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Quantum Information and Computation

Quantum lower bound for recursive Fourier sampling

AaronsonScott

Published Mar 1, 2003• 1 citation
Publisher

Abstract

We revisit the oft-neglected 'recursive Fourier sampling' (RFS) problem, introduced by Bernstein and Vazirani to prove an oracle separation between BPP and BQP. We show that the known quantum algor...
DOI
10.5555/2011517.2011524

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Recursive Fourier Sampling (RFS) was one of the earliest problems to demonstrate a quantum advantage, and is known to lie outside the Merlin-Arthur complexity class. This work contains a new description of quantum algorithms in phase space terminology, demonstrating its use in RFS, and how and why this gives a better understanding of the quantum advantage in RFS. Most importantly, describing the computational process of quantum computation in phase space terminology gives a much better understanding of why uncomputation is necessary when solving RFS: the advantage is present only when phase coordinate garbage is uncomputed. This is the underlying reason for the limitations of the quantum advantage.