diff --git a/applications/chemistry/qpe_for_molecules/qpe_for_molecules.ipynb b/applications/chemistry/qpe_for_molecules/qpe_for_molecules.ipynb index 62252214a..b39178863 100644 --- a/applications/chemistry/qpe_for_molecules/qpe_for_molecules.ipynb +++ b/applications/chemistry/qpe_for_molecules/qpe_for_molecules.ipynb @@ -234,7 +234,7 @@ "outputs": [ { "data": { - "image/png": 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", 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1XzyxbKNfqldccYWpvdNmg+BO0fF4/06dB07RjtkayAaOnj148GBSkqdWd24n4jNL1GehwUW/fv1CPqYDAmoaiasd++2uBjXR0Z+hRnMG01GMdtOazviiP9C1VioUO6gLrs3VmqpQy7XJV9/zCy+8YP7W/2twUZPg7WpDB6PZn0dwIJ2M8kR6rGmNV6jjT0fzOql1Dd+fiZxZSgdqaGtBqMFLoZbZdN9qTX+k6LMXA81tEyoit5tEtQpbI3ntB6FfKoFDsbVaXLPIa7NFJM18do6x4BNAn19raLSPVaiAxv6C0vW0v5X2X/v2228r/aLWvnw10QuL9iXQ7POhZirQzyHS9xppmZ0QSbmDxat84fahBlXBTRh64mu/jXBT4cSyjU1Heek+11FmoZoh4vH+nToPnKLlCd73OuuNkzUHkaru3E7EZ5aIz0Jz6OnFNLDJOdpgz+k+e9rnUWuU9H1qud59991qa0fsvoSB54Tuh08++aQiaAmkAZIdYNnvX0d91iRwu9rS2jMV/N2XrPJEeqxpDbB+v9n9Cu3KE62Fc0J5hN+f4c7NeNDPRn9c6zU6sB+hBnqaCSEc7euoP1QiRc1eDLRKWvvUXHTRReYXlDYz6K9PzcGkvyq1KdfuD6JfQPrlrL8g9Jejpk/QgyrSuRm1T4G69957zReUpmDQviN6MGo6CA08NQ2DDqPXE1ibO/Qg0Jobu+lDL/Jz5841v+a0HFq9ryeaftEFnlTh6PByre7WPGqawkR/TegJqL+G9YtTO7xG+l4jLbMTIil3sHiUL9w+1I7KmoZA+3nqBU37A+lraJqC4LxtNm2WiXYbO/3Oww8/bFJN6Jf99OnTKz2uTbfxev9OnAdO+fnPf25S0OgFXN+bDrTS92WniEik6s7tRHxmifgstH+Yqi7Y02NYL/KJ6LOnAZt+xhqgae2ofi/a/afC0e8N/XH09NNPmxpX/SGp54k2B+qcu5rOSvu+duvWzayv36n2+VTT+w8UuF1taf8z7a+s+1NzZtqSVZ5IjzU9D3R6N722agonvc5qihbtduLEQI7SCL8/w52b8aLHkF6rtAZc88BqUDp58mSzD0PNL665KfW7WHN9Rizicbuo8P7775uh1D/4wQ+sxo0bV0yddvPNN1vfffddpXULCgqsn/70p2Y9HVp91llnWYsXL660jj08W4euh6JTsrVt29akEQke2q2vp8PI27dvb9WrV8/Kzc21Bg0aZP3hD3+o9Bx/+9vfrF69epmyHn/88dazzz4b1XRpmrZFU5kcd9xxVoMGDcxz6OseOnQoqvcaaZmdSL0SSblDbRdJ+cLts3DlCLUPtQx33HGH1b17d5NSo1GjRub/U6dODbsfIt0muBw1pa+Idv+EEm7fOHUeODFdmqZJueaaa6wWLVqYsmiZ/vWvf5l0D4GpU8KVRdfRz7ym14o0NUR153ZtPrNIXr+2n0UkqS4mTpxo1vniiy9CPq5TavXp08dKBP0u0M/aTrOi0/tFStOVaDn1O6RZs2bWvffea9I36XVA02O89NJLZr3y8nKzr+zURTW9f1vwdk548sknzX4NTHvidHlqOgdtkR5rStPAaDobvVadfPLJ1vTp0x1LvXIoiu/cUOdmdd9R1aVeieTcmT9/vtWjRw/zvnXa1eeff9667bbbTNq0YJrqp0OHDlFNl5am/zgbowIA4B46UlprSbXPo9aczp8/v0piaidoMl5NFBxtWo9Yt6uONldqDZ/WBAemCkpWeRA97Yqktd+Bfe61dl9bEO+66y4ZPXp0xM9Fnz0AgGdpagsdbauBnjaHazeOeAR6tenn5mT/OJs2mersKzraNNqsDPEoD6qn6VcCaYCn4wACp51UOqpZm5WjzfVHsAcA8Cyt/dAkukr7K2tetermiQ686Xyn0dC+sbEESbFuVxPt/2aP4HZDeRCe1sLefffdZvo9zfeo01ZqajcN2ANpkKeDLUOlMqoOzbgAAM/SOUcjyTwQitai6Fy4QLzpwE4dHKcjpjWQ0xHVOsjQqbmTCfYAAJ61efNm2bdvX8z52MJN4wakEoI9AAAAD6PPHgAAgIeRVNmFdOSUDnnXqasSOW0LAACInTaWavJmnZUj2oEx8USw50Ia6CVyvlAAAOCcTZs2mdk63IJgz4W0Rs8+WBI5bygAAIhdSUmJqayxr+NuQbDnQnbTrQZ6BHsAAKSWNJd1wXJPgzIAAAAcR7AHAADgYQR7AAAAHkawBwAA4GEEewAAAB5GsAcAAOBhBHsAAAAeRrAHAADgYQR7AAAAHsYMGj5SfsySf6zfIztKD0rLJhlyauccqVvHXVm+AQCAswj2fGLu6m0ybnahbCs+WLGsdXaGPHB+vpzbtXVSywYAAOKHZlyfBHo3Ti+oFOip7cUHzXJ9HAAAeBPBng+abrVGzwrxmL1MH9f1AACA9xDseZz20Quu0QukIZ4+rusBAADvIdhz2DfffCNDhgyRxo0bS4sWLWTkyJFSVlaWtPLoYAwn1wMAAKmFARoOKi4uloEDB0qbNm1kxowZsmfPHrn11lvlu+++k7feeispZdJRt06uBwAAUgvBnoN+//vfy86dO2X58uXSsmVLsywzM1MuueQSWbFihfTq1SvhZdL0KjrqVgdjhOqVp4lXcrP/nYYFAAB4D824DpozZ46p2bMDPfWLX/zCNOm+++67SSmT5tHT9CoqOKOe/bc+Tr49AAC8yfPB3ldffSXPPPOMXH311dKtWzdJT0+XtLQ0GT9+fETba3PsgAEDpFmzZtKoUSPp3r27TJw4UY4cOVJl3cLCQvnhD39YaZm+3kknnSRr1qyRZNE8etOG9zQ1eIH0b11Onj0AALzL882406ZNk0mTJsW07S233GK21YBNa+y0hm7BggUyduxYmT17tnz44Yemmdb2/fffS9OmTas8jwaK2n8vmTSgG5yfywwaAAD4jOdr9rp27Sq33367vPrqq6Z2bcSIERFt9/bbb5tATwO8pUuXygcffGAGWaxdu9bUEC5atEjuv/9+SSUa2PXNay4X/LituSfQAwDA+zxfs3fddddV+rtOncji20cffdTc33XXXdKzZ8+K5ZpOZerUqXL66afL5MmTTcCXnZ1dUYO3d+/eKs+lNX4nnnhiLd8JAABA9DxfsxeLLVu2yLJly8z/L7/88iqP9+/fX9q3by+HDh0ygzJs2l8vuG9eeXm5fP3111X68gEAACQCwV4IK1euNPc5OTnSuXPnkOuccsopldZVmkx54cKFJv2KTfv27du3T84777ywr6dBY0lJSaUbAACAEwj2Qli/fr2579ChQ9h1tGYvcF31m9/8xgSIF1xwgbz//vvy2muvyQ033GD+toPDUB577DHTFGzf7OcGAACoLYK9EEpLS829ploJRwduqMBaOB2Jq6N1s7Ky5Je//KXcfPPNcuGFF8r06dOrfb27777bzL5h3zZt2uTYewEAAP7m+QEaiaY59ebOnRvVNg0aNDA3AAAAp1GzF0KTJk3MfVlZWdh1tB+e0lo8AAAAt6JmL4ROnTqZ++qaU+3H7HVTSfkxyyRX3l58QPaUHZacxg0kN4skywAAeBHBXgg9evQw97t37zYDMEKNyF2+fLm5D8zBlwrmrt4m42YXyrbig1Uea52dYebJZfo0AAC8g2bcENq1aye9e/c2/9cRtcF09gyt2dN+dppuxSlTpkyR/Pz8iteOR6B34/SCkIGe0uX6uK4HAAC8gWAvjHvuucfcT5gwQQoKCiqWa23fyJEjzf9vuummitkznDBq1CgpLCysSOjsdNOt1uhZEayr6+n6AAAg9aVZluXpq7oGanZwpoqKimTXrl2m9q5t27YVy2fNmiWtW1duvhw9erQ8/fTTUq9ePRk0aJBJxTJ//nwzJVq/fv1k3rx5kpmZ6XiZNZ2LBpGahsWpASBLinbLsOc+i3j91/+rj5k/FwAAJO/67YR0P3zwS5curbJ88+bN5hY4i0WwSZMmmaBOm1cXL14sR44ckby8PDNf7pgxY6R+/fqSKnaUHozr+gAAwJ08H+wNGDBAalN5OXToUHNLdS2bZMR1fQAA4E702fMJTauio21roolXdD1dHwAApD6CPReJ52hczZ+naVUiyaKn65FvDwAAb/D8AI1UFM8OnuTZAwAgPhigAVfQQG5wfi4zaAAA4BMEez6kAR1pVQAA8Af67AEAAHgYwR4AAICHEewBAAB4GMGeT1KvAAAAfyL1igu5deg2AABIves3NXsAAAAeRrAHAADgYQR7AAAAHkawBwAA4GHMoAEpP2YxfRoAAB5FsOdzc1dvk3GzC2Vb8cEqj7XOzpAHzs838+kCAIDURDOuj/PsaaB34/SCkIGe0uX6uK4HAABSE3n2fJqnR5tu+z++IGygZ9NG3NzsDFk0diBNugAAVIM8e3AV7aNXU6Cn9JeArqfrAwCA1EOw51M7Sg/GdX0AAOAOBHs+1bJJRlzXBwAA7kCw51OaVkVH29ZEe+npero+AABIPQR7PqWDLTStSiRDLnQ9BmcAAJCaCPZ8TPPnTRveM2wNny7Xx8mzBwBA6iKpss9pIDc4P5cZNAAA8CiCPZclVdZbeXl5Ql9XA7q+ec0T+poAACAxSKrsQm5NyggAAFLv+k2fPQAAAA8j2AMAAPAwgj0AAAAPI9gDAADwMII9AAAADyPYAwAA8DDy7KGK8mMWSZYBAPAIgj1UMnf1Nhk3u1C2FR8MOX2azpPL9GkAAKQOmnFRKdC7cXpByEBP6XJ9XNcDAACpgWAPFU23WqMXyXQqup6uDwAA3I9gz0V0Xtz8/Hzp3bt3wl9b++iFq9ELpCGerqfrAwAA9yPYc5FRo0ZJYWGhLFu2LOGvvaP0YFzXBwAAyUGwB6Nlk4y4rg8AAJKDYA+GplXR0bY10cQrup6uDwAA3I9gD4bmz9O0KpFk0dP1yLcHAEBqINhDBc2fN214z7A1fLpcHyfPHgAAqYOkyqhEA7nB+bnMoAEAgEcQ7KEKDej65jVPdjEAAIADaMYFAADwMII9AAAAD6MZF9XSadHovwcAQOoi2ENYc1dvM/PghppGTUfmagoWRuYCAOBuNOMibKB34/SCsPPl6nJ9XNcDAADuRbCHkE23WqNnRbCurqfrAwAAdyLYQxXaRy9cjV4gDfF0PV0fAAC4E8Gei0yZMkXy8/Old+/eSS3HjtKDcV0fAAAkDsGei4waNUoKCwtl2bJlSS1Hyyahp0sLZ8Ou/XErCwAAqB2CPVShaVXCzY8byv9+9DUDNQAAcCmCPVSh+fM0rUo0WfQYqAEAgDsR7CEkzZ83bXjPiGr4GKgBAIB7Eeyh2oBv0diBctNZJ0S0PgM1AABwH4I91Nik2++EFnEZ2AEAAOKPYA8RD9gI14dPl+vjuh4AAHAXgj1EPGBDBQd89t/6uK4HAADchWAPUQ3YyA0asKF/63J9HAAAuE96sguA1KEB3eD8XDPqVgdjaB89bbqlRg8AAPci2ENUNLDrm9c82cUAAAARohkXAADAwwj2AAAAPIxgDwAAwMMI9gAAADyMYA8AAMDDCPYAAAA8jGAPAADAwwj2AAAAPIxgDwAAwMMI9lxkypQpkp+fL7179052UQAAgEekWZZlJbsQqKykpESys7OluLhYsrKykl0cAACQwtdvavYAAAA8jGAPAADAwwj2AAAAPIxgDwAAwMMI9gAAADyMYA8AAMDDCPYAAAA8jGAPAADAwwj2AAAAPIxgDwAAwMMI9gAAADyMYA8AAMDDCPYAAAA8jGAPAADAwwj2AAAAPCw92QVAaio/Zsk/1u+R7cUHZE/ZYWnasL7s3e/cfU7jBpKblSGnds6RunXSkv12AQBIWQR7iNrc1dtk3OxC2VZ8MO6v1To7Qx44P1/O7do67q8FAIAX0YyLqAO9G6cXJCTQU/o6+nr6ugAAIHoEe4iq6VZr9KwEv66+3oN//dK8PgAAiA7BHiKmffQSVaMXbHvJIZm84JukvDYAAKmMYA8R21GanEDP9tRHX9OcCwBAlAj2ELGWTTKSXQTTjExzLgAAkSPYQ8Q0DYqOjk0mbUZ+8K+rZdbKLbKkaDeBHwAANSDYc9g333wjN9xwg/Ts2VPq1asnnTp1Eq/QfHeaBiXZWe9e+exbGfPmKhn23GfS//EFNO0CAFANgj2Hffnll/Luu++aIK9r167iNZrvbtrwnkmv4bORmgUAgOqlWZZFO5iDjh07JnXq/DuG1hq+uXPnyoYNG6J6jpKSEsnOzpbi4mLJysoSv8ygsafskExeWCTFB45EVRataczNzpBFYwcy2wYAIGlKXHr9ZgYNh9mBntdpUNU3r7njz9s+p6HcML0gqm2s/9TwafAZjzIBAJDKUi4y+eqrr+SZZ56Rq6++Wrp16ybp6emSlpYm48ePj2j7GTNmyIABA6RZs2bSqFEj6d69u0ycOFGOHImuNgnxaya+tl+nlEwNAwCAG6Vczd60adNk0qRJMW17yy23mG01QBw4cKA0btxYFixYIGPHjpXZs2fLhx9+KJmZmY6XGdE5Oz9XXvg0uqZvt6SGAQDAbVKuZk8HPdx+++3y6quvypo1a2TEiBERbff222+bQE8DvKVLl8oHH3wgb731lqxdu9bUEC5atEjuv//+Stu89NJLptawptvMmTPj9G79KdoUL9pLT9fX7QAAQIrX7F133XUx9ZF79NFHzf1dd91l0qLYWrRoIVOnTpXTTz9dJk+ebAI+7VypLrroIunTp0+Nz922bdso3wUiSfGio2wjHT2k6zM4AwAADwR7sdiyZYssW7bM/P/yyy+v8nj//v2lffv2smnTJpkzZ44MGzbMLNegzw78kJwULzpjRnXz8WqNngZ6uj4AAPBpsLdy5Upzn5OTI507dw65zimnnGKCPV3XDvaQXBrADc7PDZniJadxA8nN+nfTLTV6AAD4PNhbv369ue/QoUPYdbRmL3DdWO3fv9/UDqp169aZv+0+fb1795aOHTtW2ebQoUPmFpinB/FN8QIAgF/4ItgrLS0195pqJRwduOFEoLVjxw659NJLKy2z/37xxRdNyphgjz32mIwbN65WrwsAAODbYC+RdJq0aCclufvuu+XWW2+t+FsDTrumEQAAoDZ8Eew1adLE3JeVlYVdZ9++feY+GdObNGjQwNwAAACclu6X2jalAzDCsR+z14W72XPz6qwZmkyZgRoAAPg42OvRo4e53717txmAEWpE7vLly819YA4+uNPc1duqpGQhBQsAAB6ZQSMW7dq1MyNh1WuvvVblcZ09Q2v2tCl1yJAhkixTpkyR/Pz8irIidKCnyZaDc+/p3zdML5Bxf10tS4p2m5o/AADgk2BP3XPPPeZ+woQJUlBQULFca/tGjhxp/n/TTTclNYnyqFGjpLCwsCIBNCrTAE5r9KoL415cvFGGPfeZ9H98gQkMAQDwuzQr2qGjSaaBmh2cqaKiItm1a5epvQuctmzWrFnSunXlJr3Ro0fL008/LfXq1ZNBgwaZVCzz58+XvXv3Sr9+/WTevHmSmZkpyaajcTXoLC4uTsqAEbfSGjsN5CKlPfh0Fg6adgEAfr5+p6fiB7l06dIqyzdv3mxutsAkxbZJkyaZoE6bSxcvXixHjhyRvLw8M1/umDFjpH79+nEvP2KngzGipTWBOgsHgzcAAH6VcsHegAEDos5jF2jo0KHmhtSjo26jYf2nL5+O2mUWDgCAX/mmzx5Sn6ZX0VG3iagRBADAKwj2XITRuNXTplhNrxLvGkEAALwk5QZo+IFbO3i6xZwvtspNr6+UmrKraC+93OwMWTR2IH32AAC+vX5Ts4eUM+RHbWTysMiSX2tNIIEeAMDPCPaQkob8qLU8O7xn2D58upy0KwAApOBoXMCmgZymVdHRttuLD8iessOS07iB5GYxVy4AADaCPaQ0DehIqwIAQHg04wIAAHgYwZ6LkHoFAAA4jdQrLuTWodsAACD1rt/U7AEAAHgYAzTgKeXHLEbnAgAQgGAPnjF39TYZN7tQthUfDJl3TxMsk3cPAOA3UQV7AwcOdLwAV199tVx55ZWOPy/8F+jdOL1AwnVA1QBQHyfRMgDAb6IK9j7++GPHCzBgwADHnxP+a7rVGr1IRhrpepqImSZdAIBfRBXsrV+/3vECNG3a1PHnhL9oH71QTbfBNBjU9V76dL1c3a8zAR8AwBeiCvY6duwYv5LA5NnTW3l5ebKLklJ2lNYc6AV6+L018vyi9fThAwD4Ann2XMiteXrcaknRbhn23GcxbTvm7BPlpoEnUssHAPDs9dux0bg7duyQli1bOvV0QMQ0rYqOto2kKTfYUx+tlRcWrZdz8ltJvxOPI00LAMBzHEuq3KZNG1m5cqX5/0MPPSSzZ8+WjRs3OvX0QFgamGmTbKzhWcnBozKzYIuMeXOVqSHs//gCM7oXAAAvcKwZ97333pNevXpJbm6utG/fXrZs2SJpaWmmGvNHP/qRdO/eveLWtWtXycjIcOJlPcmt1cCpnGcvWho4kqYFAOCF63fc+uzt2bNHPv/880q3wsJCOXz4sNStW1eOHDkSj5f1BLceLKmShkVH2+ogjNoGe7nZGbJo7ECadAEAKX39jtsMGjk5OXLWWWeZm+3o0aOyZs0a+eKLL+L1svA5Dcw0rYqOtq1NDZ+dpkXTuvTNa+5oGQEASJk+e5s2bYpq/fT0dOnWrZtcccUVtXlZIK59+GqT1gUAAE8FeyeffLLcdtttsnv3budKBDhA+9ppn7vcrAa1ep6WTehbCgDwcbB37rnnylNPPSV5eXny8MMPS1lZWcj1Jk+eLPfcc09tXgqIKeD79K5BMubsk6LeVmsFNZ2LpmEBAMC3wd5f/vIXWbFihZx++uny4IMPmqDvmWeeqTT44tChQzJ9+nSZOHGiE+X1NJ09Iz8/X3r37p3soniqSXf02SfKs8N7muAtGtoUzOAMAECqq9VoXJ3Wa9KkSfLOO+/IsmXL5ODBgybdynHHHWcSLOuo282bN5tm3h//+MdSUFDgbOk9yq2jebwwUlcHXGwvPiCffrNL5q3ZIcUHqo4K16CQqdQAAF65ftdqNO4jjzwi48aNE40XGzZsKG3btjXL9+/fL6tXrzaBnw7KOO2002Tq1KlOlRmIidbS2SNrL+rZrlLwt6fssOQ0bsAMGgAAz6lVsPfKK69IZmamzJo1SwYPHlwpxcqTTz4p48ePN4HfxRdfbBIrA24N/gAA8Kpa9dnTJtpzzjmnUqCntDbvzjvvNImUNci74447ZMaMGbUtKwAAABIZ7LVq1crU3IXTuXNnmTdvnkmwrPPlAgAAIIWCPa3VW7hwoaxatSrsOs2bN5eBAwfKunXravNSAAAASHSwp021OuJ20KBB8vLLL4ddb+3atVKnTq1eCgAAADGoVQR2wgknmLx6e/fulWuuucZMhaajcz/++GMT4Gk6lquvvtrU/HXp0qU2LwUAAIBEj8ZV1157rTRt2lRuvvlm+fLLL6WwsLDS43Yav1tvvbW2LwUAAIAoOdK2eskll8iGDRvk9ddfl+HDh5s5czMyMkzuvT59+piRuEOHDnXipQAAAJCoGTTg/HRpetOZSb7++mvXZeAGAACpN4MGwZ4LufVgAQAAqXf9ZogsAACAh0U1QEPz5TlNR+teeeWVjj8vAAAAogz2NKWK0wYMGOD4cwKxKD9myT/W75HtxQdkT9lhadqwvuzd///3OY0bSG5WhpzaOcfMqwsAgOeCvfXr1zteAE3bAiTb3NXbZNzsQtlWfLDGdVtnZ8gD5+fLuV1bJ6RsAADUBgM0XMitHTy9HOjdOL1AojkRtF5v2vCeBHwAANdfv2udVBlI9aZbrdGL9hePrn/nzM9l054DktOIZl4AgHsR7MHXtI9eJE23oZQcLJdH5qypsjw7I10G57eSvnkt6PMHAEg6gj342o7S2AK96hQfPCozC7aYWyj0+QMAJBJ59uBrLZtkJPw1tSZR+whqX0EAAOKNYA++pk2qWtOWDNpXUPsMAgAQTwR78DXtO6dNqonuQWf9p4ZP+wwCABBPBHvwPe07p2lUklHDF48+gwAABGKABvCfgG9wfm6VGTT2lB2SyQuLpPjAEc/0GQQA+AvBnotMmTLF3MrLy5NdFN826fbNa15lefuchlEnXa6JNhvnZv87DQsAAPHEDBou5NYM3H4WzXRqkWAGDgDwnhKXXr+p2QNq0cxrJ01eUrRL5q3ZEVFzL3n2AACJRLAH1LKZV13Sq51JoxIuGGQGDQBAshDsAQkIBgEASBZSrwAAAHgYNXtAgtDMCwBIBoI9wGWjeRnAAQBwEs24QAICPc3TF2naFl1P19ftAACoLYI9IM5Nt1qjF0syS91OtwcAoDYI9oA40j56sSRi1hBPt9PtAQCoDYI9II52lB5M6vYAABDsAXHUsklGUrcHAIBgD4gjTaOio2ujpYlXdDvdHgCA2iDYA+JI8+VpGpVYsubpduTbAwDUFsEeEGeaL2/a8J4R1/Dpero+efYAAE4gqTKQABq4Dc7PZQYNAEDCEewBCaIBXN+85skuBgDAZ2jGBQAA8DCCPQAAAA8j2AMAAPAwgj0XmTJliuTn50vv3r2TXRQAAOARaZZlMdO6y5SUlEh2drYUFxdLVlZWsosDAABS+PpNzR4AAICHEewBAAB4GMEeAACAhxHsAQAAeBjBHgAAgIcR7AEAAHgYwR4AAICHEewBAAB4GMEeAACAhxHsAQAAeBjBHgAAgIcR7AEAAHgYwR4AAICHEewBAAB4GMEeAACAhxHsAQAAeFh6sgsA4N/Kj1nyj/V7ZHvxAdlTdliaNqwve/dXvt9Tdkj2HjgiliXSrGF9yWn078dyGjeQ3KwMObVzjtStk5bstwIAcBGCPcAF5q7eJuNmF8q24oO1ep7W2RnywPn5cm7X1o6VDQCQ2mjGBVwQ6N04vaDWgZ7S59Dn0ucEAEBRswckuelWa/QsB59Tn+vOmZ/Lpj0HaOYFABDsAcmkffScqNELVnKwXB6Zs6bKcpp5AcB/aMYFkmhHqfOBXnVo5gUA/yHYA5KoZZOMpLyuNh1rEzIAwPsI9oAk0j502rSaSNZ/avi0CRkA4H0Eew6bOXOmXHTRRdKhQwdp2LChdOnSRX73u9/JkSNHkl00uJAOltA+dMkYMvHmsm/lrRWb5YW/r5NZK7fIkqLd1PYBgAelWZamZ4VT+vTpI506dZILL7xQWrVqJYsXL5bx48fL0KFD5U9/+lNEz1FSUiLZ2dlSXFwsWVlZcS8zvJNnr7ayM9JlcH4r6ZvXolJCZ0bzAkDqXr8J9hy2c+dOOe644yot02Dv/vvvl+3bt5sAMFUPFrhrBo3szHoy9eMiKT6QuFpjRvMCQOpdv0m94rDgQE/16tXL3G/dujWiYA/+pDVmffOaR7VNx+YNzejaRP1i05rHG6YXyFV9O0iHnEYhA9JQ99QMAkDypFyw99VXX8mHH34oK1asMLc1a9ZIeXm5PPzww3LffffVuP2MGTNkypQp8vnnn8vhw4flhBNOkCuuuELGjBkj9erVi0uZP/nkE6lfv77k5eXF5fnhX1rDNm14z4Q3Af9pybcxbUfNIAAkXsoFe9OmTZNJkybFtO0tt9xitk1PT5eBAwdK48aNZcGCBTJ27FiZPXu2CSIzMzMdLW9hYaF5zeuvv95VVbrwDg2cBufnVmkCXrR2p8xatVXcxM7zpwEqAR8AJEbKjcbt2rWr3H777fLqq6+aWr0RI0ZEtN3bb79tgi4N8JYuXSoffPCBvPXWW7J27Vrp1q2bLFq0yPSrC/TSSy9JWlpajTcdgRvKrl27zEANrT2cMGGCI+8fqK4J+KKe7eTa04+XS3q1k6G9O4hbkecPABIn5Wr2rrvuukp/16kTWbz66KOPmvu77rpLevbsWbG8RYsWMnXqVDn99NNl8uTJJuDTzpVKU6jo6NqatG3btsqy0tJS+dnPfmaaij/++GNp1KhRROUEnM7hl+wRvtXl+Yu2jyIAwAfBXiy2bNkiy5YtM/+//PLLqzzev39/ad++vWzatEnmzJkjw4YNM8s16LMDv2gcOnRILrjgAtmwYYOpMWzTpo0D7wKILYdfIgdwuHmqOADwq5Rrxo3FypUrzX1OTo507tw55DqnnHJKpXVjpYNFLrvsMhNcauB48sknRxQc6nDtwBvg5ACORM/S4eap4gDAb3xRs7d+/Xpzr7NahKM1e4HrxmrUqFGmf6CODtbA77PPPqt4LD8/P+Qgjccee0zGjRtXq9cFoh3AYadGWVK0S+at2ZHQfH2N6teRT9bukNVbiqVFE9KyAEA8+SLY0/5zqrp+czpwQ9W2Vm3u3LnmXvv+BQ/4WLhwoQwYMKDKNnfffbfceuutFX9rGezgE4h3Dj8dzBEuofO3e/bLn5ZsdLw8ZYePybSP11VaRloWAIgPXwR7iaT99KLVoEEDcwPcGAzq8kTk8SNhMwDEhy+CvSZNmpj7srKysOvs27fP3JMLD4iuGTjcvU7tNnlh9NO5kbAZAJzli2CvU6dO5l5H24ZjP2avC6B2U7ktKdqd0H6Ads3gNad1lHO6tKamDwD8NBq3R48e5n737t1hB2AsX77c3Afm4Es0ncZNB3H07t07aWUAUj21youLN8qw5z6T/o8vkLmrtyWlDADgJr4I9tq1a1cRQL322mtVHtdceFqzp/3mhgwZIsmiI3l1ejU7JyCQypKdWsWemo2AD4Df+aIZV91zzz1mRgydtkxntrBr8LS2b+TIkeb/N910U0xJlAG4cwYPTSZ958zPZdOeA5LTiAEfAPwpzbIsNybXD6ugoKAiOFNFRUVmDlqtvQuctmzWrFnSunXljtqjR4+Wp59+WurVqyeDBg0yqVjmz58ve/fulX79+sm8efMkMzNTkk1Tr2jQWVxczIARpDStVXPrDB41YcAHAK9cv1Mu2NN5Zs8666wa19O+eaEGW/z5z382feNWrVolR44ckby8PBk+fLiMGTNG6tevL27g1oMFiDXgS0TqlnjQej2dgYSAD0AqX79TLtjzA7ceLECsApM279p3SPYeOCLf7NgnH3z5nbg92MvNzpBFYwfSpAsgZa/fvumzlwq0xlFvOs0a4IfULW6v9dNfwlo2DVSjTT0DAG5BzZ4LufWXARAP4aZqq+k+XlO5hTLpsh/LBT/+/z7BAJBK129q9gCkXMLmRE/lluw0MgBQG77IswfAm3TghPane/Xan0h2Zj3Hnz/tP6NyNQ0LAKQqgj0AKV8z2O/EFvL4Jd1McOY0Tb/C4AwAqYxmXACeqeXTNClONetmZ6TL4PxWUnaoXF74+zqSLgNIWQzQcCG3dvAEvDzgQ++XFO2SeWt2SPGBIzW+DkmXAaTK9ZuaPRch9QqQvAEfmgbmrYItEc/2Yc+9S9JlAG5HzZ4LufWXAeDl2sD+jy+IuvmXpMsAUuH6zQANAL6nzb6x9PMLTLoMAG5FsAfA93aUHkzq9gAQT/TZA+B7tU2avHDNd7Kj5JDkNKp+EAgjeQEkA8EeAN/T4EtH18aasuXtz7eZW6QYyQsgkWjGBeB7WsumwVei6trskbw6AhgA4o1gDwACkjJrrVuiaAJoHQkMAPFEM66LkGcPSH7ANzg/t0pS5lWbvpdXPvvW0dcKHMkbS15AAIgUefZcyK15egC/emfVFhn9xqq4PPeFP24jp594HAM4AA8ocen1m5o9AIjzaN3qvL1qq7kFYgAHACfRZw8AIhytmygM4ADgJII9AHDZaF0bAzgAOIE+ey7k1jZ/wO+0pk0DsFjz8cViRJ8O8uP2zapN1kzSZsAdSlx6/SbYcyG3HiwAxNS02aN1d+07JHsPHBH9Fm3WsH7IGTQWrd0ps4L65MVbdka6DM5vJX3zWtQYJO4pq/k9EGgCqX39ZoAGAERBA5loUqW0aZqZ8GCv+OBRmVmwxdwSLZpA08l7gk0gPII9AHDxVGypJpmBpmIkM1AVAzQAwIODO/yKkcxAVdTsuQgzaADenoot0YM7/Eo7ot8x83PZd/CoFB84QhMwfI8BGi7k1g6eAJwb3BHPqdgQG5qA4dXrN8GeC7n1YAEQnwCw/+MLqPFzCa3X01pYAj546fpNnz0ASCL69LkPyazhNdTsuZBbfxkA8FbCZkSWzJo+fUj16zfBngu59WABkPg+fZHmmltStEvmrdlhBiQgPujTh1S9fhPsuZBbDxYA3gsWnZhBw0+BJn36kIrXb4I9F3LrwQIA8aiVjOU+K7OePPRuoZQePJrwYC83O0MWjR1Iky5S5vpNnj0AQMKnkXNCk4x0k0A5kTUW+lrar1ID20S/XyBWjMYFAKR0smrtS5doO0oZSIPUQc0eACClA77B+blRNyHXNpl1yyaJDzCBWBHsuQjTpQFAYpqQL+zRVj5asyOmVDdZGXVl9ZZi2br3AKlZkBIYoOFCbu3gCQBey23oZJ8/UrOgxKXXb/rsAQB8yek+f1pLqMGjBpGAm9CMCwDwrXB9/jT/4OSFRVHnDtRawjtnfi6b9hyIKmdhrPkOaUJGJAj2AAC+FqrP35Ki3TEniS45WC6PzFkjiUQTMqpDMy4AACmeWoUmZFSHmj0AADyQWiVUEzLNvFAEewAABNHgSJtGY0nNkkzhmpBp5vU3Uq+4kFuHbgOAnzidmsUNrurbQTrkNIp4DmJqBr1x/SbYcyG3HiwA4MeAb9zswpSr4XNadka6DM5vJX3zWhAMpuD1m2DPhdx6sACAH5UfsxxLzeJVNBO7+/pNnz0AAGKYjq19TkPPNfPWdjSwJqn2e8DnRqReAQDABTNweIE2eWtNKNyFZlwXcms1MAAgsmbeSGfOiGUGDbc3IV/xk/amnGny7xrRPsc3901/vhKXXr8J9lzIrQcLAMAdUmmkcNOG9WTCxd180bxb4tLrN824LjJlyhTJz8+X3r17J7soAAAXS6Um5L37j8gNzO6RVNTsuZBbfxkAAFKjCfnbPfvlT0s2iptoYLpo7EBPN+mWuPT6zWhcAAA8NlJY6XI35QjUcmhgGq68iB+CPQAAPNrUOzg/N+bBI0uKdsm8NTscHQiyo9QdgaffEOwBAODDmr+aXNKrXchm4lWbvpdXPvs2puds2cT9fQy9iGAPAABEHCxe2KOtfLRmR9TNw9pnT6dVQ+IxGhcAAEQVAOrUaNEOs9BtvDw4w80I9gAAQNxSvzRrWE+eZRq1pCL1igu5deg2AACBQvXpi2Y2kOrucxo3kNysfzf9pkqNYIlLr9/02QMAAI4OANEEyk6lfdHaQ20CpmYwdjTjAgAAx6dycyq/nz6PPh8zcMSOYA8AADjWrKs1evHoH6bPq8+P6BHsAQAAR2j/vXjM2GEFzMCB6BHsAQCAlJghgxk4YkOwBwAAHBHvGTKYgSM2BHsAAMARmiYlktx70dLEK8zAETuCPQAAkNTZNSLBDByxI88eAABwfHYNp/LsZWeky+D8VlJ2qFxe+Ps6Tydljhdm0HAht2bgBgCgNrNrRDqDxpKiXTJvzQ4pPnAkpZIyl7j0+k3NHgAASNjsGjXR5MlvFWxxLFfftv8kZdbaRr/OwkGwBwAAPJ2U2RKRO2d+Lpv2HKiYq9dPzbwEey4yZcoUcysvL092UQAA8ExSZlVysFwembNG/Dj3LqNxXWTUqFFSWFgoy5YtS3ZRAABIuGQkTd7mg7l3CfYAAIArJDNp8jgPz71LsAcAADydlNnvc+8S7AEAAM8nZfbz3LsEewAAwHVJmZNRw9fSo3PvMhoXAAC4LuAbnJ8bdVLmPWWHZPLCoqiTMaeJSK6H594l2AMAAJ5Jytw+p6EZXRvtUIsHPDz3Ls24AADAt83ArbMzPD+7BjV7AADAd83AOcygAQAA4L9mYC+iGRcAAMDDCPYAAAA8jGAPAADAwwj2AAAAPIxgDwAAwMMI9gAAADyMYA8AAMDDCPYAAAA8jGAPAADAw5hBw4Us69/TN5eUlCS7KAAAIEL2ddu+jrsFwZ4LlZaWmvv27dsnuygAACCG63h2dra4RZrltvATcuzYMdm6das0adJE0tLSHP/VoUHkpk2bJCsry9HnRuTYD+7AfnAH9oM7sB9qT0MqDfTatGkjdeq4p6ccNXsupAdIu3bt4voaeiJzMicf+8Ed2A/uwH5wB/ZD7bipRs/mnrATAAAAjiPYAwAA8DCCPZ9p0KCBPPDAA+YeycN+cAf2gzuwH9yB/eBdDNAAAADwMGr2AAAAPIxgDwAAwMMI9gAAADyMYM8nZsyYIQMGDJBmzZpJo0aNpHv37jJx4kQ5cuRIsovmGVdffbVJgl3d7eDBgyG3XbFihVx66aXSqlUrycjIkM6dO8vNN98sO3bsSPj7SAVfffWVPPPMM+Yz79atm6Snp5vPd/z48TVu+9FHH8mQIUOkRYsWkpmZKT/4wQ/k3nvvlX379lW73TfffGNeT3Ngagd2vde/161bJ34Vy3548MEHazxP/vWvf4Xdnv1QmX6Hz58/X+644w7p3bu3NG3aVOrVqye5ubnyi1/8Qt57771qt+d88AkdoAFvGz16tA7CsdLT061zzjnHuvjii62mTZuaZf3797f279+f7CJ6wlVXXWU+0379+pn/h7odPny4ynYzZsww+0a37d27tzV06FDr+OOPN3+3atXKWrt2bVLeTyoc08G3hx9+uNrtnnzySbNeWlqadcYZZ1iXXnqplZuba5adfPLJ1s6dO0Nut2jRIqthw4ZmvS5duli/+tWvzL3+3ahRI2vJkiWWH8WyHx544AGzTvfu3cOeJ1u3bg25Lfuhqnnz5lV87nosn3feeeY7pGvXrhXLr7/+euvYsWNVtuV88A+CPY+bNWuWOQEbN25srVixomK5nsTdunUzj912221JLaPXgr0XX3wx4m22bNlS8aX5+9//vmL50aNHreHDh1cEgKG+qP3sueees26//Xbr1VdftdasWWONGDGixiCjoKDAXNTq1q1rzZkzp2J5WVmZNWjQILP9JZdcUmU7fbxNmzbm8bvvvrvSY/q3Lm/fvr0vfzTFsh/sYE/vo8F+CG3+/PnmuP3kk0+qPPbGG2+Y410/mz/96U+VHuN88BeCPY/TQEFPvvHjx1d57O9//7t5rEGDBtbevXuTUj6/B3t33HGH2ebss8+u8lhpaamVnZ1tHp87d67DpfXmZ19dkKG1FrrOddddV+WxDRs2WHXq1DGPa9ASaMqUKWb5SSedZJWXl1d6TP/W5fr4s88+a/ldJPsh1mCP/RCba6+91nwuGsAF4nzwF/rsediWLVtk2bJl5v+XX355lcf79+9vJr0+dOiQzJkzJwklxKxZs8Lun8aNG5s+N+ovf/lLwsvmJYcPH67ouxTqs+7YsaP069ev0j6x2X9fdtllVSY2179/9atfmf+zj+KL/RCbHj16mPtNmzZVLON88J/0ZBcA8bNy5Upzn5OTYzr8h3LKKaeYLwFdd9iwYQkuoTctXLhQ/vnPf0ppaak0b95cTj31VNMBOjgrvT6unZzt/RCKLn/llVcq9iVi8/XXX8v+/ftr/Kz//ve/V/ms7b+r2y5wPUSmoKBA7rrrLtmzZ4+ZOF6DkvPPP1+aNGkScn32Q2zWrl1r7lu3bl2xjPPBfwj2PGz9+vXmvkOHDmHX0Zq9wHVRey+//HKVZfpF+8c//lHOPffcimUbNmyo+H+4fcT+cYb9+elIxXDBRKjPWgPy3bt3R7SPdu7cKWVlZWa0O2o2e/ZscwukQd/TTz8tV155ZaXl7IfYbN++XV566SXz/0suuaRiOeeD/9CM62F6YqrqTjZtKlQlJSUJK5dXaTqbSZMmyerVq83n+d1338mHH34op512mmzbts00yX788cdV9k91+4j9k9xzIZp9FLwtQsvLy5NHH33U1PxorZ7eFi1aJD//+c+luLhYrrrqKnn11VcrbcN+iN7Ro0dl+PDh5jPVtDi/+c1vKh7jfPAfavYAh4wZM6bS3/qLefDgwXL22WfLRRddJO+8847ccsstsmrVqqSVEUi2ESNGVFmm/cO0lu+3v/2tydun55Lmnaxfv35SyugFN9xwg8m/p11JZs6cyWfpc9TseZhdPa9V6eHYiTOzsrISVi6/0SSx48aNM////PPPKzpKBzafhNtH7J/kngvR7KPgbRE9Tbhct25d0wS4dOnSiuXsh+iMHj1aXnjhBZNEf968eXLSSSdVepzzwX8I9jysU6dOVUZhBbMfs9dFfPzwhz+s+P/mzZsrRrzZvv3225DbsX+cYX9+e/furdQUVdNnrRc3HeAUyT7SGQjon1Q7+lm3bNmy0nmi2A+Ru+2220y/R+2Pp91I7NG4gTgf/Idgz8Psk1w71Ibr4L98+XJz37Nnz4SWzW/sTs2Bv471V+8JJ5xQaT8EY/844+STT5aGDRvG9Fnbf7OP4q+8vNz0MVPBAwfYDzW788475cknnzQDXTTQCzdilvPBfwj2PEznKtS5EtVrr71W5XHtFK2/wjQliKYGQfy88cYbFQGeftHatC9fuP2jzSH2aMWLL744YWX1Iu2vdN5554X9rDdu3CiLFy+utE9s9t+6D48dO1bpMf37zTffNP9nH9XeX//6V5MSRLs+BAcq7IfqaRqbJ554wgR62nRrf/eHwvngQ8nO6ozkTJe2a9cupktz0MqVK6133nnHOnLkSJWM8s8//7yVkZFhPuv77rsv7HRpf/jDHypNl2ZPPcV0ac7M3KDHvz091Pvvvx/T9FD33HNPpcf0b13erl07poeKYD9s3LjReuWVV6wDBw6E/K7Kyckx2+tUgcHYD+Hde++95v3rnOf/+Mc/ItqG88Ff0vSfZAeciH9nXe3DUa9ePRk0aJDpR6GjtLS/ho6C01+BmZmZyS5mSnv77bfNL17tEK3NF61atTKfr6Zhsfu2aNJqzcGXnl55EPyMGTPMY9qE9ZOf/MT0kdGZT9atW2eeR2tg7eZe/H9C3pEjR1b8XVRUJLt27TK12W3btq2U7T8wmexTTz0lt956q6k5OvPMM03/ME0cq6lxtMZVP2vtaxTs008/lXPOOcfUOnXt2tXcdN/qTc+njz76SPr06SN+E+1+0JHo2r1E03Pova5z4MABKSwsrEj+e9ZZZ5kavsAUHjb2Q1X6WV1wwQXm/1ob2qVLl5Dr6XH9P//zP5WWcT74SLKjTSTGm2++aZ1xxhlWVlaWlZmZaXXt2tWaMGGCdejQoWQXzRPWrVtn3XLLLVb//v2ttm3bmpo8nXO4Q4cO1i9/+Uvrvffeq3b75cuXWxdffLF13HHHWfXr17c6duxojRo1ytq+fXvC3kMqWbhwoalBqOm2fv36KtvOmzfPOvfcc00tku6jE0880UzgXlJSUu1rrl271rryyitNrUa9evXMvf79zTffWH4V7X7QFoWxY8daAwcONOdGo0aNzGfZunVr6+c//7n12muvVZlvNRj7oTKdizuSfaDfKaFwPvgDNXsAAAAexgANAAAADyPYAwAA8DCCPQAAAA8j2AMAAPAwgj0AAAAPI9gDAADwMII9AAAADyPYAwAA8DCCPQBIsH379plp87Kyssw0eQAQTwR7AJBgS5cuNUGezh9at27dZBcHgMcxXRoAJFhxcbGZbL5Zs2bSqlWrZBcHgMcR7AEAAHgYzbgAkED6+7pp06ZSp04dU8MHAPFGsAcACVRUVGSCvLy8PMnOzk52cQD4AMEeACTQihUrzH3Pnj2TXRQAPkGwBwAJVFBQYO579eqV7KIA8AmCPQBIQs0ewR6ARGE0LgAkUE5Ojnz//feyZ88ek3oFAOKNmj0ASJD169ebQK9z584EegAShmAPABKEJlwAyUCwBwAJwkhcAMlAsAcACcJIXADJwAANAEiQFi1ayO7du2XXrl3SvHnzZBcHgE9QswcACbBx40YT6HXo0IFAD0BCUbMHAADgYdTsAQAAeBjBHgAAgIcR7AEAAHgYwR4AAICHEewBAAB4GMEeAACAhxHsAQAAeBjBHgAAgIcR7AEAAHgYwR4AAICHEewBAAB4GMEeAACAhxHsAQAAiHf9H419Aqpb9eAmAAAAAElFTkSuQmCC", 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" ] @@ -352,6 +352,14 @@ "$$\n", "and approximate each power with Suzuki-Trotter for appropriate order and repetition parameters, keeping the same error per QPE iteration. You can thus use the bound above to define a powered Suzuki-Trotter `qfunc` for the specific molecule.\n", "\n", + "In particular, in QPE the powered unitary $U^k$ is applied for getting $U^k|\\psi\\rangle = e^{2\\pi i k\\theta}|\\psi\\rangle $ for eigenstate $|\\psi\\rangle $and eigenphase $\\theta$ of $U$. Thus, if we approximate $\\tilde{U}\\approx U$ such that it has an eignphase $|\\tilde{\\theta}-\\theta| < \\epsilon$, keeping the same relevant error for $U^k$ means that $\\tilde{U}^{(k)}\\approx U^k$ has an eignephase $|k\\tilde{\\theta}-k\\theta| < k\\epsilon$. Finally, if we replace $t$ with $k$ in Eq. (1) (since the power of $e^{iH}$ corresponds to the evolution time $t$, according to Eq. (2)), we have \n", + "$$\n", + "r(k) \\leq \\left(\\frac{2^5\\gamma_2}{3\\epsilon(k)}\\right)^{1/2} k^{3/2}= \\left(\\frac{2^5\\gamma_2}{3\\epsilon k}\\right)^{1/2} k^{3/2}\n", + "= \\left(\\frac{2^5\\gamma_2}{3\\epsilon}\\right)^{1/2} k^{1/2}.\n", + "\\tag{3}\n", + "$$\n", + "This is the relation between the repetitions $r$ and the power of a second-order Suzuki-Trotter formula (in a sense of an upper bound).\n", + "\n", "First, define a classical auxiliary function that help evaluate the right-hand-side side of Eq. (1):" ] }, @@ -444,18 +452,18 @@ "output_type": "stream", "text": [ "The theoretical bounds for the repetitions for QPE size 7, keeping an error 0.1 per QPE iteration are:\n", - "[ 5. 12. 33. 93. 261. 737. 2084.]\n" + "[1. 1. 2. 2. 3. 4. 6.]\n" ] } ], "source": [ "EPS = 0.1\n", "gamma_2_LiH = calculate_gamma_2(normalized_mol_hamiltonian)\n", - "theoretical_r0 = np.sqrt(2**5 * gamma_2_LiH / (3 * EPS)) * (2 * np.pi) ** (3 / 2)\n", + "theoretical_r0 = np.sqrt(2**5 * gamma_2_LiH / (3 * EPS)) * (2 * np.pi) ** (1 / 2)\n", "\n", "print(\n", " f\"\"\"The theoretical bounds for the repetitions for QPE size {QPE_SIZE}, keeping an error {EPS} per QPE iteration are:\n", - "{np.ceil(theoretical_r0*qpe_powers**(3/2))}\"\"\"\n", + "{np.ceil(theoretical_r0*qpe_powers**(1/2))}\"\"\"\n", ")" ] }, @@ -478,7 +486,7 @@ "output_type": "stream", "text": [ "The repetitions for QPE size 7, taking a naive QPE, per QPE iteration:\n", - "[ 5. 9. 17. 33. 66. 131. 261.]\n" + "[ 1. 