  Quantum computing technologies have become a hot topic in academia and
industry receiving much attention and financial support from all sides.
Building a quantum computer that can be used practically is in itself an
outstanding challenge that has become the 'new race to the moon'. Next to
researchers and vendors of future computing technologies, national authorities
are showing strong interest in maturing this technology due to its known
potential to break many of today's encryption techniques, which would have
significant impact on our society. It is however quite likely that quantum
computing has beneficial impact on many computational disciplines.
  In this article we describe our vision of future developments in scientific
computing that would be enabled by the advent of software-programmable quantum
computers. We thereby assume that quantum computers will form part of a hybrid
accelerated computing platform like GPUs and co-processor cards do today. In
particular, we address the potential of quantum algorithms to bring major
breakthroughs in applied mathematics and its applications. Finally, we give
several examples that demonstrate the possible impact of quantum-accelerated
scientific computing on society.
