Sum of squares spectral amplification (SOSSA)

SOSSA is a new method for compiling efficient block encodings which exploits the low-energy of the initial state and relies on sum of squares optimization. The method was used in G.H. Low et al., arXiv:2502.15882 (2025) to improve state-of-art quantum chemistry compilations, improving the runtime of phase estimation on FeMoCo from days to just hours. This talk will go through the ideas behind the new technique, and in particular how sum of square optimization connects to Hamiltonian simulation and phase estimation.