CC BY
13
i к St. Petersburg Polytechnic University Journal: Physics and Mathematics. 2022 Vol. 15, No. 3.2 Научно-технические ведомости СПбГПУ. Физико-математические науки. 15 (3.2) 2022
Conference materials UDC 53.084.6
DOI: https://doi.org/10.18721/JPM.153.265
Application of a broadband Josephson parametric amplifier
A. E. Dorogov 3B, G. P. Fedorov 2 3, D. A. Kalacheva 2 4, A. Yu. Dmitriev ', A. N. Bolgar 1 4, N. N. Abramov 2, O. V. Astafiev 14 1 Moscow Institute of Physics and Technology, Moscow, Russia;
2 National University of Science and Technology MISIS, Moscow, Russia;
3 Russian Quantum Center, Moscow, Russia; 4 Skolkovo Institute of Science and Technology, Moscow, Russia H Dorogov.AE@phystech.edu
Abstract. We examine the performance of a Josephson Parametric Amplifier (JPA) which uses an array of SNAILs (Superconducting Nonlinear Asymmetric Inductive eLements) as the source of nonlinearity and leverages the technique of impedance engineering (introducing a positive linear slope in the imaginary part of the input impedance seen by the SNAILs) to overcome a traditional gain-bandwidth product and increase the 1-dB compression point. We experimentally demonstrate an 18 dB gain over a 586 MHz band, along with a 1-dB compression point -101.9 dBm. All these characteristics are of great importance for the quantum devices measurements and in particular for the single-shot readout of a multi-qubit system. The signal-to-noise ratio after the application of the JPA was increased by 3 times. That led to the improvement of separation fidelity of single-shot dispersive measurements of a transmon qubit from 30.6% to 97.2%.
Keywords: parametric amplifier, Josephson junction, gain-bandwidth product, 1-dB compression point, single-shot readout
Funding: Russian Science Foundation Grant No. 21-72-30026.
Citation: Dorogov A. E., Fedorov G. P., Kalacheva D. A., Dmitriev A. Yu., Bolgar A. N., Abramov N. N., Astafiev O. V., Application of a broadband Josephson parametric amplifier, St. Petersburg State Polytechnical University Journal. Physics and Mathematics. 15 (3.2) (2022) 352-357. DOI: https://doi.org/10.18721/JPM.153.265
This is an open access article under the CC BY-NC 4.0 license (https://creativecommons. org/licenses/by-nc/4.0/)
Материалы конференции УДК 53.084.6
DOI: https://doi.org/10.18721/JPM.153.265
Применение широкополосного джозефсоновского параметрического усилителя
А. Е. Дорогов 1 3И, Г. П. Федоров 1 2 3, Д. А. Калачева 1 2 4, А. Ю. Дмитриев А. Н. Болгар 1 4, Н. Н. Абрамов 3, О. В. Астафьев 1 4
1 Московский физико-технический институт, г. Москва, Россия; 2 Национальный исследовательский технологический университет «МИСиС», г. Москва, Россия; 3 Российский квантовый центр, г. Москва, Россия; 4 Сколковский институт науки и технологий, г. Москва, Россия н Dorogov.AE@phystech.edu
Аннотация. В данной работе исследуется применение широкополосного джозефсоновского параметрического усилителя на основе сверхпроводящих нелинейных асимметричных индуктивных элементов SNAIL в качестве источника нелинейности и с использованием
© Dorogov A. E., Fedorov G. P., Kalacheva D. A., Dmitriev A. Yu., Bolgar A. N., Abramov N. N., Astafiev O. V., 2022. Published by Peter the Great St. Petersburg Polytechnic University.
_Radiophysics
техники трансформации импеданса (введение частотной зависимости мнимой части входного импеданса) для увеличения gain-bandwidth product и мощности насыщения. Были экспериментально продемонстрированы коэффициент усиления 18 дБ в полосе 586 МГц и мощность насыщения -101.9 дБм. Эти характеристики очень важны для измерений квантовых устройств, и в частности для проективного считывания многокубитной системы. Благодаря использованию усилителя отношение сигнал-шум измерительной цепи было увеличено в три раза. Это привело к улучшению точности погрешности разделения состояний проективного дисперсионного считывания кубита-трансмона с 30.6% до 97.2%.
