Quantum Database Search by a Single Query
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Quantum Search on Structured Problems
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Quantum and classical tradeoffs
Theoretical Computer Science
On the Complexity of Searching for a Maximum of a Function on a Quantum Computer
Quantum Information Processing
Quantum set intersection and its application to associative memory
The Journal of Machine Learning Research
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We provide a tight analysis of Grover''s recent algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine the number of iterations necessary to achieve almost certainty of finding the answer. Furthermore, we analyse the behaviour of the algorithm when the element to be found appears more than once in the table and we provide a new algorithm to find such an element even when the number of solutions is not known ahead of time. Using techniques from Shor''s quantum factoring algorithm in addition to Grover''s approach, we introduce a new technique for approximate quantum counting, which allows to estimate the number of solutions. Finally we provide a lower bound on the efficiency of any possible quantum database searching algorithm and we show that Grover''s algorithm nearly comes within a factor 2 of being optimal in terms of the number of probes required in the table.