近日，北京量子信息科学研究院超导量子计算团队以「Travelling-wave Parametric Amplifier Induced Qubit Dephasing: Analysis and Mitigation」¹为题在Chip上发表研究论文，研究了行波参量放大器在读取中引起量子比特退相干的机制及解决方案。第一作者为张颖珊，通讯作者为刘伟洋、薛光明。本文为特刊（Cryogenic Chips）文章之一，此特刊为Chip发起的首个特刊。Chip是全球唯一聚焦芯片类研究的综合性国际期刊，是入选了国家高起点新刊计划的「三类高质量论文」期刊之一。
约瑟夫森行波参量放大器（Josephson traveling-wave parametric amplifiers，TWPAs）²⁻³由于其接近量子极限的噪声、宽带和高增益而被广泛应用于量子比特读取。然而，它们可能会导致量子比特相位退相干。这个缺点源于阻抗不匹配和正向波和反向波的混合。此外，不足的隔离可以使反射信号到达量子比特芯片，导致量子比特相移（图1）。
图1 | TWPA的增益和测量线路设置。a, 典型的使用TWPA进行量子比特读出的示意图。不同颜色的箭头表示不同波的传播方向。b,实验中在制冷机最低温层的线路设置。虚线框中的循环器表明它在第一次冷却时存在，在第二次冷却时被移除。c, 在工作点上的TWPA的正向和反向增益。（插图）扫描电子显微镜（SEM）图像，包含3个单元，采用伪着色表示形成SNAIL的大（蓝色）和小（橙色）约瑟夫森结。
为了减少测量诱导的相位退相干，研究人员采用了一种脉冲方法，其中TWPA泵浦被视为与量子比特测量脉冲分开的脉冲。这种方法可以实现优化的测量效率⁵，即在灵敏度和退相干之间的权衡⁶。较低的测量效率表明存在超出固有不确定性的过多相位退相干。通过使用脉冲模式，研究人员在量子比特操作期间的退相干可以与关闭模式相媲美，同时在量子比特测量期间实现与连续模式几乎相同的高信噪比（SNR）。
图3 | 使用a关闭模式，b连续模式和c脉冲模式提取修改后的测量效率。
研究人员使用测量效率作为指标，评估了三种读出模式（关闭模式、连续模式和脉冲模式），在量子比特芯片和TWPA之间没有循环器的情况下（图3）。脉冲模式展示了在量子比特操作期间实现高信噪比和低反向作用的优势，证实了他们的猜测。然而，相位退相干的来源，特别是泵浦泄漏，仍然会对测量诱导的相位退相干、ac-Stark效应和加热产生影响。研究人员认为脉冲模式和循环器的结合对于容错量子计算架构具有潜力，同时实现对大规模量子比特阵列的高效读出仍然具有挑战性。
总结起来，作者研究了量子比特连接到TWPA进行读出时的相位退相干的来源。文章的重点在于理解和减轻了泵浦诱导的相位退相干效应对于实现容错所需的高质量读出的重要性。脉冲模式读出显示出在增强信噪比的同时最大程度减少对相位退相干的影响的价值。持续优化量子比特和微波泵浦放大器之间的接口可以为实现容错量子计算所需的高质量读出铺平道路。
Travelling-wave parametric amplifier induced qubit dephasing: analysis and mitigation¹
Josephson traveling-wave parametric amplifiers (TWPAs) ²⁻³ are widely used in qubit readout due to their near-quantum-limited noise, wide bandwidth, and high gain. However, they can inadvertently dephase qubits and degrade their performance. This drawback arises from impedance mismatch and mixing of forward and reflected waves. Moreover, insufficient isolation can allow reflected signals to reach the qubit chip, causing qubit dephasing (Fig. 1).
Fig. 1 | Gain and measurement setup of TWPA. a, Sketch of a typical qubit readout setup using a TWPA. Different colored arrows indicate the direction of propagation for various waves. b, Experimental setup on the mixing chamber (MC) stage in our experiment. A circulator in a dasher box indicates that it was present during the first cooldown and removed during the second cooldown. c,Forward and backward gain of the TWPA at the operating point. (inset) A scanning electron microscopy (SEM) image which contains 3 cells of the TWPA with false coloring to indicate large (blue) and small (orange) junctions forming SNAILs.
