Flux-bias-free flux qubit driven by low-power single-flux-quantum driver on monolithically integrated circuit

Flux-bias-free flux qubit driven by low-power single-flux-quantum driver on monolithically integrated circuit | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Flux-bias-free flux qubit driven by low-power single-flux-quantum driver on monolithically integrated circuit Duong Pham, Tomoharu Ueda, Shigeyuki Miyajima, Hirotaka Terai, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9230218/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 10 You are reading this latest preprint version Abstract Controlling a large number of superconducting qubits is a key challenge for realizing a fault-tolerant quantum computer. Implementing a qubit control system operating at the proximal millikelvin stage of the dilution refrigerator is a promising approach to reduce the number of coaxial cables required for qubit control. Single-flux-quantum (SFQ) logic circuits are one candidate for realizing such cryogenic control systems; however, their power dissipation must be minimized to avoid any negative impact on qubit performance. In this study, we demonstrate the operation of a flux-bias-free (FBF) flux qubit controlled by an SFQ driver on a monolithic chip. Here, the critical current ( I C ) of the Josephson junctions in the SFQ driver was set to a few µA, which is two orders of magnitude smaller than that in a typical SFQ circuit operating at 4 K, significantly reducing power consumption. Using this low-power SFQ driver, we successfully demonstrate single-qubit operation without any reduction of the energy relaxation time of the FBF qubit. Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Superconducting quantum circuits have emerged as a leading platform in the race to develop scalable quantum computers 1 . Advances in microwave pulse techniques and fabrication processes have enabled gate and measurement fidelities of superconducting qubits to reach a criterion for fault-tolerant quantum computing 2 . However, the conventional qubit control using electric devices operating at room temperature requires a large number of coaxial cables between the room temperature environment and the sample stage at millikelvin, as well as bulky microwave components. This approach has clear scalability limitations due to the thermal load and the physical space inside the dilution refrigerator 3 . A promising approach to overcome this challenge is to employ a cryogenic control system, such as single-flux-quantum (SFQ) circuits operating in the cryogenic environment 4 – 6 . SFQ circuits are extremely low-power digital circuits that operate at clock frequencies exceeding 40 GHz, and a systematic design methodology has already been established for the foundry process based on Nb/Al/AlO x /Nb junctions 7 , 8 . By distributing the control signals to the qubits using SFQ circuits that operate at the millikelvin stage of the dilution refrigerator, the number of coaxial cables connected to the millikelvin stage can be significantly reduced. Many attempts have been made to control qubits by SFQ circuits 9 – 16 , and Al-based transmons have been successfully operated by using SFQ circuits made of Nb/Al/AlO x /Nb junctions with the critical current density ( J C ) of 1 kA/cm 2 integrated on the same chip or as a multi-chip module 6 , 17 . In these works, it was revealed that a large critical current ( I C ) of the Josephson junctions could result in the nonequilibrium quasiparticle poisoning in the qubit due to local heating from the SFQ circuit 6 . A smaller I C would be preferable not only to suppress the quasiparticle poisoning but also to allow the integration of a larger number of control circuits within the limited cooling capacity at the millikelvin stage. Furthermore, the high-bandwidth SFQ pulses can generate quasiparticles in the superconducting electrode of the qubits, which can limit the gate fidelity 6 , 17 , 18 . Therefore, SFQ circuits with lower I C would be desirable because they can yield SFQ pulses with broader temporal widths. In this paper, we demonstrate coherent qubit control using an SFQ driver with an I C of a few µA. As the superconducting qubit, we adopted a flux-bias-free (FBF) flux qubit instead of the transmon. The concept of the FBF flux qubit was proposed in refs. 19, 20, and the coherence time in the microsecond range has been demonstrated recently 21 . Using the FBF flux qubits in combination with SFQ drivers offers several advantages. First, the FBF flux qubits exhibit anharmonicity on