2. 3. 6. 11. 21. 42.]\n" ] } ], @@ -494,8 +502,6 @@ "id": "26", "metadata": {}, "source": [ - "While this naive QPE results in a shallower circuit, compared to taking repetitions according to the theoretical bounds (due to smaller values of repetitions), it is unclear whether it keeps the same operator error per phase bit.\n", - "\n", "In practice, the bounds given in the literature are quite loose. This tutorial therefore takes a more experimental approach, assuming that the scaling of the bound with the evolution time $t$ is similar to Eq. (1), but taking a smaller prefactor." ] }, @@ -510,15 +516,15 @@ "output_type": "stream", "text": [ "The experimental repetitions for QPE size 7, per QPE iteration are:\n", - "[ 1. 1. 1. 2. 4. 10. 26.]\n" + "[1. 1. 1. 2. 2. 3. 4.]\n" ] } ], "source": [ - "experimental_r0 = 0.05\n", + "experimental_r0 = 0.5\n", "print(\n", " f\"\"\"The experimental repetitions for QPE size {QPE_SIZE}, per QPE iteration are:\n", - "{np.ceil(experimental_r0*qpe_powers**(3/2))}\"\"\"\n", + "{np.ceil(experimental_r0*qpe_powers**(1/2))}\"\"\"\n", ")" ] }, @@ -546,7 +552,7 @@ " pauli_operator=qubit_op_to_pauli_terms(normalized_mol_hamiltonian),\n", " evolution_coefficient=-2 * np.pi * p,\n", " order=2,\n", - " repetitions=ceiling_qmod(experimental_r0 * p ** (3 / 2)),\n", + " repetitions=ceiling_qmod(experimental_r0 * p ** (1 / 2)),\n", " qbv=state,\n", " )" ] @@ -643,7 +649,7 @@ }, { "data": { - "image/png": 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", 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", 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" ] diff --git a/applications/chemistry/qpe_for_molecules/qpe_for_molecules.qmod b/applications/chemistry/qpe_for_molecules/qpe_for_molecules.qmod index c5388665a..a644feffc 100644 --- a/applications/chemistry/qpe_for_molecules/qpe_for_molecules.qmod +++ b/applications/chemistry/qpe_for_molecules/qpe_for_molecules.qmod @@ -397,7 +397,7 @@ qfunc powered_st2_for_LiH_expanded___0(p: int, state: qbit[6]) { } ], num_qubits=6 - }, (-6.2832) * p, 2, ceiling(0.05 * (p ** 1.5)), state); + }, (-6.2832) * p, 2, ceiling(0.5 * (p ** 0.5)), state); } qfunc unitary_with_power_0_lambda___0_0_expanded___0(p: int, state_captured__main__0: qbit[6]) { diff --git a/applications/chemistry/qpe_for_molecules/qpe_for_molecules.synthesis_options.json b/applications/chemistry/qpe_for_molecules/qpe_for_molecules.synthesis_options.json index b42d2d40f..70b83d9fe 100644 --- a/applications/chemistry/qpe_for_molecules/qpe_for_molecules.synthesis_options.json +++ b/applications/chemistry/qpe_for_molecules/qpe_for_molecules.synthesis_options.json @@ -6,28 +6,28 @@ "preferences": { "custom_hardware_settings": { "basis_gates": [ - "ry", - "u2", - "s", - "x", - "tdg", - "p", - "sxdg", - "z", "rx", - "y", "sdg", - "h", + "p", "rz", - "id", + "ry", "u1", - "u", - "cz", - "sx", "t", "r", "cy", - "cx" + "cz", + "u", + "tdg", + "id", + "h", + "z", + "x", + "u2", + "s", + "cx", + "sx", + "sxdg", + "y" ], "is_symmetric_connectivity": true }, @@ -36,7 +36,7 @@ "optimization_level": 1, "output_format": ["qasm"], "pretty_qasm": true, - "random_seed": 3315368948, + "random_seed": 130624170, "synthesize_all_separately": false, "timeout_seconds": 600, "transpilation_option": "auto optimize"