  Quantum algorithms that can speed up certain tasks, such as factorisation and
unstructured search, have driven a decades-long development of quantum
computers and quantum technologies. Yet, outside specialized applications,
quantum computers are believed to offer no advantage over classical computers.
Here, we present a method which exploits quantum effects to speed up all
possible classical computations. This method-which we call Coherent
Parallelization (CP)-exploits quantum correlations generated by higher-order
Hamiltonians to speed up any possible classical computation by a factor that
depends on the classical algorithm. This factor is quadratic in the size of the
input for a large set of interesting problems, leading to a strong commercial
application in the emergent area of quantum technologies. We present important
theoretical consequences of CP for both quantum physics and the theory of
algorithmic complexity and computability, and discuss how CP can be implemented
using real-world systems with natural or engineered Hamiltonians.