To reduce measurement-induced dephasing, researchers adopted a pulse method where the TWPA pump is treated as a separate pulse from the qubit measurement pulse. This approach allows for optimized measurement efficiency⁵, which quantifies the trade-off between sensitivity and decoherence⁶. Lower measurement efficiency indicates excess dephasing beyond the inherent uncertainty. By using pulse mode, the researchers hypothesize that qubit dephasing during qubit operation can be comparable to the off mode, while achieving the high signal-to-noise ratio (SNR) of the continuous mode during qubit measurement.
Researchers evaluated the three readout modes (off, continuous, and pulse) using measurement efficiency as a metric, without a circulator between the qubit chip and TWPA (Fig. 3). The pulse mode demonstrated the advantage of achieving both a high SNR and low backaction during qubit operation, supporting our conjecture. However, dephasing sources, particularly pump leakage, still contribute to measurement-induced dephasing, ac-Stark shifts, and heating. The researchers argue that the combination of pulse mode and circulators holds promise for fault-tolerant quantum computing architectures, achieving simultaneous high-efficiency readout of large qubit arrays remains challenging.
Fig. 3 | Extraction of modified measurement efficiency with a off mode, b continuous mode, and c pulse mode.
In conclusion, the researchers investigated the sources of dephasing when a qubit is connected to a TWPA for readout. The researchers highlighted the importance of understanding and mitigating pump-induced dephasing effects for achieving high-quality readout required for fault tolerance. The pulse-mode readout showed its value in enhancing SNR while minimizing compromise to dephasing. Continued progress in optimizing the interface between qubits and microwave-pumped amplifiers can pave the way for achieving the high-quality readout required for fault-tolerant quantum computing.
参考文献：
1. Zhang, Y. et al. Traveling-wave parametric amplifier–induced qubit dephasing:analysis and mitigation. Chip 2, 100067 (2023).
2.Planat, L. et al. Photonic-crystal Josephson traveling-wave parametric amplifier. Phys. Rev. X 10, 021021 (2020).
3. Macklin, C. et al. A nearequantum-limited Josephson traveling-wave parametric amplifier. Science 350, 307–310 (2015).
4. Gambetta, J. et al. Qubit-photon interactions in a cavity: measurement-induced dephasing and number splitting. Phys. Rev. A 74, 042318 (2006).
5. Bultink, C. C. et al. General method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. Appl. Phys. Lett. 112, 092601 (2018).
6. Clerk, A. A. et al. Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155 (2010).
论文链接：
https://doi.org/10.1016/j.chip.2023.100067
作者简介
张颖珊，在清华大学获得博士学位，北京量子信息科学研究院高级工程师，主要研究方向为量子计算中的超导量子器件设计。邮箱：zhangys@baqis.ac.cn.
Zhang Yingshan is a senior engineer at the Beijing Academy of Quantum Information Sciences, specializing in superconducting quantum device design for quantum computation. She holds a PhD from Tsinghua University. Contact: zhangys@baqis.ac.cn.
薛光明，在中国科学院物理研究所获得博士学位，北京量子信息科学研究院副研究员，主要研究方向为超导量子计算以及约瑟夫森参量放大器。邮箱：xuegm@baqis.ac.cn
Xue Guang-Ming is an associate research scientist at the Beijing Academy of Quantum Information Sciences. His research interests include quantum computation and Josephson parametric amplifier. He has a PhD in physics from Institute of Physics Chinese Academy of Sciences. Contact: xuegm@baqis.ac.cn.
关于Chip
Chip（ISSN：2772-2724，CN：31-2189/O4）是全球唯一聚焦芯片类研究的综合性国际期刊，已入选由中国科协、教育部、科技部、中科院等单位联合实施的「中国科技期刊卓越行动计划高起点新刊项目」，为科技部鼓励发表「三类高质量论文」期刊之一。
Chip期刊由上海交通大学出版，联合Elsevier集团全球发行，并与多家国内外知名学术组织展开合作，为学术会议提供高质量交流平台。
Chip秉承创刊理念: All About Chip，聚焦芯片，兼容并包，旨在发表与芯片相关的各科研领域尖端突破性成果，助力未来芯片科技发展。迄今为止，Chip已在其编委会汇集了来自14个国家的70名世界知名专家学者，其中包括多名中外院士及IEEE、ACM、Optica等知名国际学会终身会士（Fellow）。
Chip第二卷第四期已于2023年12月在爱思维尔Chip官网以金色开放获取形式（Gold Open Access）发布，欢迎访问阅读本期最新文章。
爱思唯尔Chip官网：
https://www.sciencedirect.com/journal/chip