Ключевые слова: параметрический усилитель, джозефсоновский переход, мощность насыщения, дисперсионное считывание
Финансирование: Грант РНФ 21-72-30026.
Ссылка при цитировании: Дорогов А. Е., Федоров Г. П., Калачева Д. А., Дмитриев А. Ю., Болгар А. Н., Абрамов Н. Н., Астафьев О. В. Применение широкополосного джозефсоновского параметрического усилителя // Научно-технические ведомости СПбГПУ. Физико-математические науки. Т. 15. № 3.2. С. 352-357. DOI: https://doi. org/10.18721/JPM.153.265
Статья открытого доступа, распространяемая по лицензии CC BY-NC 4.0 (https:// creativecommons.org/licenses/by-nc/4.0/)
Introduction
As the field of quantum computing is rapidly evolving, quantum devices incorporate more and more qubits, inevitably forming a demand for broadband parametric amplifiers which can be used for multiplexed qubit readout. Commercially available HEMT amplifiers are not sufficient because of high added noise, ?HEMT =3-5 K. Josephson Parametric Amplifiers (JPAs) are capable of reaching the minimum added noise imposed by quantum mechanics, Tq ~ 0.3 K, and consequently can increase the signal-to-noise ratio (SNR) several-fold. Enhancement of SNR is a vital task for qubit measurements because it allows to speed up readout and improve the fidelity.
Moreover, JPAs have to provide a decent gain GJPA to overcome the noise from the subsequent HEMT amplifiers, as follows from the expression for the chain noise:
T = T + Themt (1)
chain JJPA ^ g ' (1)
GJPA
Thus, the crucial requirements which define the performance of the JPA are low added noise, high gain (15-20 dB), large bandwidth and dynamic range, as well as ease of operation.
Generally, a parametric amplifier is just a nonlinear oscillator, where the nonlinearity provides the power transfer from the strong pump to the weak quantum signal. JPAs employ the Josephson junctions (JJs) to introduce the required nonlinearity: their inductance depends on the phase drop Ф across the JJ as
Фо/10 , cos(9)'
where Ф0 is a magnetic flux quantum and I0 is the junction's critical current.
The performance of JPAs is fundamentally confined by several factors. First of all, there is a trade-off between the power gain and the bandwidth of amplification, namely the 'gain-bandwidth product' [1]:
G -1 1
G = 1 +-——, Г <x , . (2)
1 + (® / г)2' jgmac -1
Thus, there is no sense to strive to reach the gain more than 15-20 dB because that is enough to overcome the noise from HEMT amplifiers and further increase in gain will just lead to the decrease in bandwidth.
© Дорогов А. Е., Федоров Г. П., Калачева Д. А., Дмитриев А. Ю., Болгар А. Н., Абрамов Н. Н., Астафьев О. В., 2022. Издатель: Санкт-Петербургский политехнический университет Петра Великого.
^ St. Petersburg Polytechnic University Journal. Physics and Mathematics. 2022 Vol. 15, No. 3.2
Next, the amplification decreases at high signal powers as it is provided by plentiful though still depletable photons from the pump. To quantify this effect, the so-called 1-dB compression point is introduced as the signal power at which the gain drops by 1 dB.
Seeking the way to sidestep negative influence of the aforementioned factors, we study a JPA which uses an array of M = 23 SNAILs (Superconducting Nonlinear Asymmetric eLements) as a nonlinear element [2]. This architecture offers great flexibility while designing the device. A single SNAIL consists of 3 large Josephson junctions (inductance LJ) in a loop with one smaller junction (inductance L/a) (Fig. 1).
