Efficient classical simulation of the Deutsch-Jozsa algorithm

In 1985, David Deutsch challenged the Church-Turing thesis by stating that his quantum model of computation "could, in principle, be built and would have many remarkable properties not reproducible by any Turing machine". While this is thought to be true in general, there is usually no way of knowing that the corresponding classical algorithms are the best possible solutions. Here we provide an efficient classical simulation of the Deutsch-Jozsa algorithm, which was one of the first examples of quantum computational speed-up. Our conclusion is that the Deutsch-Jozsa quantum algorithm owes its speed-up to resources that are not necessarily quantum-mechanical, and when compared with the classical simulation offers no speed-up at all.