par Ozols, Maris;Roetteler, Martin;Roland, Jérémie 
Référence 3rd Conference on Innovations in Theoretical Computer Science (ITCS'12), ACM Press, page (290-308)
Publication Publié, 2012
Référence 3rd Conference on Innovations in Theoretical Computer Science (ITCS'12), ACM Press, page (290-308)
Publication Publié, 2012
Publication dans des actes
| Résumé : | Rejection sampling is a well-known technique to sample from a target distribution, given the ability to sample from another distribution. The method has been first formalized by von Neumann (1951) and has many applications in classical computing. We define a quantum analogue of rejection sampling: given a black box producing a coherent superposition of quantum states with some amplitudes, the problem is to prepare a coherent superposition of the same states with different target amplitudes. The main result of this paper is a tight characterization of the query complexity of this quantum state generation problem. We exhibit an algorithm, which we call quantum rejection sampling, and analyze its cost using semidefinite programming. We prove a matching lower bound based on symmetrizing over the automorphism group of the problem and using a hybrid argument. Perhaps interestingly, the automorphism group turns out to be continuous in this case. Furthermore, we illustrate how quantum rejection sampling may be used as a primitive in designing quantum algorithms. As an example, we derive a new quantum algorithm for the hidden shift problem for an arbitrary Boolean function whose running time is obtained by "water-filling" its Fourier spectrum. |
