The DeutschJozsa problem: de-quantisation and entanglement
The DeutschJozsa problem is one of the most basic ways to demonstrate the power of quantum computation. Consider a Boolean function f : {0,1} n ? {0,1} and suppose we have a black-box to compute f. The DeutschJozsa problem is to determine if f is constant (i.e. \(f(x) = \hbox {const, } \forall x \in \{0,1\}^n\)) or if f is balanced (i.e. f(x)=0 for exactly half the possible input strings \(x \in \{0,1\}^n\)) 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 2 n?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 DeutschJozsa problem, as well as in more general cases.
de-quantisation quantum computing deutsch-jozsa problem classical simulation