Compiling Planning into Quantum Optimization Problems: A Comparative Study
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION MOFFETT FIELD CA MOFFETT FIELD United States
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One approach to solving planning problems is to compile them to another problem for which powerful off-the-shelf solvers are available common targets include SAT, CSP, and MILP. Recently, a novel optimization technique has become available quantum annealing QA. QA takes as input problem instances encoded as Quadratic Unconstrained Binary Optimization QUBO. Early quantum annealers are now available, and more sophisticated quantum annealers will likely be built over the next decades. Specific quantum annealing hardware implementations have specific constraints, restricting the types of QUBOs each can take as input. In this paper, we introduce the planning community to the key steps involved in compiling planning problems to quantum annealing hardware a hardware-independent step, mapping, and a hardware-dependent step, embedding. After describing two approaches to mapping general planning problems to QUBO, we provide preliminary results from running an early quantum annealer on a parameterized family of hard planning problems. The results show that different mappings can lead to a substantial difference in performance, even when many superficial features of the resulting instances are similar. We also provide some insights gained from this early study, and suggest directions for future work.