对数深度量子先行进位模 $(2^n-1)$ 加法器
A Logarithmic Depth Quantum Carry-Lookahead Modulo $(2^n-1)$ Adder
AI总结：
本文提出量子先行进位模 $(2^n-1)$ 加法器QCLMA，通过树结构进位路径将深度从O(n)降至O(log n)，并在IBM Cairo上实现QSFR提升47.21%，以增强NISQ设备上的噪声保真度。
摘要：
量子计算正在朝着能够实现量子算法的机器方向取得重大进展，这些算法应用于量子密码学、量子图像处理和优化等多个领域。模加法量子算术电路的发展对于实现这些量子算法至关重要。虽然理想情况下应使用基于容错门的量子电路来克服噪声和退相干错误，但当前含噪声中等规模量子（NISQ）时代的量子计算机无法承受与容错设计相关的额外计算开销。我们的研究旨在最小化电路深度，这可以降低噪声并促进在NISQ机器上实现量子模加法电路。本文提出了量子先行进位模 $(2^n - 1)$ 加法器（QCLMA），该加法器设计用于接收两个n位数并以O(log n)深度执行它们的加法。与现有O(n)深度的工作相比，我们提出的QCLMA降低了深度并有助于提高噪声保真度。为了提高错误恢复能力，我们还专注于创建基于树结构的进位路径，不同于当前工作中基于链结构的进位路径。我们在IBM Cairo量子计算机上运行实验，以评估所提出的QCLMA相对于现有工作的性能，并定义量子态保真度比（QSFR）来量化正确输出与最高输出之间的接近程度。与现有工作相比，所提出的QCLMA在4量子比特模加法中实现了QSFR 47.21%的提升，展示了其优越的噪声保真度。
英文摘要：
Quantum Computing is making significant advancements toward creating machines capable of implementing quantum algorithms in various fields, such as quantum cryptography, quantum image processing, and optimization. The development of quantum arithmetic circuits for modulo addition is vital for implementing these quantum algorithms. While it is ideal to use quantum circuits based on fault-tolerant gates to overcome noise and decoherence errors, the current Noisy Intermediate Scale Quantum (NISQ) era quantum computers cannot handle the additional computational cost associated with fault-tolerant designs. Our research aims to minimize circuit depth, which can reduce noise and facilitate the implementation of quantum modulo addition circuits on NISQ machines. This work presents quantum carry-lookahead modulo $(2^n - 1)$ adder (QCLMA), which is designed to receive two n-bit numbers and perform their addition with an O(log n) depth. Compared to existing work of O(n) depth, our proposed QCLMA reduces the depth and helps increase the noise fidelity. In order to increase error resilience, we also focus on creating a tree structure based Carry path, unlike the chain based Carry path of the current work. We run experiments on Quantum Computer IBM Cairo to evaluate the performance of the proposed QCLMA against the existing work and define Quantum State Fidelity Ratio (QSFR) to quantify the closeness of the correct output to the top output. When compared against existing work, the proposed QCLMA achieves a 47.21% increase in QSFR for 4-qubit modulo addition showcasing its superior noise fidelity.
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