Efficient discrete-time simulations of continuous-time quantum query algorithms

Authors:
Richard Cleve;Daniel Gottesman;Michele Mosca;Rolando D. Somma;David Yonge-Mallo
Affiliations:
University of Waterloo and Perimeter Institute, Waterloo, ON, Canada;Perimeter Institute, Waterloo, ON, Canada;University of Waterloo and Perimeter Institute, Waterloo, ON, Canada;Perimeter Institute, Waterloo, ON, Canada;University of Waterloo, Waterloo, ON, Canada
Venue:
Proceedings of the forty-first annual ACM symposium on Theory of computing
Year:
2009

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Abstract

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. We show that any quantum algorithm in this model whose total query time is T can be simulated by a quantum algorithm in the discrete-time query model that makes O(T log T / loglog T) subset O~(T) queries. This is the first such 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 loglog T / log T) subset Omega~(T) in the continuous-time query model.