the order of GHz, significantly larger than the few hundred MHz of transmons, making them suitable for high-speed gate control 22 , 23 . Second, conventional flux qubits and tunable transmons generally require an external flux bias for operation. In an SFQ-qubit integrated circuit, this flux bias is undesirable because it can induce flux noise into the SFQ loop. Therefore, the elimination of the external flux bias in the FBF flux qubit is beneficial for the stable operation of the SFQ driver. In this demonstration, we used epitaxial NbN/AlN/NbN junctions with a J C of 40 A/cm 2 for both the SFQ circuits and the FBF flux qubits, allowing simple monolithic integration on the same chip. Furthermore, employing niobium nitride (NbN) as the electrode material for SFQ circuits, which has a larger superconducting gap than niobium (Nb), is expected to reduce the quasiparticle excitation to the qubit. Monolithic chip with SFQ circuit and FBF flux qubit Figure 1 (a) shows the circuit diagram of the monolithic SFQ-qubit device, with the upper part for the SFQ driver and the lower part for the FBF flux qubit. Figures 1 (b), 1(c), and 1(d) show the microscope images of the fabricated chip. As shown in Fig. 1 (d), our flux qubit consists of three superconductor-insulator-superconductor (SIS) Josephson junctions made from an epitaxial NbN/AlN/NbN structure. Two of these junctions have the same critical current, I C0 ​, while the third, smaller junction ( α junction) has a critical current of αI C0 ​. The smaller SIS junction is shunted by a cross-shaped capacitor to reduce the charge noise. A half-wave (λ/2) coplanar waveguide resonator (CPWR) with a frequency of ω r /2π = 8.265 GHz is coupled to the shunt capacitor for reading the qubit state. The difference from the conventional flux qubit is the addition of a π-junction made from a NbN/PdNi/NbN structure, which acts as a half-flux-quantum bias 24 . To confirm that the superconductor-ferromagnetic-superconductor (SFS) junction works properly as a π-phase shifter on the qubit, we fabricated a superconducting quantum interference device (SQUID) that includes two SIS junctions and an SFS junction on the same wafer as the monolithic SFQ-qubit chip. We measured the magnetic field dependence of its critical currents at 15 mK and observed a π-phase shift in the modulation pattern of the SQUID, indicating the π-state of the SFS junction. The modulation pattern and the Hamiltonian of the FBF flux qubit were presented in Supplementary Fig. 3 in the Supplementary Materials of this work and ref. 21, respectively. Design of SFQ driver circuit Figure 2 (a) shows the circuit design of the SFQ driver, which consists of a DC-to-SFQ converter (comprising JJ1 and JJ2) and a Josephson transmission line (JTL) (comprising JJ3 and JJ4). The designed parameters for the SFQ circuit are listed in Table I. The shunt resistor for JJ1 is 36.3 Ω, while those for JJ2, JJ3, and JJ4 are 44.6 Ω, designed to achieve the McCumber parameters ( β c = 2π I c R 2 C /Φ 0 ) of approximately 1. In this SFQ driver, we used junctions with critical currents approximately 100 times smaller than those in conventional SFQ circuits to reduce power consumption. Consequently, the operating speed, determined by the time constant L / R ~ 1/ \(\:\sqrt{{I}_{C}}\) , is 10 times slower than that of conventional SFQ circuits. To generate a train of SFQ pulses, a microwave trigger tone ( ω d ) is applied to the input of the DC-to-SFQ converter, while the direct currents (DC1 and DC2) serve as biases for the converter and JTL. When the total currents induced by the microwave trigger and DC biases exceed the critical current of the junctions, SFQ pulses are generated and transferred to the qubit. Under the coherence driving conditions, where ω d = ω 01 / n ( n = 1, 2, 3, …), the qubit is coherently driven by the SFQ pulses. In the simulation, the maximum current induced by the trigger signal is 6 µA, and the total DC bias currents are approximately 5.7 µA. The SFQ pulses generation begins at a trigger current of 3 µA. As shown in Fig. 2 (b), the SFQ driver operates correctly at the input frequency up to 6.057 GHz 25 , 26 . The generated SFQ pulse train is transmitted to the qubit via a passive transmission line (PTL), designed with an impedance of 50 Ω to match the coplanar waveguide connected to the qubit. By using NbN with a T C of ~ 16 K as the electrode material, it is expected that the generation of quasiparticles to the qubits due to the high-bandwidth SFQ pulses can be mitigated. SFQ circuits consisting of