Abstract

Since the 1970s, the potential of quantum computing has been a field of extensive research, particularly its advantages and disadvantages over classical computing. This research, however, was theoretical since physical quantum devices were unavailable. With the recent availability of the first (alleged) adiabatic computers, or quantum annealers, computational mathematics and statistics (as all other computational sciences) are provided with a new means of great potential. This talk will begin with an introduction to quadratic unconstrained binary optimisation (qubo) and hardware aiming to solve such optimisation problems via quantum annealing, and proceed with a presentation of experimental results. Special focus will be given to two topics: Solving the NP-hard problem of finding maximal cliques in a graph and the reduction of binary quadratic forms for scalable quantum annealing. To stimulate discussion, the talk will highlight future directions of research, for instance the characterisation of problem classes allowing formulations suitable for quantum annealing, the manipulation of qubo instances while preserving global optima, the statistical analysis of the (empirical) distribution of annealing solutions, and the exploitation of the inherent randomness in adiabatic computing for statistical purposes.