Reinforcement Quantum Annealing: A Hybrid Quantum Learning Automata

We introduce the notion of reinforcement quantum annealing (RQA) scheme in which an intelligent agent searches in the space of Hamiltonians and interacts with a quantum annealer that plays the stochastic environment role of learning automata. At each iteration of RQA, after analyzing results (samples) from the previous iteration, the agent adjusts the penalty of unsatisfied constraints and re-casts the given problem to a new Ising Hamiltonian. As a proof-of-concept, we propose a novel approach for casting the problem of Boolean satisfiability (SAT) to Ising Hamiltonians and show how to apply the RQA for increasing the probability of finding the global optimum. Our experimental results on two different benchmark SAT problems (namely factoring pseudo-prime numbers and random SAT with phase transitions), using a D-Wave 2000Q quantum processor, demonstrated that RQA finds notably better solutions with fewer samples, compared to the best-known techniques in the realm of quantum annealing.