Determination of the number of shots for Grover’s search algorithm
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Mathieu Kessler acknowlegdes the support of Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia (Grant 20911/PI/18).Fecha de publicación
2023-11-08Editorial
SpringerOpenCita bibliográfica
Kessler, M., Alonso, D. & Sánchez, P. Determination of the number of shots for Grover’s search algorithm. EPJ Quantum Technol. 10, 47 (2023). https://doi.org/10.1140/epjqt/s40507-023-00204-yRevisión por pares
siPalabras clave
Computación cuánticaAlgoritmo de Grover
Coleccionista de cupones
Número de shots
Resumen
This paper focuses on Grover’s quantum search algorithm, which is of paramount importance as a masterpiece of Quantum Computing software. Given the inherent probabilistic nature of quantum computers, quantum programs based on Grover’s algorithm need to be run a number of times in order to generate a histogram of candidate values for solutions, which are then checked to identify the valid ones. In this paper, the distribution of the required number of shots to find all or a fraction of all the solutions to the Grover’s search problem is studied. Firstly, considering the similarity of the probability problem with the well-known coupon collector’s problem, two formulae are obtained from asymptotic results on the distribution of the required number of shots, as the number of problem solutions grows. These expressions allow to compute the number of shots required to ensure that, with probability p, all or a fraction of all the solutions are found. Secondly, the probability mass function of ...
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