利用量子物理现象，量子计算应在传统计算中的数值处理能力中提前[1,2]。The experimental work being undertaken currently in this field focuses on improving the devices that would ultimately perform the function of transistors in classical processors - the quantum bits (qubits).
目前研究的最有前途的竞争者之一是超导Qubits[3, 4]。由于它们是基于纯电控和微制造技术，因此超导Qubits提供了一个清晰的路线图，用于在单个处理器中大量集成数百Qubbits。
在过去几年中实现的相干时间的稳步提高激发了可信度，即设备可以设计成支持实用数值算法的质量。
增长复杂性
Complex pulsed microwave signals on multiple channels with accurate synchronization are required to control superconducting qubits. With the increase in the number of channels and qubits, standardized, strongly integrated, and highly reliable electronic control solutions are essential.
This demand is addressed by the Zurich Instruments UHFLI instrument, as it combines an arbitrary waveform generator (AWG) that synthesizes precisely shaped pulsed signals, and a 600 MHz lock-in amplifier equipped with digitizer for detection.
By combining generation and detection in one device, the setup complexity and rack space can be reduced, synchronization can be improved, and advanced control methods can be enabled based on feed-forward from detection to generation, for example, sequence branching.
本文讨论了uhfli仪器如何用于在其相干时间，qubit状态寿命和频率方面表征超导Qubits。调整用于生成量子计算序列的脉冲形状也由本文中提供的测量提供。
The circuit quantum electrodynamics architecture,[5]可以扩展到多Qubit实验，用于执行本文讨论的实验。测量在瑞士埃特拉克·奥尔拉夫的Quantum设备实验室中进行了测量。
Setup and Sample
Quantum computing devices are developed to enable control and readout of a qubit’s quantum state. The quantum state is generally a quantum superposition of two physical configurations of the qubit device, which encodes the data processed in a quantum computer.
Figure 1(a) displays a sample consisting of niobium- and aluminum-based resonant circuits on a sapphire chip. The actual qubit is a nonlinear resonator formed of an on-chip capacitor (orange in the image) and a small superconducting quantum interference device (SQUID).
With the SQUID design, the qubit frequency can be tuned over a frequency range between 4 and 7.5 GHz by modifying a small magnetic field applied to the device.
A coplanar waveguide (green) directs external signals directly to the qubit for its control. The qubit is coupled with a coplanar-waveguide resonator (blue)[5]在4.78 GHz。片上滤波器将读出谐振器连接到一对同轴电缆，该电缆提供用于读出量子位的量子状态的接口。
图1（b）示出了测量设置的示意图，其中样品安装在稀释冰箱中，以提供良好的隔离低温环境，保护样品的量子特性。
![(a) Optical micrograph of the sample showing the readout resonator (blue) and the qubit capacitor plates (orange). The resonator is coupled to input and output lines via a Purcell filter [6] (cyan). Insets show magnified views of the qubit and the coupler between resonator and Purcell filter. (b) Simplified diagram of the experimental setup based on the UHFLI instrument integrating a lock-in amplifier and an AWG. The superconducting qubit sample is cooled in a dilution refrigerator.](https://d12oja0ew7x0i8.cloudfront.net/images/Article_Images/ImageForArticle_13264(1).jpg)
Figure 1.(a) Optical micrograph of the sample showing the readout resonator (blue) and the qubit capacitor plates (orange). The resonator is coupled to input and output lines via a Purcell filter[6](cyan). Insets show magnified views of the qubit and the coupler between resonator and Purcell filter. (b) Simplified diagram of the experimental setup based on the UHFLI instrument integrating a lock-in amplifier and an AWG. The superconducting qubit sample is cooled in a dilution refrigerator.
用两个AWG通道执行微波信号的正交调制以产生控制脉冲。将其中一个AWG标记通道馈送到信号发生器的栅极输入有助于为Qubit读数产生脉冲。
The pulses are amplified after they are transmitted through the readout resonator, and then the readout signal is down-converted to an intermediate frequency f如果。One of the UHFLI lock-in amplifier channels is then used to measure the pulses.
Measurements
Qubit Spectroscopy
The spectroscopic measurements of the line-width and frequency of the qubit and the readout resonator are measured first. The optimum magnetic field bias is set by using a small coil at the sample, and can also be determined using spectroscopy.
