Physics – Quantum Physics
Scientific paper
2008-11-26
Proc. 41st Ann. Symp. on Theory of Computing, 409-416 (2009)
Physics
Quantum Physics
12 pages, 6 figs
Scientific paper
10.1145/1536414.1536471
The continuous-time query model is a variant of the discrete query model in which queries can be interleaved with known operations (called "driving operations") continuously in time. Interesting algorithms have been discovered in this model, such as an algorithm for evaluating nand trees more efficiently than any classical algorithm. Subsequent work has shown that there also exists an efficient algorithm for nand trees in the discrete query model; however, there is no efficient conversion known for continuous-time query algorithms for arbitrary problems. We show that any quantum algorithm in the continuous-time query model whose total query time is T can be simulated by a quantum algorithm in the discrete query model that makes O[T log(T) / log(log(T))] queries. This is the first upper bound that is independent of the driving operations (i.e., it holds even if the norm of the driving Hamiltonian is very large). A corollary is that any lower bound of T queries for a problem in the discrete-time query model immediately carries over to a lower bound of \Omega[T log(log(T))/log (T)] in the continuous-time query model.
Cleve Richard
Gottesman Daniel
Mosca Michele
Somma Rolando D.
Yonge-Mallo D. L.
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