DE-QUANTIZING THE SOLUTION OF DEUTSCH'S PROBLEM

Abstract

Probably the simplest and most frequently used way to illustrate the power of quantum computing is to solve the so-called Deutsch's problem. Consider a Boolean function f: {0,1} → {0,1} and suppose that we have a (classical) black box to compute it. The problem asks whether f is constant [that is, f(0) = f(1)] or balanced [f(0) ≠ f(1)]. Classically, to solve the problem seems to require the computation of f(0) and f(1), and then the comparison of results. Is it possible to solve the problem with only one query on f? In a famous paper published in 1985, Deutsch posed the problem and obtained a "quantum" partial affirmative answer. In 1998, a complete, probability-one solution was presented by Cleve, Ekert, Macchiavello and Mosca. Here we will show that the quantum solution can be de-quantized to a deterministic simpler solution which is as efficient as the quantum one. The use of "superposition," a key ingredient of quantum algorithm, is — in this specific case — classically available.