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fix name
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TomerGoldfriend committed Mar 6, 2025
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12 changes: 6 additions & 6 deletions applications/chemistry/qpe_for_molecules/qpe_for_molecules.ipynb
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"id": "eacde622-296a-4c80-8369-8af68648c973",
"metadata": {},
"source": [
"Next, we draw a histogram for the energies, by taking the output of the `phase` variable and multiplying back the normalization factor."
"Next, we draw a histogram for the energies, by taking the output of the `phase` variable and multypling back the normalization facor."
]
},
{
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"id": "d295b803-a203-47e5-82e8-5820b0e31b26",
"metadata": {},
"source": [
"Recall that we are looking for a signal from the smallest eigenvalue, under the assumption that the initial state has some overlap with the ground state. Below we estimate the energy as the first peak of the histogram, such that the corresponding probability is larger than `ASSUMED_OVERLAP`*0.4 (0.4 is the case for ASSUMED_OVERLAP=1, and `ASSUMED_OVERLAP` given by the user).\n",
"Recall that we are looking for a signal from the smallest eigenvalue, under the assumption that the initial state has some overlap with the ground state. Below we estimate the energy as the first peak of the histogram, such that the corresponding probability is larger than `ASSUMED_OVERLAP`*0.4 (0.4 is the case for ASSUMED_OVERLAP=1).\n",
"\n",
"*Note that this is a very rough and simplistic analysis of the QPE algorithm result. One can utilize more complex tools of spectral analysis, such as Gaussian mixtures, etc. Additional assumptions, such as the difference between adjacent eigenvalues or the number of overlapping eigenstates, can facilitate the analysis further.*"
"*Note that this is a very rough and simplistic analysis of the QPE algorithm result. One can utilize more complex tools of spectral analysis, such as Gaussian mixtures, etc. Additional assumptions, such as difference between adjacent eigenvalues or number of overlapping eigenstates, can facilitate the analysis further.*"
]
},
{
"cell_type": "code",
"execution_count": 19,
"execution_count": 21,
"id": "342f2fdd-1f07-4005-aecd-10155222dab4",
"metadata": {},
"outputs": [
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" return data_sorted[maxima[0]][0]\n",
"\n",
"\n",
"measured_phase = estimate_energy(energy_results, ASSUMED_OVERLAP)\n",
"print(f\"\\nLowest eigenvalue: {measured_phase} Ha\")\n",
"measured_energy = estimate_energy(energy_results, ASSUMED_OVERLAP)\n",
"print(f\"\\nLowest eigenvalue: {measured_energy} Ha\")\n",
"print(f\"Precision: {(2**(-QPE_SIZE))* normalization} Ha\")\n",
"print(f\"Classical solution:, {classical_sol} Ha\")"
]
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