In order to measure the readout resonator, a continuous microwave tone is applied to a resonator and the amplitude of the down-converted transmitted signal is measured with the lock-in amplifier. The tone’s frequencyvres扫过频率fres谐振器。图2（b）显示了一种这种测量。谐振器的传动线厚度是freson top of a broader peak, which is the result of the on-chip Purcell filter[6]。
使用双音微波技术来测量Qubit过渡频率。第一种微波音在靠近谐振f的固定频率上施加resto the readout resonator. A second tone is applied to the qubit gate line and its frequency νqb在衡量传输幅度的同时扫过宽范围。
由于读出谐振器与QUB比特之间的分散耦合，当ν时有变化qbbecomes resonant with the qubit transition at fqb[5]。如（a）所示，这导致F处的特征qb。
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Figure 2.Spectra of the qubit (a) and of the readout resonator (b). The measurement in (a) is obtained by measuring the transmission at a fixed frequency νrfclose to the cavity resonance (b) and sweeping the qubit drive frequency νqb。（c）对磁通F的弧形依赖性对于这种类型的Qubit是特征。随着QUBBit频率通过（d）中的横轴交叉读出谐振器的频率，两个呈现避免的交叉。颜色尺度示出了放大后通过读出谐振器发送的信号的幅度。
In Figure 2 (c) and (d), the qubit and resonator spectra can be seen as a function of magnetic field. The qubit transition frequency exhibits a characteristic, arc-shaped dependence on magnetic field[7]。如（d）中可以看出，读出谐振器和量子位展示了避免的交叉。谐振器和量子位之间的强耦合是该真空Rabi分裂的原因。
In order to probe the qubit’s dynamic properties, the subsequent measurements are pulsed rather than continuous. A pulse sequence that consists of a readout part and a control part form the basis of these measurements. Pulses are applied to the qubit gate line at a frequency close to fqb在控制部分期间。
These resonant pulses result in Rabi oscillations, a coherent oscillation of the qubit between its ground and excited state. After the control part, a pulse is applied to the readout resonator at a frequency close to fres并且在通过样本传输之后执行信号的触发测量。
为了实现这一目标，返回信号首先在模拟域中转换为f如果= 28.125 MHz。然后通过锁定放大器在数字域中解调。使用数字锁定技术而不是直接转换为DC，测量免受放大器偏移电压漂移和1 / F噪声的影响[8]。
To increase the signal-to-noise ratio and average out quantum fluctuations, the entire cycle is repeated several thousand times. Conventionally, the averaging of raw data is done before the down-conversion. With theUhfli数字解调器，可以在平均之前执行下转换。
该方法从实验中删除一个数据处理步骤，并且它消除了选择与重复率相比相称的中间频率的要求。在执行解调信号必须快速可用的前馈协议期间也是必要的。
Rabi Oscillations
Applying a control pulse results in a distinct change of qubit state, which can be used as a single-qubit gate operation. Such operations are necessary for implementing quantum computing algorithms,in a similar way that the logical inversion is required for classical computing algorithms. The pulse parameters for a given gate operation can be determined using a Rabi oscillation measurement.
A control pulse with an envelope shaped by smooth edges (rise/fall time 3.9 ns) and a flat plateau with a variable width are generated for this measurement. Following this control pulse is a readout pulse, which is a microwave burst with an approximately rectangular envelope.
The probability of the qubit being in the excited state follows a sinusoidal evolution as a function of the control pulse area, which is also proportional to its width at half maximum. This evolution is reflected in the signal measured during the readout phase that is plotted in Figure 3.
The curve enables the width of the qubit gate pulses relevant for the next measurements to be identified: the Π -pulse width corresponds to the first maximum, the Π/2-pulse width corresponds to the first quarter period. While the p-pulse brings the qubit from its ground to the excited state, the Π/2-pulse brings the qubit to an equal coherent superposition of ground and excited state. All control pulses were repeated 4000 times at a rate of 13 kHz, for this measurement.
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Figure 3.Rabi oscillation measurement. As a function of the width of the control pulse, the qubit evolves periodically from ground state to excited state and back. This results in a sinusoidal readout signal amplitude as a function of the pulse width (horizontal axis) as seen in the color plot in (a). (b) Time-dependent readout signal at two values of the pulse width marked in (a). The time between about 1.2 µs and 5.8 µs corresponds to the readout pulse. (c) Rabi oscillation plot obtained by averaging the data in (a) and normalizing the result to obtain a mean excited-state population. The measurement allows us to determine the parameters for Π- and Π/2-pulses (red marks).
