Application of Ising machines and a software development for Ising machines

An online advertisement optimization, which can be represented by a combinatorial optimization problem is performed using D-Wave 2000Q, a quantum annealing machine. To optimize the online advertisement allocation optimization, we introduce a generalized version of the Markowitz mean-variance model which is a basic model of portfolio optimization. The obtained optimization performance using D-Wave 2000Q is higher than that using the greedy method which is a conventional method. Additionally, to conveniently use Ising machines including a quantum annealing machine, new software called PyQUBO is developed. The first half of the paper gives a review of several combinatorial optimization problems and how to represent them using the Ising model or the quadratic unconstrained binary optimization (QUBO) form. We show the results of the online advertisement allocation optimization and the explanation of PyQUBO in the last half of the paper.