arXiv:quant-ph/0003035quant-ph
One Complexity Theorist's View of Quantum Computing
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Abstract
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools of computational complexity theory should come to bear on these important questions. Quantum computing often scares away many potential researchers from computer science because of the apparent background need in quantum mechanics and the alien looking notation used in papers on the topic. This paper will give an overview of quantum computation from the point of view of a complexity theorist. We will see that one can think of BQP as yet another complexity class and study its power without focusing on the physical aspects behind it.
It has been claimed that "we can simulate a BQP machine using efficiently computable entries from the set {−1, −4/5 , − 3/5 , 0, 3/5 , 4/5 , 1}" [1]. So any part of reality that you can reduce to an efficient computation on a quantum computer, admits a description using the…
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