Quantum Resource Estimation of Arithmetic Primitives

This project aimed to investigate the quantum computational resources needed for arithmetic primitives such as addition, multiplication, and exponentiation for integers and/or reals in floating point notation. This student team looked at the various primitives that are described in the quantum computing literature and set to analyze their efficiency in terms of the quantum resources that are needed to execute them in a fault tolerant manner. The resource estimation framework that was to be used is the one described in "Assessing requirements to scale to practical quantum advantage" by Michael E. Beverland, Prakash Murali, Matthias Troyer, Krysta M. Svore, Torsten Hoefler, Vadym Kliuchnikov, Guang Hao Low, Mathias Soeken, Aarthi Sundaram, and Alexander Vaschillo, 2022, arxiv.2211.07629. When possible the analysis used the Resource Estimation tool available on Azure Quantum. The primary scope of the project was to investigate the algorithms and circuits that already exist in the literature. The project also attempted to look at potential improvements on the existing results. The main outcome of the project was intended to be a comprehensive and consistent overview of the quantum resources needed to implement arithmetic primitives using a realistic fault tolerant quantum architecture. This overview seeks to give a better quantitative understanding of how the quantum algorithms for these primitives have improved over the past 25 years.

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