAgBvM/FmoU6eOiouL3Y4BwGPaXyrt/bdUdCj6bTVJk+o3i347QHXUNEPavSE2p/KfcZbUskf02wEAxBczzSvgJCsry+0IEbOY2Wtq1JFSr5RWPS+pnAvhhXNV0zqNpLaZsUxWfVHX1ZPPJ6X2lz6eLx3+ofz1nJ6PCTWkTldLfl6hVFsW5xCLmQGLzJw2DDiZM2eO2xEiZjGzF53dWup8jXS6t2dNPkfqOqjkRTOiR11XX7XqSd2yS95UOh2JNaUug6Tks2MaC8ZYnEMsZgYsonlF3Bg9erTbESJmMbNXndNO+tHQCG9z4ys5NfGCG6Wk2pUWrdqhrqu3M86Seg6TGqdE9riGraWet0h1z62UWDDE4hxiMTNgESflIG7k5ua6HSFiFjN7WZ2zpQtukvZskj5fKX27o+z1AknSeakln9E746wqjVgtUNdIrCV1ulJqmi7tyJd2b5RCZVy2wueTGrYpeS42aF7yPWBxDrGYGbCI5hVAXPH7pXPal/wrOiR9v1s68K0UCpY0rcmNpDManP4pxgDCV69Jyb+UH0uFX5f8CxZJvoBU56ySN5wCiW6nBABYQfMKIG4l1Cg5mqPmbicBqjd/gnRm45J/AACcLo49IG6sX7/e7QgRs5gZcEJdA4iGxTnEYmbAIppXxI0FCxa4HSFiFjMDTqhrANGwOIdYzAxYxGnDDtKTk03uu0n9GAYxsF9Juvfee5Wdne1egNNgMTPghLoGEA2Lc4jFzIBFNK8OHmof4bX+PWLgBW4nAAAAAIDY4bRhAAAAAIDn0bwibsyePdvtCBGzmBlwQl0DiIbFOcRiZsAimlfEjdTUVLcjRMxiZsAJdQ0gGhbnEIuZAYtoXhE3MjMz3Y4QMYuZASfUNYBoWJxDLGYGLKJ5BQAAAAB4Hs0rAAAAAMDzuFUOTOjQoYPjOvfee29Y61UlpzxezAxUxOpzEYA3WJxDLGYG4hVHXhE3fve737kdIWIWMwNOqGsA0bA4h1jMDFhE8woAAAAA8DyaVwAAAACA59G8AgAAAAA8j+YVAAAAAOB5NK8AAAAAAM+jeQUAAAAAeB7Nq4OxY8cqIYHb4QIAAAC5ublKTU1VmzZt9N///d8qLi52O5KjX/7yl2ratKmp1/Sff/65LrvsMnXs2FGpqan6n//5H7cjheWKK65QRkaGOnfurEGDBun777+P6fZpXivw9ttvq7Cw0O0YAAAAgOuCwaD++7//WwsXLtRnn32m77//XvPmzXM7lqPBgwdr+fLlbseISEJCgu6//36tX79eK1eu1DvvvKMXXnjB7ViOFi5cqPz8fK1evVpNmzbVjBkzYrp9mtdyHDp0SBMmTND06dPdjgIAAAC47uOPP9Z5552nlJQUSdKIESO0aNEil1M5u/jii9W4cWO3Y0Tk3HPP1QUXXCBJSkpKUpcuXbR9+3aXUzmrW7eupJI3Og4ePCifzxfT7dO8luO+++7TiBEjdPbZZ7sdBQAAAHDdjh071KxZs2PfN2/eXJ9//rmLiaqHvXv36vnnn9fll1/udpSwXHfddWrUqJE+/fRT3XHHHTHdti8UCoViusU48K9//Uu/+tWv9Nprr8nn8ykhIUFFRUVuxwIAAAAiEgwGNX/Jm/p633eSpF1ffSNJOrfRWaW+PirzR+nKSGlT5rZycnK0ePFiPfvss5Kk9evX6yc/+YlWrlwZ89xrN23T6++sOPZ9RbnrnXmGbh5whQKBio/LVfZr+iNFRZq76FUV7j/gmFmSruzzI7Vt2bTCbR4+fFj9+vXTVVddFfNG8KiPVm3Q+5+sPfZ9Rbkbn91A2VdlOR5RPXz4sEaMGKHLLrtMt9xyS8yycuS1DO+++67WrVun888/Xy1btlRxcbFatmwZ8w8cAwAAAJXJ7/frku6d9eWevccaEUmnfL3rq2+UEAioc4dW5W6rWbNmpY60bt++XU2bVtx8na6ObVqoVs2kY9kqyn3RBZ0dG9eqkJiQoF7dUsPKXO/MM9SmRZMKt1dcXKyf/OQnysjIqLTGVZK6pLZRMBh0zP3VN/vUu0daWKcCJyUl6YYbbtDixYtjmtX9/8seNHr0aH3xxRfatm2btm3bpkAgoG3btunMM890OxoAAAAQkeZNzlGfXl0qXCcxIaDsq7MU8JffHlxwwQXasWOH1q1bJ0n6y1/+ooEDB8Y061F+n0+Dr8xSjaTECte7+ILOjk1gVUpp00Ld0zpUuM4ZtWpqYL/ejk3gyJEjlZycrIceeiiWEU+RmJCgIddcWuH/e0m64pLupY4cn6ygoEC7du2SVHLEf8mSJUpNTY1pVppXAAAAIM5ddmFXNWncsNyfX3VpL53doF6F2wgEAvrzn/+sQYMGqXXr1qpTp46GDh0a46TH1a+brP+6/KJyf97orPr6cWZ3x+2MGjVKTZs2VXFxsZo2baqxY8fGMuYprr60pxrUTS7359f1u0TJZ9SucBvvvvuunnzySS1fvlxdunRRRkaGHn744VhHPea8Rmfp8ksuKPfnLZs21iXdO1e4jYKCAv3Xf/2X0tLSlJaWpqKiIt19990xzclnXiMUCoViftUsAAAAoLJ99fU+PfzX51RUVPrerO3Ob6bhg/t58jVuKBTSs8+/rjUbt5ZaHvD7NeanA9TknPIbcjdt2/GlHvvbizq51erWqZ0GX5XlTigHwWBQj89/Sdt2fFlqeY2kRP3y1kEVNuRVhSOvEcr7cJWeff41FRm4ITMAAABwVKOG9dU/80elltWuWUOD+jufwuoWn8+n6358ieqcUavU8r4Xd/Ns4yqVHKnM/FF6qWX1zqyja/pe6FIiZ36/X9lXZSnppFO1r7nsQk80rlIcNK+rV6/W9ddfr4YNG6pmzZpq27atJk6cWCn7OnTosN76cJUOHylSQiBQKfsAAAAAKkuvbqmlPiM64MeX6MzkM1xM5OyM2jU1qH/mse9bNDlHvU9qDL2o78Xdjn1G1Ccp++o+qlkjyd1QDhrUO1PXXNbr2PcpbVuqW+d2LiYqzXTzumLFCvXs2VNr167Vgw8+qKVLl2rChAn68ssvnR98Gt77ZK32Hzykvhd1q5TtAwAAAJWp5EJImapZI0kZKW2UVsHVhb2kQ+vm+lFGRyUlJij7qj6OFxfygoRAQEOu7qNAwK9LeqSpVbNz3Y4Ulgs6t1fHNi1Up3YtDex3iaeOypv+zGtWVpbWrVunTZs2qW7duhE9dsL9j1dSKgAAAABAuKbdNTKs9bz/lkU59u/fr7fffls33nhjxI0rAAAAAMCWBLcDnK59+/YpGAye9o2Rw+3upZLPut7/p/lqdl4jDR/c/7T2BwAAAAA4fWab1/r168vv92vnzp2n9fjTOW340y2fc7oxAAAAAMRQ3J82XLt2bfXu3Vvz58/X999/73YcAAAAAEAlMn3BphUrVqh3795q0aKFfvOb36hFixbavn273n77bf35z3+OyT6Wvb9S/3zrY40dOkDNzmsUk20CAAAAACJj9rRhSerWrZvef/99/fa3v9X48eN18OBBNWvWTDfccENMtn/o0GG9/dG/1L5VMxpXAAAAAHCR6SOvlW3XV99o3vOv6YarL6V5BQAAAAAX0bw6CAaD8hu4CTIAAAAAxDOaVwAAAACA53FIEQAAAADgeTSvAAAAAADPo3kFAAAAAHgezSsAAAAAwPNoXgEAAAAAnkfzCgAAAADwPJpXAAAAAIDn0bwCAAAAADyP5hUAAAAA4Hk0rwAAAAAAz6N5BQAAAAB4Hs0rAAAAAMDzaF4BAAAAAJ5H8woAAAAA8DyaVwAAAACA59G8AgAAAAA8j+YVAAAAAOB5NK8AAAAAAM+jeQUAAAAAeB7NKwAAAADA82heAQAAAACeR/MKAAAAAPA8mlcAAAAAgOfRvAIAAAAAPI/mFQAAAADgeTSvAAAAAADPo3kFAAAAAHje/we491QuZTfsugAAAABJRU5ErkJggg==\n"
},
"metadata": {},
"execution_count": 8
}
],
"source": [
"for i in range(n):\n",
" circuit.measure(i,i) #measure all Query qubits\n",
" \n",
"circuit.draw('mpl')"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"simulator = qiskit.Aer.get_backend('qasm_simulator') #access Aer Simulator\n",
"job = qiskit.execute(circuit,simulator,shots=1024) #run circuit 1024 times, to get probability distribution"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Correct!\nThe hidden bit string was 0000\n..and we measured 0000\n"
]
}
],
"source": [
"result = job.result()\n",
"measurements = result.get_counts() #returns dictionary, with output string as keys \n",
" #and count as the respective value\n",
"\n",
"#get the result which occurred the most\n",
"measurement = max(measurements, key=measurements.get)\n",
"\n",
"measurement = measurement[::-1] #flip result\n",
"\n",
"if measurement == hidden_bits: #confirm the algorithm works\n",
" print('Correct!')\n",
" print('The hidden bit string was',str(hidden_bits))\n",
" print('..and we measured',str(measurement))\n",
"\n",
"else:\n",
" print('Not quite right. Try checking over your program')"
]
}
]
}
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