Two of the most well-known quantum algorithms, those introduced by Deutsch–Jozsa and Bernstein–Vazirani, can solve promise problems with just one function query, showing an oracular separation with deterministic classical algorithms. In this work, we generalise those methods to study a family of quantum algorithms that can, with just one query, exactly solve promise problems stated over Boolean functions. We also show that these problems can be naturally ordered, inducing a partially ordered set of promise problems. We study the properties of such a poset, showing that the Deutsch–Jozsa and Bernstein–Vazirani problems are, in a certain sense, extremal problems in it, determining some of its automorphisms and proving that it is connected. We also prove that, for the problems in the poset, the corresponding classical query complexities can take any value between 1 and 2^n-1+1 .

Quantum computing (QC) is one of the most promising new technologies for High Performance Computing. Its potential use in High Energy Physics has lead CERN, one of the top world users of large-scale distributed computing, to start programmes such as the Quantum Technology Initiative (QTI) to further assess and explore the applications of QC. As a part of QTI, CERN offered, in November–December 2020, a free, online series of lectures on quantum computing. In this paper, we report on the experience of designing and delivering these lectures, evaluating them in the broader context of computing education and training. Traditional textbooks and courses on QC usually focus on physical concepts and assume some knowledge of advanced mathematical and physical topics from the student. Our lectures were designed with the objective of reducing the prerequisites to the bare minimum as well as focusing on hands-on, practical aspects of programming quantum computers and not on the mathematical analysis of the algorithms. This also allowed us to include contents that are not usually covered in introductory courses, such as quantum machine learning and quantum annealing. The evaluation of the reception of the lectures shows that participants significantly increased their knowledge, validating the proposed approach not focused on mathematics and physics but on algorithmic and implementation aspects.