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Quantum lower bounds by quantum arguments (2000)
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| Venue: | In Proceedings of the ACM Symposium on Theory of Computing |
| Citations: | 190 - 19 self |
BibTeX
@INPROCEEDINGS{Ambainis00quantumlower,
author = {Andris Ambainis},
title = {Quantum lower bounds by quantum arguments},
booktitle = {In Proceedings of the ACM Symposium on Theory of Computing},
year = {2000},
pages = {636--643}
}
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Abstract
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a superposition of inputs. If the algorithm works correctly, its state becomes entangled with the superposition over inputs. We bound the number of queries needed to achieve a sufficient entanglement and this implies a lower bound on the number of queries for the computation. Using this method, we prove two new Ω ( √ N) lower bounds on computing AND of ORs and inverting a permutation and also provide more uniform proofs for several known lower bounds which have been previously proven via variety of different techniques. 1
