Speaker
Description
The hopping-parameter expansion (HPE) of the logarithm of the Wilson-fermion determinant expresses the coefficient of $\kappa^n$ as a sum over closed loops of length $n$. It is widely used in studies of heavy-quark QCD and in stochastic estimators of the fermion determinant. Although the expansion through sixth order, corresponding to LO and NLO, is well established, higher-order terms have rarely been constructed because the number of loop classes grows combinatorially. Through a collaboration between human researchers and AI coding agents, we have developed efficient algorithms for evaluating the N$^2$LO–N$^4$LO terms. Starting from a loop classification designed by the researchers, the AI agents proposed a trie-based algorithm that reuses partial matrix products shared by multiple loops, thereby reducing the computational cost of evaluating these higher-order contributions on a given gauge configuration. All results were verified to agree exactly with those obtained using a reliable but computationally expensive reference implementation. In this talk, we present the algorithms and discuss their potential applications.