The Deutsch-Jozsa Problem: De-quantisation and Entanglement
Abstract
The Deustch-Jozsa problem is one of the most basic ways to demonstrate the power of quantum computation. Consider a Boolean function f : 0,1n to 0,1 and suppose we have a black-box to compute f. The Deutsch-Jozsa problem is to determine if f is constant (i.e. f(x) = const forall x in 0,1n) or if f is balanced (i.e. f(x) = 0 for exactly half the possible input strings x in 0,1n) using as few calls to the black-box computing f as is possible, assuming f is guaranteed to be constant or balanced. Classically it appears that this requires at least 2n-1+1 black-box calls in the worst case, but the well known quantum solution solves the problem with probability one in exactly one black-box call. It has been found that in some cases the algorithm can be de-quantised into an equivalent classical, deterministic solution. We explore the ability to extend this de-quantisation to further cases, and examine with more detail when de-quantisation is possible, both with respect to the Deutsch-Jozsa problem, as well as in more general cases.