Abstract Body

Recent advances in quantum technology allow the precise manipulation of quantum states. This capability can be applied to many fields of application. In particular, quantum computation, quantum sensing, and quantum cryptography are the fields under intense research. Among the various types of qubits for these applications, superconducting qubits are one of the most promising candidates as a building block for realizing large-scale quantum computers [1].

Such a superconducting quantum technology is also applied in the field of sensing. For example, microwave parametric amplifiers based on Josephson junctions achieve the noise performance bounded by quantum theory. This amplifier can be applied to any field requiring ultra-low noise microwave amplifiers, such as radio astronomy [2] or electron spin resonance (ESR) spectroscopy [3].

Superconducting qubits themselves can also be applied to sensing. Among many types of superconducting qubits, we especially focus on a superconducting flux qubit as a sensitive detector of magnetic field [4, 5] because of the strong interaction between a circulating current in the qubit and the magnetic field.

The magnetometer based on a superconducting flux qubit is shown in Fig. 1(a). The flux qubit is connected to a readout circuit, namely a superconducting quantum interference device. The transition frequency of a superconducting flux qubit can be controlled by an out-of-plane magnetic field B⊥ [Fig. 1(b)]. This is because the balance of the two eigenbases of the flux qubit, the clockwise and counterclockwise currents through the loop, is changed by the interaction with the out-of-plane magnetic field. A flux qubit is designed to have a transition frequency in the microwave range and an operating flux range of 0.1% of the magnetic flux quanta. This means that a small magnetic perturbation will change the transition frequency of the flux qubit. Thus, the flux qubit works as a transducer from the magnetic flux to the resonance frequency [Fig. 1(b)].

To use the flux qubit for the magnetometry of materials, the target sample should be placed in the vicinity of the flux qubit. To polarize electron spins in the sample, an in-plane magnetic field B|| is applied in addition to B⊥. In the absence of sample magnetization, the transition frequency of the flux qubit remains the same as in the stand-alone case. In contrast, in the presence of sample magnetization, the transition frequency of the flux qubit is shifted, depending on the intensity of the magnetization [(Fig. 2(b)].

This magnetometer can also be used as an ESR spectrometer, because the magnetization of the target sample can be controlled by microwave irradiation, namely the spin resonance phenomenon. For this purpose, microwave excitation lines are designed on the flux qubit chip [Fig. 1(a)] to flip the electron spins in the sample.

As a demonstration of the ESR spectroscopy, impurities in semiconductors are analyzed using a flux qubit magnetometer. The target sample here is a type-IB diamond crystal with high concentration of compound defects formed by a nitrogen impurity and a vacancy (NV center). Corresponding to the zero-field splitting of the NV center (2.88 GHz), we successfully observed dips in the ESR spectrum [Fig. 1(c)] [4]. From the qubit design and parameters, we can estimate the sensitivity and sensing volume of the spectrometer to be 12 spins/√Hz and of 5 fL [6].

The target sample is not limited to solid state materials as in the previous case. As an example of biological applications, rat hippocampal neurons are characterized [7]. In this case, we qualitatively extract the concentration of ferric ion in the neurons to be 8 μg/g from the magnetometry results.

In this talk, we will discuss in detail the experimental setup, the design of the qubit and the measurement system, the limitation of the sensitivity, and the applications. Future research directions will also be discussed.

References

[1] F. Arute et al., Nature, 574, 505-510 (2019)

[2] Z. Wang et al., Nature, 619, 276-281 (2023)

[3] H. Toida et al., Commun. Phys., 2, 33 (2109)

[4] R. P. Budoyo et al., Appl. Phys. Lett., 116, 194001 (2020)

[5] H. Toida et al., arXiv: 2406.14948

[6] H. Toida et al., Commun. Phys., 6, 19 (2023)

[7] K. Kakuyanagi et al., New J. Phys., 25, 013036 (2023)

Acknowledgment

This work was supported by CREST (JPMJCR1774), JST.

Figure 1. (a) Experimental setup. (b) Principle of the magnetometer. (c) Example of an ESR spectrum using a superconducting flux qubit. These figures are adaptation (some labels are modified) of the published work [3] under a Creative Commons Attribution 4.0 International License.

Keywords: Superconducting qubit, Quantum sensing, Biosensing, Electron spin resonance spectroscopy, Magnetometry, Thermometry

Abstract Body

Ferrite-based non-reciprocal cryogenic isolators are one of the critical components in the superconducting circuits that limit the realization of the large-scale system for radio astronomy and superconducting quantum computer due to their size. In a receiver frontend of a radio telescope, isolators are used between a superconductor-insulator-superconductor (SIS) mixer and cryogenic low-noise amplifier to mitigate the multiple reflection and provides the ideal condition in order for the cryogenic active components to be independently operated in the system. Performance of the microwave ferrite-based isolators reported in recent has greatly improved, showing acceptable low insertion loss over multi-octave bandwidths [1]. However, these conventional isolators are in principle physically large compared to scale of the superconducting millimeter/microwave integrated circuits. This makes it difficult to minimize physical size of the receiver frontend, and therefore, provides limitation of the number of pixels in multibeam heterodyne receivers.

