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Quantum algorithms that can speed up certain tasks, such as factorisation andunstructured search, have driven a decades-long development of quantumcomputers 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 allpossible classical computations. This method-which we call CoherentParallelization (CP)-exploits quantum correlations generated by higher-orderHamiltonians to speed up any possible classical computation by a factor thatdepends on the classical algorithm. This factor is quadratic in the size of theinput for a large set of interesting problems, leading to a strong commercialapplication in the emergent area of quantum technologies. We present importanttheoretical consequences of CP for both quantum physics and the theory ofalgorithmic complexity and computability, and discuss how CP can be implementedusing real-world systems with natural or engineered Hamiltonians.

Quantum Correlations Can Speed Up All Classical Computation