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kevinsung committed Nov 3, 2023
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"metadata": {},
"source": [
"Time evolution by $\\mathcal{M}$ can be implemented with the following steps:\n",
"\n",
"- Compute the numbers $\\set{\\lambda_i}$ and the matrix $\\mathbf{W}$ by performing an eigendecomposition of $\\mathbf{M}$.\n",
"- Perform the orbital rotation $\\mathcal{W}^\\dagger$, which corresponds to the matrix $\\mathbf{W}^\\dagger$.\n",
"- Perform time evolution by the operator $\\sum_{i,\\sigma} \\lambda_i n_{i,\\sigma}$.\n",
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"cell_type": "markdown",
"metadata": {},
"source": [
"As mentioned above, the function `apply_num_op_sum_evolution` can actually apply the orbital rotation for you if you pass it as an argument, as demonstrated below. Calling the function this way is expected to give better performance."
"As mentioned above, the function `apply_num_op_sum_evolution` can actually apply the orbital rotation for you if you pass it as an argument, as demonstrated below. Calling the function this way may give better performance."
]
},
{
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