To break through this limitation, we propose a novel isolator that could be fully integrated on a superconducting planar circuit. This isolator consists of two frequency converters (mixers), two phase-delay components that have phase shifts of π/4+nπ/2 (where n is an arbitrary integer), and a local oscillator (LO) source. The up-converted signals in the upper and lower sidebands at the first mixer are combined at the subsequent mixer in certain phase differences. Because each sideband is synthesized in phase for one direction and out of phase for the other direction, the circuit principally functions as an isolator with broadband from near DC to LO frequency. An isolator using commercially available microwave components successfully demonstrated more than 17 dB of isolation across 0.01–1.50 GHz at an LO frequency of 2.30 GHz [2]. Additionally, we conducted a proof-of-concept experiment using waveguide SIS mixers that have a positive gain [3]. This result showed a gain of 0–3 dB and an isolation of 20 dB across 0.1–5.0 GHz. Those results open up a new possibility of an on-chip superconducting isolator without using the ferrite material. At this conference, we will introduce the principle of the isolator, the results of the experiments using commercially available microwave components, and those of the experiments using W-band waveguide SIS mixers.

References

[1] L. Zeng, C. E. Tong, R. Blundell, P. K. Grimes and S. N. Paine, "A low-loss edge-mode isolator with improved bandwidth for cryogenic operation", IEEE Trans. Microw. Theory Techn., vol. 66, no. 5, pp. 2154-2160, May 2018.

[2] S. Masui, T. Kojima, Y. Uzawa and T. Onishi, "A Novel Microwave Nonreciprocal Isolator Based on Frequency Mixers," in IEEE Microwave and Wireless Technology Letters, vol. 33, no. 7, pp. 1051-1054, July 2023.

[3] T. Kojima, S. Masui, W. Shan and Y. Uzawa, "Characterization of a low-noise superconductor–insulator–superconductor-based microwave amplifier with local oscillator phase-adjusting architecture", Appl. Phys. Lett., vol. 122, no. 7, Feb. 2023.

Acknowledgment

This work was supported in part by JST [Moonshot R&D] Grant Number [JPMJMS2067] and JSPS KAKENHI Grant Numbers JP18H03881, JP19H02205, JP22H04955, and JP23K19203.

Keywords: Superconducting non-reciprocal device, SIS mixer, Isolator, Gyrator

Abstract Body

A traveling-wave parametric amplifier (TWPA) is utilized to increase the readout fidelity of superconducting qubits. More than 2,000 junctions are implemented in TWPAs, which adopt Josephson junctions (JJs) as a part of transmission lines, for increasing the amplification [1]. Since the size variation in fabricated JJs affects the amplification characteristics, it has been recognized as a challenge to improve the manufacturing yield of TWPA across a wafer. Our aim is to increase the manufacturing yield of TWPA where the amplification in wide frequency region is stabilized. A sample is fabricated by the superconducting multi-layer process [2], which has a precise controllability of JJ fabrication with uniformity across the wafer. Deviation of the characteristics (L, I_c, etc.) in the sample is evaluated at 4.2 K. We study co-optimization of design and fabrication in TWPA by clarifying impact of JJ size variation on amplification characteristics through both simulation and experiment.

TWPA is composed of repeated unit cells where a phase matching is adopted in every three cycles as similarly in Ref [1]. The circuit parameters are designed to increase the manufacturing yield by taking into account the alignment margin, with particular focus on the JJs and via interconnections between superconducting multi-layers. To reduce the size variation of JJs, the junction size is set to 2 um square. An oxidation condition for forming JJs is controlled so that a critical current (I_c) is 4 uA. Figure 1(a) shows the simulation results of the amplification characteristics for the input signal. The blue line shows the amplification calculated using commonly available JosephsonCircuit [3]. The orange line is the result of the simulation using JoSIM [4], which implements the circuit of TWPA. Since JoSIM performs time-domain analysis, the input, idler, and pump signals can be obtained simultaneously, which allows for verification of the phase matching (delta-k = 0). The results calculated by JoSIM are converted to frequency-domain characteristics by the fast Fourier transform. In the 3-5 GHz region and at the edge of the stop-band, quantitative agreement between the two calculations is observed. In the 5-7.5 GHz region, the average value of JoSIM corresponds to the JosephsonCircuit characteristics. Oscillations are observed in the results of JoSIM. This may be due to the difference in criteria for the convergence conditions between the two simulations; JosephsonCircuit sometimes outputs anomalous characteristics when the convergence conditions are not met in the iteration. We will investigate the cause of the oscillation by both simulation and experiment. Note that our simulation adopts the standard deviation as a parameter in order to clarify impact of fabrication variation (Dev.). The results at Dev. of 1-2% are shown in Fig. 1(b). The margin-aware design ensures that the amplification characteristics are maintained even at Dev. of 2 %. No amplification characteristics were observed at Dev. of 10 %.

