Provable quantum advantage in randomness processing
Howard Dale, David H. Jennings, Terry Rudolph · Nature Communications · 2015
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics exactly coincides with the class computable quantum mechanically. It is strongly believed, but not proven, that quantum computing provides exponential speed-up for a range of problems, such as factoring. Here we address a computational scenario of randomness processing in which quantum theory provably yields, not only resource reduction over classical stochastic physics, but a strictly larger class of problems which can be solved. Beyond new foundational insights into the nature and malleability of randomness, and the distinction between quantum and classical information, these results also offer the potential of developing classically intractable simulations with currently accessible quantum technologies. Although quantum alternatives of various classical tasks are considered advantageous, this is typically extremely difficult to concretely prove. Here, the authors show that a quantum approach to randomness processing provides a reduction in resources and a larger class of solvable problems.