Construction of Boolean Logic Gates Using QFT-Based Adder Architecture

Ayda Kaltehei, Murat Kurt, Azmi Gençten, Selçuk Çakmak · 2025 · arXiv 预印本

| 编号 QQFT029 | 主题 量子傅里叶变换 | 链接 arXiv:2504.17090 |

摘要

摘要保留原文（英文）

摘要取自 arXiv，未作翻译，以保证与原文一致。

In this study, we construct the quantum reversible counterparts of the logical AND, OR, XOR, NOR, and NAND gates. We utilize a quantum Fourier transform (QFT)-based adder circuit that replicates the functionality of a digital half-adder, which computes the sum and carry of two input bits using XOR and AND gates, respectively. To realize different logic gate operations, we apply pre- and post-processing to the QFT-adder using quantum gates, leveraging Boolean algebra properties to enable conversions between various logical functions. Although the number of elementary quantum logic gates increases for a small number of inputs-making the approach appear inefficient at first glance-the overall required qubit count is reduced compared to non-QFT-based designs as the number of inputs increases.

读法提示

摘要末句是本条目的关键结论，且是一个取舍而不是单向改进：初等门数量在小输入时上升、总比特数在输入数增大后才优于非 QFT 设计。因此它属于”用门换比特”的样本，与QFT 算术里”进位没有线”的动机同源，但不能当成 T 数上的改进。

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