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Be a bit careful about complexity of the sparse Hamiltonian #1512

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mpharrigan merged 2 commits into from
Dec 19, 2024
Merged

Be a bit careful about complexity of the sparse Hamiltonian #1512

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Be a bit careful about complexity
fdmalone Dec 18, 2024
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Merge branch 'main' into resource_estimation_correctioin
mpharrigan Dec 19, 2024
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4 changes: 2 additions & 2 deletions qualtran/bloqs/chemistry/resource_estimation.ipynb
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Expand Up @@ -64,12 +64,12 @@
"\n",
"| Name | $$V_{pqrs} $$ | Space complexity |\n",
"| :---- | :---- | :---- | \n",
"| [Sparse](sparse/sparse.ipynb) | $$\\tilde{V}_{pqrs}$$ | $$O(N^3)$$ |\n",
"| [Sparse](sparse/sparse.ipynb) | $$\\tilde{V}_{pqrs}$$ | $$O(N^4)$$ |\n",
"| [Single Factorization](sf/single_factorization.ipynb) | $$\\sum_X^{L} L_{pq}^X L_{rs}^X $$ | $$O(N^3)$$ |\n",
"| [Double Factorization](df/double_factorization.ipynb) | $$\\sum_X^{} \\left(\\sum_k^{\\Xi} U^{X}_{pk}f_k^X U_{qk}^{X*}\\right)^2$$ | $$O(N^2\\Xi)$$ |\n",
"| [Tensor Hypercontraction](thc/thc.ipynb) | $$\\sum_{\\mu\\nu}^{M} \\chi_p^{\\mu}\\chi_q^{\\mu}\\zeta_{\\mu\\nu}\\chi_r^\\nu\\chi_s^\\nu$$ | $$O(N^2)$$ |\n",
"\n",
"where the space complexity column represents the amount of classical data ($\\Gamma$, say) required to specify the Hamiltonian. The Toffoli complexity for state preparation for all of these approaches goes roughly like $\\sqrt{\\Gamma}$. "
"the space complexity column represents the amount of classical data ($\\Gamma$, say) required to specify the Hamiltonian. The Toffoli complexity for state preparation for all of these approaches goes roughly like $\\sqrt{\\Gamma}$. Note under certain conditions sparsity may lead to $O(N^3)$ non-zero elements. "
]
},
{
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