Watch a 24-minute conference talk from the 18th Theory of Quantum Computation, Communication and Cryptography Conference (TQC 2023) exploring classical approximation methods for eigenvalues of sparse Hamiltonians. Learn about a novel 1/(qk+1)-approximation technique for maximum eigenvalues of k-sparse fermionic Hamiltonians with q-local terms, including a specific 1/(4k+1)-approximation for combined 2-local and 4-local terms. Discover how these methods extend to achieve 1/O(q*k^2)-approximation for k-sparse fermionic Hamiltonians with terms of locality at most q, while also providing constant-factor approximations for k-sparse, q-local spin Hamiltonians with improved q dependence. Presented at the University of Aveiro, Portugal, this theoretical quantum computing research advances understanding of eigenvalue approximation techniques for quantum systems.