Classical and Quantum Computation
Classical and Quantum Computation
Quantum computing without entanglement
Theoretical Computer Science
Quantum Computer Science: An Introduction
Quantum Computer Science: An Introduction
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The Deutsch---Jozsa problem is one of the most basic ways to demonstrate the power of quantum computation. Consider a Boolean function f : {0, 1} n 驴 {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. $$f(x) = \hbox {const, } \forall x \in \{0,1\}^n$$ ) 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驴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.