Novel Optimized Designs of Modulo $2^n+1$ Adder for Quantum Computing

Bhaskar Gaur, Himanshu Thapliyal · 2024 · arXiv

| 编号 QA038 | 主题 加法与减法 | 链接 arXiv:2406.07486 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

Quantum modular adders are one of the most fundamental yet versatile quantum computation operations. They help implement functions of higher complexity, such as subtraction and multiplication, which are used in applications such as quantum cryptanalysis, quantum image processing, and securing communication. To the best of our knowledge, there is no existing design of quantum modulo $(2^n+1)$ adder. In this work, we propose four quantum adders targeted specifically for modulo $(2^n+1)$ addition. These adders can provide both regular and modulo $(2^n+1)$ sum concurrently, enhancing their application in residue number system based arithmetic. Our first design, QMA1, is a novel quantum modulo $(2^n+1)$ adder. The second proposed adder, QMA2, optimizes the utilization of quantum gates within the QMA1, resulting in 37.5% reduced CNOT gate count, 46.15% reduced CNOT depth, and 26.5% decrease in both Toffoli gates and depth. We propose a third adder QMA3 that uses zero resets, a dynamic circuits based feature that reuses qubits, leading to 25% savings in qubit count. Our fourth design, QMA4, demonstrates the benefit of incorporating additional zero resets to achieve a purer zero state, reducing quantum state preparation errors. Notably, we conducted experiments using 5-qubit configurations of the proposed modulo $(2^n+1)$ adders on the IBM Washington, a 127-qubit quantum computer based on the Eagle R1 architecture, to demonstrate a 28.8% reduction in QMA1’s error.

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