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arXiv · 2301.04627

Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians

Daniel Hothem·Ojas Parekh·Kevin Thompson
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Abstract

We give a classical $1/(qk+1)$-approximation for the maximum eigenvalue of a $k$-sparse fermionic Hamiltonian with strictly $q$-local terms, as well as a $1/(4k+1)$-approximation when the Hamiltonian has both $2$-local and $4$-local terms. More generally we obtain a $1/O(qk^2)$-approximation for $k$-sparse fermionic Hamiltonians with terms of locality at most $q$. Our techniques also yield analogous approximations for $k$-sparse, $q$-local qubit Hamiltonians with small hidden constants and improved dependence on $q$.

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Daniel Hothem, Ojas Parekh, Kevin Thompson. 2023-01-11. Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians. https://doi.org/10.4230/lipics.tqc.2023.6

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