a) b)
Fig. 1. Design (top) and false color scanning electron micrograph (bottom) of the structure (a); the Al-based tunnel junctions are shaded in pink and blue for two different evaporation angles, respectively. Nonlinear resonator composed of a capacitively shunted SNAIL array (red) coupled to the source impedance via two transmission line segments (blue) introducing a positive linear slope in the imaginary part of the input impedance ZJra] (b). Implementation of the circuit in (b) using microstrip geometry (c); the transformer and the pump filter are fabricated on separate chips
The Hamiltonian of such amplifier can be approximated as [2]:
= ©aa^ a + g3(a + a^)3 + g4(a + a^)4. (3)
H JPA
h
Then the power gain for a signal at frequency and the pump at ra is
4k2 | g |2
G[®] = 1 +-^-,
(A2-®2 + 14-4|g|2)2 + (™)2 ( )
® p . ® p 32 . l2
where ® = , g = 2g3ap, Ap =®a~ + y g4 | ap | ;
ap is the mean intracavity amplitude and k is the dissipation rate defined by coupling to the transmission line. The performance of an amplifier depends only on raa, g3, g4 and k, which can be tuned via engineering L, M, a, ra0.
The expression for G[ro] (4) may lead to a confusion that the gain-bandwidth product can be set arbitrarily large by applying a stronger pump. However, that is not so. Higher-order terms will appear in Hamiltonian (3) with the extreme increase in pump power making the further analysis invalid. Moreover, as regards experimental setup, huge pump may cause the increase in the cryostat base temperature and interfere with the experimental process.
The device under study leverages another technique to go beyond the gain-bandwidth product, impedance engineering [1]. The design uses a combination of a X/4 and a X/2 impedance transformers to introduce the frequency dependence of the environmental impedance:
Zn [<»] = R + (5)
It turns out that by tuning £ it is possible to eliminate the leading-order quadratic dependence of GTra].
Thereby the modified gain-bandwidth product can be rewritten as:
1
G [co] = 1+ Gmax 1
г x
1 + (® / г)4' 4Gmax - 1 '
(6)
As one can see, application of impedance engineering makes the trade-off between gain and bandwidth less severe.
SNR measurement can be used to estimate the JPA's added noise. When the pump is off JPA provides no amplification so the only active amplifiers in the chain are HEMTs:
SNRU
T
J- u
(7)
After turning the pump on, the signal A is amplified in JPA as well:
^HEMT^JPAA _ A _ A
SNRjpa =--_ -
JPA G G T + G T T T
HEMT JPA JPA HEMT HEMT T + HEMT chain
JPA g
GJPA
Combining (7) and (8),
T = T
JPA i HEMT
snrhemt themt
snrjpa gjpa
(8)
(9)
Eq. (9) provides an easy way to learn 7JPA in situ.
Materials and Methods
The fabrication of the device starts with the aluminum evaporation on a silicon substrate followed by etching of a patterned optical resist mask in Cl2 plasma. To minimize the amount of native oxide on silicon substrate, piranha solution and buffered HF treatment were implemented [3]. The Josephson junctions for the device were fabricated using electron lithography and the aluminum was evaporated using Dolan bridge technique [4].
Results and Discussion
The characterization is done by monitoring the transmission through the amplifier while sweeping the signal frequency and the pump power. The results are shown in Fig. 2,a. The flattest gain profile is shown in Fig. 2,b. The saturation power measurement is shown in Fig. 2,c, demonstrating the high 1-dB compression point -101.9 dBm which is on par with the best reported amplifiers [2], [1].
Fig. 2. Characterization of amplifier: amplification (color) versus signal frequency and pump
power (a), the huge bandwidth is detected in a wide range on the pump power scale; slice of the dependence in (a) at the pump power -80 dBm (b), 18 dB gain is reached in a bandwidth of 586 MHz; 1-dB compression point measurement (c) (signal frequency 7.34 GHz)
4
St. Petersburg Polytechnic University Journal. Physics and Mathematics. 2022 Vol. 15, No. 3.2
Fig. 3. Application of the amplifier. Comparison between the transmission profiles through the readout line of the 5-qubit sample with active JPA (red, pump signal on) and inactive (blue, pump signal off) (a): in 'off-state, the JPA has almost no effect on transmission. The SNR at resonator frequencies (sharp dips in transmission) in 'on'-state is increased by approximately 3 times (see Table 1). Applying the device for single-shot qubit measurements (resonator II at 7.232 GHz) (b): the |0> and |1> states are nearly indistinguishable after I-pulse (blue) and n-pulse (red) without JPA (b) providing poor separation fidelity of 30.6%. After turning on the JPA, the state histograms become well-separated with decent fidelity of 97.2% (c)
For the ease of application of the amplifier for any quantum device the optimization algorithm was developed. It takes as input the needed gain and bandwidth and seeks for the parameters (bias magnetic flux, pump frequency and power) which provide the best performance. Using it, a suitable working regime for a 5-qubit device was found. The improvement of the SNR is shown in Fig. 3,a. Due to improved SNR, the fidelity of single-shot IQ-clouds measurement [5] was also enhanced (Fig. 3 b, c).
