Tight Bounds on Quantum Searching

1998/06/01 by Michel Boyer, Gilles Brassard, Peter Høyer +1 · 736 citations
Computer Science · Physics and Astronomy · #Element (criminal law) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum algorithm #Quantum phase estimation algorithm #SIMPLE algorithm #Simple (philosophy) #Table (database) #Upper and lower bounds

paper · open access · doi:10.1002/(sici)1521-3978(199806)46:4/5<493::aid-prop493>3.0.co;2-p

published in Fortschritte der Physik 46(4-5), 493-505 (Wiley)

openalex publication_date 1998/06/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We provide a tight analysis of Grover's 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. Finally, we provide a lower bound on the efficiency of any possible quantum database searching algorithm and we show that Grover's algorithm comes within 2.62% of being optimal.

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