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动力学解耦技术能有效地抑制由低频环境噪声导致的退相干过程, 因此在量子信息领域获得了广泛的应用. 传统的动力学解耦方案通过对简单的二能级体系, 如量子比特, 施加特定的π脉冲序列来实现解耦效果. 随着量子计算研发的深入, 对于像超导量子比特这种天然的多能级系统, 研究者不再局限于二能级子空间, 而是提出和实现了一系列基于多能级体系的量子调控手段和量子算法. 目前对于如何抑制这些体系中的退相干尚缺乏深入研究. 本文利用较易在实验中实现的紧邻能级间的π脉冲, 构建了多种针对多能级系统的动力学解耦序列. 结果表明这些序列可以很好地消除准静态噪声的影响. 此外, 通过计算滤波函数, 还分析了这些序列及其拓展方案对于高斯噪声的抑制作用, 并结合控制函数对滤波效果给出了物理解释. 研究结果对于多能级体系中的相关噪声研究, 包括噪声功率谱密度和关联性的刻画以及退相干的抑制等, 均具有启发意义.
Dynamical decoupling refers to a family of techniques that are widely used to suppress decoherence in various quantum systems, caused by quasi-static environmental noise. They have broad applications in the field of quantum information processing. Conventional dynamical decoupling targets at noise in two-level system such as qubits and often consists of specifically engineered sequences of $ \pi $ pulses that swap between two different states. On the other hand, researchers do not limit their study within simple two-levels systems any more, but go and seek for even more efficient quantum hardware. A variety of quantum algorithms and schemes of quantum control using multi-level systems, such as qutrits and qudits, for quantum information processing have been proposed and implemented successfully. However, decoherence in such a multi-level system is inherently more sophisticated than that in two-level systems. So far there has been little systematic research on how to tackle decoherence problems in such systems.In this work, we propose several sequences of dynamical decoupling for multi-level systems that only rely on $ \pi $ pulses linking neighboring levels, which is easy to implement experimentally. Our results show that these sequences can efficiently suppress quasi-static noise presented in multi-level systems. In addition, by calculating the corresponding filter functions of these sequences, we are able to further analyze their effect on generic Gaussian noise that may not be quasi-static. We also give a physical explanation of the noise filtering mechanism of these sequences by considering their control functions. Other topics discussed in our work include power spectral density and correlation of noise in multi-level systems. Our work may be regarded as a first step towards a more systematic investigation of dynamical decoupling techniques applicable to multi-level systems.-
Keywords:
- multi-level system/
- noise/
- decoherence/
- dynamic decoupling/
- filter function
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