To establish the TWPA process, a test chip is fabricated and the value of Dev. is experimentally investigated. (Fig. 1(c)). In the presentation, we will show the controllability of the junction variation across the wafer by experiment. The amplification characteristics of TWPA with the Dev. evaluated from experiment and the method of co-optimization will be discussed.

References

[1] C. Macklin et al., Science 350 (2015) 307.
[2] M. Hidaka et al.: “Fabrication process of superconducting flux qubits for quantum annealing,” Proceedings in 14th Superconducting SFQ VLSI Workshop and 3rd Workshop on Quantum and Classical Cryogenic Devices, Circuits and Systems (2021).
[3] https://github.com/kpobrien/JosephsonCircuits.jl
[4] J. Delport et al., IEEE Trans. Appl. Supercond., 29 (2019) 1300905.

Figure 1 (a) The simulation results of the amplification characteristics in TWPA. (b) The gain analysis at 6 GHz using JoSIM with size variation of JJs. (c) Test chip design.

Abstract Body

We report numerical and experimental evaluation of the cascade connection of flux transfer circuits using π-shift Josephson junctions (π-junctions) that can be used for enhanced couplers between spins in a quantum annealer. In recent years, quantum annealers using superconductor flux qubits [1] have been actively researched and developed. The quantum annealers are expected to solve large-scale combinatorial optimization problems in a realistic time frame, such as the traveling salesperson problem and factorization problems that would take an enormous amount of time using conventional computers. The state-of-the-art quantum annealers show significant progress in integration; for example, D-Wave’s Advantage2 prototype is planned to be equipped with over 1,200 flux qubits [2]. However, the number of spins that can be connected to each other limits the flexibility in problem mapping because of signal attenuation over long-distance wiring.

To address these issues, we proposed a flux transfer circuit using π junctions (π-FTC) that allows for more efficient flux transmission [3]. The negative inductance nature of a π-junction inserted in the superconductor loops is utilized for the current enhancement. Because the current-enhancement effect is constrained by the loop inductance not to show a hysteresis characteristic, we connect multiple stages of π-FTCs to achieve longer distance wirings. We reported the numerical analysis of the current-enhancement effect of multi-stage connections using a current source [4]. This study aims to evaluate the cascade connection of π-FTCs as a coupler toward quantum annealer application.

First, we numerically simulated two spins connected by π-FTCs, including classical, thermal noise. In this study, a SQUID containing a π-junctions serves as a spin device in a quantum annealer. Our numerical simulation showed that the cascade connection of π-FTCs could contributes to enhancing the coupling currents, resulting in strong interaction of two spins. （The one stage of π-FTC connects the both spins 5% stronger, the two has 8% and the three has 4% stronger connection than conventional FTCs. Then, we fabricated test circuits using cascade connection of π-FTCs with 1, 3 and 5 stages. The π-junctions were the magnetic Josephson junctions of the Nb/Pd89Ni11/Nb structure [5], and we formed them on a chip fabricated with the AIST Nb four-layer process. The figure shows the fabricated test circuit. Because the critical current density of the conventional Josephson junctions is relatively high (10kA/cm²) in this fabrication, the junction critical current was around 50 µA, and we conducted the measurement at 4.2 K. The detailed measurement results will be given in the presentation.

References

[1] M. W. Johnson et al., “Quantum annealing with manufactured spins,” Nature, vol. 473, no. 7346, pp. 194–198, 2011.

[2] D-Wave Quantum Inc., “D-Wave Announces 1,200+ Qubit Advantage2™ Prototype in New, Lower- Noise Fabrication Stack, Demonstrating 20x Faster Time-to-Solution on Important Class of Hard Optimization Problems,” https://www.dwavesys.com/company/newsroom/press-release/ (accessed on August 20, 2024).

[3] M. Higashi, et al., “Flux transfer circuits breaking conventional limit in transfer coefficient based on a negative inductance of a π-junction”, Supercond. Sci. Technol., vol. 37, no. 4, p. 045003, 2024.

[4] H. Hori, et al., “Circuit applications of the negative inductance of a π-junction,” to be presented at Applied Superconductor Conference, 2EPo1B-07, 2024.

[5] H. Ito, et al., “Fabrication of superconductor–ferromagnet–insulator–superconductor Josephson junctions with critical current uniformity applicable to integrated circuits,” Applied Physics Express, vol. 10, no. 3, p. 033101, 2017.

Acknowledgment

This work was supported by the JSPS KAKENHI, Grant Numbers 23H05447, 22H01548 and 23K13376. The circuits were partly fabricated at Qufab, AIST.