Towards Datalog on Quantum Annealers: Compiling Recursive Logic Programs with Bottom-up Semantics to 2-local Ising Models

Abstract

Quantum annealers solve problems by finding the lowest-energy (ground) state of a programmable physical system, a 2-local Ising model, whose energy function is the Hamiltonian. We compile recursive Datalog programs into such models so that the ground state projects onto the program's minimal Herbrand model. The compiler has four stages: binarization, grounding, reduction to a Min-Ones SAT formula, and Ising encoding. Each rule becomes an energy penalty on the one assignment that violates it, and a small uniform cost on every true atom selects the minimal model. We contribute both in theory and in practice with per-stage correctness lemmas and a correspondence theorem, verified in Lean 4, establishing that the ground state of the compiled model projects onto the program's minimal Herbrand model. We map the compiled models onto the topologies of commercial annealers and characterize, under classical and simulated-quantum annealing, whether and when that certified ground state is attained.