Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians

Autor:	Hothem, Daniel, Parekh, Ojas, Thompson, Kevin
Rok vydání:	2023
Předmět:	Quantum Physics Fermionic Hamiltonians Mathematics of computing → Approximation algorithms Qubit Hamiltonians Sparse Hamiltonians FOS: Physical sciences Extremal eigenvalues Quantum Physics (quant-ph) Approximation algorithms Theory of computation → Approximation algorithms analysis
DOI:	10.48550/arxiv.2301.04627
Popis:	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 $q$. Comment: 6 pages, No Figures, edited typos and added additional details on the qubit results, accepted to TQC2023
Databáze:	OpenAIRE
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