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 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 quantum annealing and proceed with a presentation of recent advances in the field. Special focus will be given to two topics: Solving the NP-hard problem of finding cliques in a graph and the reduction of binary quadratic forms for scalable quantum annealing. Further relevant works will be discussed, especially those exploring the statistical properties of quantum annealing. To stimulate discussion, the talk will highlight future directions of research, in particular the statistical analysis of the (empirical) distribution of annealing solutions, the characterisation of classes of statistical methods allowing formulations suitable for quantum computation (and hence almost instant solutions), and the exploitation of the inherent randomness in adiabatic computing for statistical purposes.