Physics – Quantum Physics
Scientific paper
2001-09-20
Phys. Rev. A 65 050304 (2002).
Physics
Quantum Physics
4 pages, 1 figure; Final version, with an extended discussion of oracle inverses. To appear in Phys Rev A
Scientific paper
10.1103/PhysRevA.65.050304
A standard quantum oracle $S_f$ for a general function $f: Z_N \to Z_N $ is defined to act on two input states and return two outputs, with inputs $\ket{i}$ and $\ket{j}$ ($i,j \in Z_N $) returning outputs $\ket{i}$ and $\ket{j \oplus f(i)}$. However, if $f$ is known to be a one-to-one function, a simpler oracle, $M_f$, which returns $\ket{f(i)}$ given $\ket{i}$, can also be defined. We consider the relative strengths of these oracles. We define a simple promise problem which minimal quantum oracles can solve exponentially faster than classical oracles, via an algorithm which cannot be naively adapted to standard quantum oracles. We show that $S_f$ can be constructed by invoking $M_f$ and $(M_f)^{-1}$ once each, while $\Theta(\sqrt{N})$ invocations of $S_f$ and/or $(S_f)^{-1}$ are required to construct $M_f$.
Banaszek Konrad
Kashefi Elham
Kent Adrian
Vedral Vlatko
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