An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz-type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner. The choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with Fourier analysis. Multigrid analysis results are verified by numerical experiments. High wavenumber Helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner.

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 and potentially disruptive 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.