Quantum Correlations Can Speed Up All Classical Computation

Abstract: 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.