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In this chapter we introduce the Quantum Fourier Transform (QFT), which is a key ingredient of many quantum protocols, and estimate the number of quantum gates to implement it. Then, we apply the QFT to the phase estimation problem and address the factoring algorithm proposed by Shor. In particular, we highlight the role of the QFT in the order-finding protocol that allows overcoming the computational limits of the best classical algorithms.

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Quantum Fourier Transform and Shor’s Factoring Algorithm

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  • 发表日期：

    2025年

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  • Stefano Olivares

摘要

In this chapter we introduce the Quantum Fourier Transform (QFT), which is a key ingredient of many quantum protocols, and estimate the number of quantum gates to implement it. Then, we apply the QFT to the phase estimation problem and address the factoring algorithm proposed by Shor. In particular, we highlight the role of the QFT in the order-finding protocol that allows overcoming the computational limits of the best classical algorithms.