Quantum algorithms for continuous problems

Many problems in science and engineering are formulated using continuous mathematical models. Usually they can only be solved numerically and therefore approximately. Since they are often difficult to solve on a classical computer it’s interesting to investigate whether they can be solved faster on a quantum computer. After a brief introduction to quantum algorithms we report on a wide range of applications including high dimensional integration, path integration, Hamiltonian simulation, and ground state energy estimation. We provide a rather extensive bibliography. PACS numbers: 03.67.Ac, 03.67.Lx, 02.60.-x