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arXiv:2402.01891 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Resource Estimation of Quantum Multiplication Algorithms

Ethan Hansen, Sanskriti Joshi, Hannah Rarick

Published Sep 17, 2023• 4 citations
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Abstract

As quantum computers progress towards a larger scale, it is imperative that the “top” of the computing-technology stack is improved. This project investigates the quantum resources required to compute primitive arithmetic algorithms, particularly multiplication. By using various quantum resource estimators, like Microsoft's Azure Quantum Resource Estimator, one can determine the resources required for numerous quantum algorithms [8]. In this paper, we will provide a comprehensive resource analysis of numerous quantum multiplication algorithms such as Karatsuba, schoolbook, and windowed arithmetic for different qubit platforms (trapped ion, superconducting, and Majorana) using the new Azure Quantum Resource Estimator.

DOI
10.1109/qce57702.2023.10211

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As quantum computers progress towards a larger scale, it is imperative that the “top” of the computing-technology stack is improved. This project investigates the quantum resources required to compute primitive arithmetic algorithms, particularly multiplication. By using various quantum resource estimators, like Microsoft's Azure Quantum Resource Estimator, one can determine the resources required for numerous quantum algorithms [8]. In this paper, we will provide a comprehensive resource analysis of numerous quantum multiplication algorithms such as Karatsuba, schoolbook, and windowed arithmetic for different qubit platforms (trapped ion, superconducting, and Majorana) using the new Azure Quantum Resource Estimator.
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Quantum computing has advanced rapidly in recent decades, driven by developments across the technology stack, including quantum error-correcting codes and efficient quantum algorithms. Among these, quantum arithmetic circuits serve as fundamental building blocks for various promising algorithms. Despite their crucial role, the design of quantum arithmetic circuits faces challenges arising from the no-cloning theorem, qubit limitations, and circuit depth constraints, which significantly impact the efficiency of large-scale quantum computing. We provide an overview of quantum arithmetic circuits in the context of public-key cryptanalysis, with particular emphasis on optimization strategies such as measurement-based uncomputation and conditionally clean ancilla. We review state-of-the-art designs for essential arithmetic operations in public-key cryptanalysis such as addition, multiplication, and modular exponentiation. We also present an overview of the techniques used for fault-tolerant runtime and resource estimation in quantum cryptanalysis. In brief, this chapter emphasizes strategies for designing resource-efficient quantum arithmetic circuits, providing a basis for realistic evaluations of quantum cryptanalytic capabilities.
In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared with their classical counterparts, with Shor's algorithm serving as a prominent illustration. Quantum arithmetic circuits, which are the fundamental building blocks in numerous quantum algorithms, have attracted much attention. Despite extensive exploration of various designs in the existing literature, researchers remain keen to develop novel designs and improve existing ones. In this review article, we aim to provide a systematically organized and easily comprehensible overview of the current state of the art in quantum arithmetic circuits. Specifically, this study covers fundamental operations such as addition, subtraction, multiplication, division and modular exponentiation. We delve into the detailed quantum implementations of these prominent designs and evaluate their efficiency considering various objectives. We also discuss potential applications of the presented arithmetic circuits and suggest future research directions.This article is part of the theme issue 'Emerging technologies for future secure computing platforms'.