Quantum Optimization with Arbitrary Connectivity Using Rydberg Atom Arrays

Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of optimization algorithms [Ebadi et al., Science, 376, 1209 (2022)] with hundreds qubits. In particular, the maximum independent set problem so-called unit-disk graphs, was shown to be efficiently encodable in such a system. Here, we extend classes problems that can encoded by constructing explicit mappings from wide class weighted at most quadratic overhead number We analyze several examples, including: graphs arbitrary connectivity, unconstrained binary or restricted and integer factorization. Numerical simulations small system sizes indicate adiabatic time scale solving mapped is strongly correlated original problems. Our work provides blueprint using solve range combinatorial beyond restrictions imposed hardware geometry.