面向量子计算的模 $2n+1$ 加法器的新型优化设计
Novel Optimized Designs of Modulo $2n+1$ Adder for Quantum Computing
AI总结：
本文针对量子计算中尚缺的模 $(2n+1)$ 加法器，提出 QMA1 至 QMA4 四种优化设计，通过减少量子门、深度、量子比特数及改进零态制备，在 IBM 量子计算机上实现总错误降低 28.8%。
摘要：
量子模加法器是最基本但用途广泛的量子计算操作之一。它们有助于实现更高复杂度的功能，例如减法和乘法，这些功能被用于量子密码分析、量子图像处理和安全通信等应用中。据我们所知，目前尚不存在量子模 $(2n+1)$ 加法器的设计。在这项工作中，我们提出了四种专门针对模 $(2n+1)$ 加法的量子加法器。这些加法器可以同时提供普通和模 $(2n+1)$ 和，增强了它们在基于余数系统算术中的应用。我们的第一个设计 QMA1 是一种新型的量子模 $(2n+1)$ 加法器。第二个提出的加法器 QMA2 优化了 QMA1 中量子门的利用率，使 CNOT 门数减少了 37.5%，CNOT 深度减少了 46.15%，Toffoli 门数和深度均减少了 26.5%。我们提出了第三个加法器 QMA3，它使用零重置，这是一种基于动态电路的特性，可以重用量子比特，从而使量子比特数节省了 25%。我们的第四个设计 QMA4 展示了结合额外零重置以获得更纯零态的好处，从而减少了量子态制备错误。值得注意的是，我们在 IBM Washington（一台基于 Eagle R1 架构的 127 量子比特量子计算机）上使用所提出的模 $(2n+1)$ 加法器的 5 量子比特配置进行了实验，结果表明 QMA1 的错误减少了 28.8%，其中：(i) 由于 QMA2 中的门和深度减少，错误减少了 18.63%；(ii) 由于 QMA3 中的量子比特减少，错误下降了 2.53%；(iii) 由于在 QMA4 中应用额外的零重置，错误减少了 7.64%。
英文摘要：
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 $(2n+1)$ adder. In this work, we propose four quantum adders targeted specifically for modulo $(2n+1)$ addition. These adders can provide both regular and modulo $(2n+1)$ sum concurrently, enhancing their application in residue number system based arithmetic. Our first design, QMA1, is a novel quantum modulo $(2n+1)$ 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 $(2n+1)$ 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 of which: (i) 18.63% error reduction happens due to gate and depth reduction in QMA2, and (ii) 2.53% drop in error due to qubit reduction in QMA3, and (iii) 7.64% error decreased due to application of additional zero resets in QMA4.
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