In this paper, we develop a way to encode several NP-Complete problems in Abstract Argumentation to Quadratic Unconstrained Binary Optimization (QUBO) problems. In this form, a solution for a QUBO problem involves minimizing a quadratic function over binary variables (0/1), where the coefficients can be represented by a symmetric square matrix (or an equivalent upper triangular version). With the QUBO formulation, exploiting new computing architectures, such as Quantum and Digital Annealers, is possible. A more conventional approach consists of developing approximate solvers, which, in this case, are used to tackle the intrinsic complexity. We performed tests to prove the correctness and applicability of classical problems in Argumentation and enforcement of argument sets. We compared our approach to two other approximate solvers in the literature during tests. In the final experimentation, we used a Simulated Annealing algorithm on a local machine. Also, we tested a Quantum Annealer from the D-Wave Ocean SDK and the Leap Quantum Cloud Service.

Prime factorization is a difficult problem with classical computing, whose exponential hardness is the foundation of Rivest-Shamir-Adleman (RSA) cryptography. With programmable quantum devices, adiabatic quantum computing has been proposed as a plausible approach to solve prime factorization, having promising advantage over classical computing. Here, we find there are certain hard instances that are consistently intractable for both classical simulated annealing and un-configured adiabatic quantum computing (AQC). Aiming at an automated architecture for optimal configuration of quantum adiabatic factorization, we apply a deep reinforcement learning (RL) method to configure the AQC algorithm. By setting the success probability of the worst-case problem instances as the reward to RL, we show the AQC performance on the hard instances is dramatically improved by RL configuration. The success probability also becomes more evenly distributed over different problem instances, meaning the configured AQC is more stable as compared to the un-configured case. Through a technique of transfer learning, we find prominent evidence that the framework of AQC configuration is scalable -- the configured AQC as trained on five qubits remains working efficiently on nine qubits with a minimal amount of additional training cost.

The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is required for quantum and digital annealers whose goal is the optimization of a well defined metric, the objective function. However, diverse suboptimal solutions may be preferred over harder to implement strict optimal ones. In addition, the decision-maker usually has insights that are not always efficiently translated into the optimization model, such as acceptable target, interval or range values. Multi-criteria decision making is an example of involving the user in the decision process. In this paper, we present two variants of goal-seeking QUBO that minimize the deviation from the goal through a tabu-search based greedy one-flip heuristic. Experimental results illustrate the efficacy of the proposed approach over Constraint Programming for quickly finding a satisficing set of solutions.