## Multilinear Formulas and Skepticism of Quantum Computing (2004)

### Cached

### Download Links

- [www.cs.berkeley.edu]
- [arxiv.org]
- [arxiv.org]
- [arxiv.org]
- [arxiv.org]
- [www.scottaaronson.com]
- [www.cs.berkeley.edu]
- [www.cs.berkeley.edu]
- [www.scottaaronson.com]
- DBLP

### Other Repositories/Bibliography

Venue: | In Proc. ACM STOC |

Citations: | 30 - 7 self |

### BibTeX

@INPROCEEDINGS{Aaronson04multilinearformulas,

author = {Scott Aaronson},

title = {Multilinear Formulas and Skepticism of Quantum Computing},

booktitle = {In Proc. ACM STOC},

year = {2004},

pages = {118--127},

publisher = {ACM Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

Several researchers, including Leonid Levin, Gerard 't Hooft, and Stephen Wolfram, have argued that quantum mechanics will break down before the factoring of large numbers becomes possible. If this is true, then there should be a natural "Sure/Shor separator"---that is, a set of quantum states that can account for all experiments performed to date, but not for Shor's factoring algorithm. We propose as a candidate the set of states expressible by a polynomial number of additions and tensor products. Using a recent lower bound on multilinear formula size due to Raz, we then show that states arising in quantum error-correction require n## additions and tensor products even to approximate, which incidentally yields the first superpolynomial gap between general and multilinear formula size of functions. More broadly, we introduce a complexity classification of pure quantum states, and prove many basic facts about this classification. Our goal is to refine vague ideas about a breakdown of quantum mechanics into specific hypotheses that might be experimentally testable in the near future.