The SNR was measured for the resonant frequencies of the resonators for dispersive readout. Results are shown in Table 1. It can be seen that a three-fold increase in SNR was achieved in the entire band. According to Eq. (9), one can estimate the additional noise of JPA knowing the
HEMT
5 K : T
JPA
0.4 K which is comparable to the quantum noise.
Improvement of SNR for resonant frequencies
Table 1
Frequency (GHz) snrjpa off snrtpa SNRJPA off/SNRTPA on
7.086 16.6 47.2 2.8
7.232 19.0 61.9 3.3
7.262 16.4 48.4 2.9
7.374 17.9 54.1 3.0
7.429 7.3 20.4 2.8
Conclusion
The performance of the Josephson Parametric Amplifier was examined. The design leveraging the techniques of SNAILs and Impedance Engineering allows for high 1-dB compression point -101.9 dBm and power gain 18 dB in a bandwidth 586 MHz. The amplifier was used for the measurement of a 5-qubit processor. It tripled the signal-to-noise ratio and increased the separation fidelity of single-shot measurements from 30.6% to 97.2%.
Acknowledgements
A.E.D. acknowledges fruitful discussions with Alexei Tolstobrov and Oleg Li. The JPA was fabricated at the cleanroom facility of MIPT. This research is supported by Russian Science Foundation under Grant 21-72-30026.
REFERENCES
1. Roy T., Kundu S., Chand M., et al., Broadband parametric amplification with impedance engineering: Beyond the gain-bandwidth product. Applied Physics Letters 107 (26) (2015): 262601.
2. Frattini N.E., Sivak V.V., Lingenfelter A., et al., Optimizing the nonlinearity and dissipation of a snail parametric amplifier for dynamic range. Physical Review Applied 10 (5) (2018): 054020.
3. Kalacheva D., Fedorov G., Kulakova A., et al., Improving the quality factor of superconducting resonators by post-process surface treatment. AIP Conference Proceedings 2241 (1). AIP Publishing LLC, 2020.
4. Dolan G. J., Offset masks for lift-off photoprocessing. Applied Physics Letters 31 (5) (1977): 337-339.
5. Walter T., Kurpiers P., Gasparinetti S., et al., Rapid high-fidelity single-shot dispersive readout of superconducting qubits. Physical Review Applied 7 (5) (2017): 054020.
THE AUTHORS
DOROGOV Aleksandr
BOLGAR Aleksey
alexgood@list.ru
ORCID: 0000-0001-7559-2336
Dorogov.AE@phystech.edu ORCID: 0000-0003-2708-6409
FEDOROV Gleb
ABRAMOV Nikolay
abramov.nn@misis.ru ORCID: 0000-0003-0461-642X
gleb.fedorov@phystech.edu ORCID: 0000-0001-9144-6179
KALACHEVA Daria
ASTAFIEV Oleg
O.Astafiev@skoltech.ru ORCID: 0000-0001-5763-589X
d.kalacheva@gmail.com ORCID: 0000-0002-6931-0686
DMITRIEV Aleksei
dmitrmipt@gmail.com ORCID: 0000-0001-9493-6739
Received 29.07.2022. Approved after reviewing 08.08.2022. Accepted 11.08.2022.
© Peter the Great St. Petersburg Polytechnic University, 2022
