Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians

• URL: http://arxiv.org/abs/2301.04627v3
• Date: Wed, 24 May 2023 21:28:30 GMT
• Title: Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians
• Authors: Daniel Hothem, Ojas Parekh, and Kevin Thompson
• Abstract summary: We give a classical $1/(qk+1)$-approximation for the maximum eigenvalue of a $k$-sparse fermionic Hamiltonian with strictly $q$-local terms. More generally we obtain a $1/O(qk2)$-approximation for $k$-sparse fermionic Hamiltonians with terms of locality at most $q$.
• Score: 2.6763498831034043
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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