印度Harish-Chandra研究所Aditi Sen(De)团队研究了量子加法器中噪声和条带之间的权衡。2025年3月6日出版的《物理评论A》杂志发表了这项成果。

基于量子傅里叶变换的量子加法可以成为量子电路的一个组成部分，并且被证明比现有的经典波纹进位加法器更有效。该研究包括在任何任意维度上识别量子加法器中所需的量子资源，以及在电路上存在局部噪声的情况下，以及在允许有限数量的受控旋转操作时，其与性能指标的关系，这一过程称为条带化。

研究组分析证明了在所需和不完美输出之间的保真度存在任意缺陷的情况下，完成量子加法所需的受控旋转门数量的上限。当环境与单个量子相互作用时，他们在量子相干性和输出保真度之间建立了联系。

有趣的是，研究组证明了在存在噪声的情况下使用条带时，恒定深度的近似电路优于具有更高受控旋转次数的电路，从而在近似量子加法器和噪声强度之间建立了互补关系。结果证明，利用磁场来制备在特定时间内根据一维自旋链演化的初始状态，可成为在多体系统中实现量子加法电路的一种潜在技术。

附：英文原文

Author: Gaurang Agrawal, Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju, Aditi Sen(De

Issue&Volume: 2025/03/06

Abstract: Quantum addition based on the quantum Fourier transform can be an integral part of a quantum circuit and proved to be more efficient than the existing classical ripple carry adder. Our study includes identifying the quantum resource required in a quantum adder in any arbitrary dimension and its relationship with the performance indicator in the presence of local noise acting on the circuit and when a limited number of controlled rotation operations is permitted, a procedure known as banding. We analytically prove an upper bound on the number of the controlled rotation gates required to accomplish the quantum addition up to an arbitrary defect in the fidelity between the desired and imperfect output. When the environment interacts with individual qudits, we establish a connection between quantum coherence and fidelity of the output. Interestingly, we demonstrate that when banding is employed in the presence of noise, approximate circuits of constant depth outperform circuits with a higher number of controlled rotations, establishing a complementary relationship between the approximate quantum adder and the strength of the noise. We exhibit that utilizing magnetic fields to prepare an initial state that evolves according to a one-dimensional spin chain for a specific amount of time can be a potential technique to implement quantum addition circuits in many-body systems.

DOI: 10.1103/PhysRevA.111.032408

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.032408