Qubit Lifetime
由于从激励量子位状态到地状态的衰减，计算算法的持续时间受到限制。测量平均寿命T.1因此是设备表征的重要部分。
测量t时1，在序列的开头处施加π脉冲，然后存在等待变速T，并且最终测量Qubit状态。图4（a）显示了结果数据。寿命T.1= 8.8 µs is extracted from a fit to an exponential exp(–t/T1）。
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图4。（a）qubit寿命t1测量。Qubit在具有p脉冲的激发状态下初始化。然后测量随后的指数衰减以增加读出脉冲之前的延迟。（b）Ramsey边缘测量。随着两个P / 2脉冲之间的延迟变化，Qubit读出信号遵循反映相干逐渐丧失的衰减振荡演进。测量用于确定Qubit相干时间t2*. Both measurements were averaged 40’000 times at a 27 kHz repetition rate.
Waveforms and sequences can be directly generated using theUhflicontrol software LabOne®。A series of 200 patterns were generated with UHF-AWG using a sequencer loop incrementing the readout pulse delay from 0 µs to 26 µs with dynamic waiting times and run-time sequencer variables.
这意味着一个Π脉冲包络,less than 400 samples of waveform data for both channels can be used to generate all qubit control pulses. This is unlike conventional methods, where patterns for all pulse delays must be uploaded to the AWG sample-by-sample, requiring waveform data of about 200 x (26 µs) x (2 channels) x (1.8 GSa/s) = 18.7 MSa and consequently a much longer waveform transfer time.
qubit一致性时间
The free coherent evolution of the qubit is shown by the Ramsey fringe measurement. There are two Π/2-pulses separated by a varying delay time followed by a qubit readout in the Ramsey sequence. When there is no decoherence, the two Π/2-pulses combine to form a full Π-pulse and the qubit ends up in the excited state.
Relaxation and dephasing during the delay time results in the pulse addition becoming imperfect, which means the potential for being in the excited state decays with the delay time. A slight detuning of the pulse frequency relative to fqb在Qubit阶段和控制脉冲载体的相位之间产生跳动效果。这导致读出信号中的振荡贡献。t的脱模时间2* =1.2μs可以从图4（b）所示的测量中提取。
Duel-Channel AWG生成的脉冲具有112.5MHz的中频载波，使用在数字域中操作的UHF-AWG调制模式生成。然后使用模拟混频器将中频升高到量子位转换频率。使用幅度调制意味着可以在不重新编程AWG的情况下调整或扫描相位和载波频率。
Conclusion
These essential qubit measurements demonstrate the potential of theZurich Instruments’Uhfli锁定放大器和AWG在实验域中，需要定时精度，信号质量和高速。在其寿命，相干时间和工作频率方面，可以从测量获得Qubit仪器的深入表征。基于用于这些测量的基本脉冲，以直接的方式建立更复杂的实验序列，例如随机基准测试或旋转回波。
Acknowledgements
Zurich Instruments would like to thank Prof. Wallraff and his team for sharing experimental results and for their strong commitment to developing qubit experiments with Zurich Instruments technology. Special thanks go to Michele Collodo for carrying out the measurements and providing an excellent framework for the integration of the UHFLI into the existing laboratory infrastructure. We thank Theodore Walter for providing the qubit sample and Yves Salathe, Simone Gasparinetti, and Philipp Kurpiers for support with the measurements and for discussions. This work was supported by the Swiss Federal Department of Economic Affairs, Education and Research through the Commision for Technology and Innovation (CTI).
参考
[1]R. P. Feynman. Simulating physics with computers. Int. J. of Theor. Phys., 21:467, 1982.
[2]T. D. Ladd，F.Jelezko，R.Laflamme，Y.Nakamura，C. Monroe和J.L. O'Brien。量子计算机。大自然，464：45,2010。
[3]Y. Nakamura，Pashkin，Yu。A.和Tsai J.S。在一个Cooper对箱中的宏观量子状态的相干控制。大自然，398：786,1999。
[4]John Clarke和Frank K. Wilhelm。超导量子位。大自然，453：1031,2008。
[5]A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.- S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature, 431:1627, 2004.
[6]M. D. Reed，L. Dicarlo，B. R. Johnson，L. Sun，D.I.Schuster，L. Frunzio和R. J. Schoelkopf。使用Jaynes-Cummings非线性电路量子电动动力学中的高保真读数。物理。Rev. Lett。，105：173601，2010年10月。
[7]Jens Koch，Terri M. Yu，Jay Gambetta，A.A.Houck，D. I. Schuster，J. Majer，亚历山大Blais，M.H. Devoret，S. M.Girvin和R. J. Schoelkopf。源自Cooper对框的加压抑制Qubit设计。物理。Rev. A，76：042319，2007年10月。
[8]David Schuster。电路量子电动动力学。博士文论文，耶鲁大学，2007年。
This information has been sourced, reviewed and adapted from materials provided by Zurich Instruments.
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