English

Complexity limitations on quantum computation

Computational Complexity 2007-05-23 v1 Quantum Physics

Abstract

We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP. 1. BQP is low for PP, i.e., PP^BQP=PP. 2. There exists a relativized world where P=BQP and the polynomial-time hierarchy is infinite. 3. There exists a relativized world where BQP does not have complete sets. 4. There exists a relativized world where P=BQP but P is not equal to UP intersect coUP and one-way functions exist. This gives a relativized answer to an open question of Simon.

Keywords

Cite

@article{arxiv.cs/9811023,
  title  = {Complexity limitations on quantum computation},
  author = {Lance Fortnow and John D. Rogers},
  journal= {arXiv preprint arXiv:cs/9811023},
  year   = {2007}
}

Comments

13 pages, no figures; presented at the 13th annual Conference on Computational Complexity (1998); submitted to the Journal of Computer and System Sciences