Josephson junctions with small I C require large circuit inductances L to maintain the LI C product approximately equal to the single flux quantum Φ 0 , which increases the circuit footprint. To suppress this increase, we use polycrystalline NbTiN with the large kinetic inductance as a wiring, which allows the compact circuit design. Table I. The designed parameters for the SFQ circuit. Unit: R (Ω), L (pH), JJ (µA) R 1 R 2 R 3 R 4 L 1 L 2 L 3 L 4 L 5 L 6 L 7 JJ1 JJ2 JJ3 JJ4 50 33.8 35 5 38 408 34 20 193 60 92 2.5 1.9 1.9 1.9 The microscope image of the entire monolithic device is shown in Fig. 1 b. The upper area houses the SFQ driver, which is covered by an NbN ground plane (GP), while the lower area contains the FBF flux qubit coupled to λ/2 CPWR. The on-top ground plane not only acts as a common ground for the chip but also prevents the direct crosstalk from the trigger tone of SFQ driver to the qubit. The SiO 2 was used as an isolating layer for junctions on the devices. In the final step of the fabrication process, this SiO 2 layer was removed from the qubit part using the buffered hydrofluoric (BHF) wet etching method to reduce the two-level system (TLS) on the qubit. To ensure the wet etching did not induce any damage to the SFQ driver, an NbN wall was prepared between the SFQ part and the qubit part. The details of the fabrication flow process can be found in Supplementary Fig. 1 in the Supplementary Materials, and ref. 27. Spectroscopy measurements of FBF flux qubit To demonstrate that the π-junction works as a half-flux quantum bias on the qubit, we performed resonator spectroscopy at 15 mK. The λ /2 resonator has a fundamental frequency of ω r /2π = 8.265 GHz, a loaded quality factor of Q L = 0.83 × 10 4 , and an internal quality factor of Q int = 0.23 × 10 5 . A continuous wave (CW) microwave signal with a frequency range of 8.21–8.30 GHz was applied to the resonator at the coil currents from − 500 to 500 µA for the external magnetic flux bias. The power applied to the resonator was approximately − 140 dBm, corresponding to a single photon level. As shown in Fig. 3 (a), the resonator spectroscopy exhibits spectra with a 2π periodicity, corresponding to Φ 0 of the external flux bias. Notably, our qubit shows a minimum frequency at zero coil current, indicating that it was tuned to the flux-insensitive point without any external flux bias. This feature is different from the conventional flux qubit, which requires a half-flux quantum bias to achieve the flux-insensitive point. To verify that the π-phase shift in the qubit originates from the SFS π-junction and is not affected by trapped flux noise, we warmed the operation temperature to above T C of NbN and then re-cooled the system to de-flux it. The same spectrum was observed across different cooling cycles, indicating that the SFS π-junction robustly serves as a half-flux quantum bias for the qubit 21 , 24 . Figure 3 (b) shows the two-tone spectroscopy of the FBF flux qubit driven by SFQ circuit, measured at zero magnetic flux bias. In this measurement, microwave pulses with the frequency of ω d /2π ranging from 1–7 GHz were applied as trigger signals for the DC-to-SFQ converter. Another microwave tone at a frequency of ω r /2π was applied to the resonator to read the qubit state using the dispersive readout technique. As a result, we found that the FBF flux qubit had a qubit frequency ( ω 01 /2π) of 5.705 GHz. Notably, also at the subharmonic frequencies ( ω 01 /2π n ) with n = 2–5, the resonances were observed in the qubit spectrum, providing evidence for the coherent control of the qubit by the SFQ driver 4 , 6 . To generate the SFQ pulse train, the total currents induced by the trigger signal and DC bias must exceed the critical current of JJ2 in the DC-to-SFQ converter. In our circuit, a low junction critical current of 1.9 µA was designed to reduce power consumption, which is approximately two orders of magnitude smaller than that of a typical SFQ circuit. According to previous studies, the power consumption could be reduced by a similar factor 7 , 8 . Since the critical current is low, we expected that the SFQ pulse train could be generated even without the DC bias currents if the current induced from the trigger tone is sufficient to switch the junction. In our experiments, the driver actually worked either by applying a large-amplitude trigger pulse alone or by combining a reduced-amplitude pulse with DC bias currents. The simulation results using JSIM program confirmed that if the current induced by the trigger signal is larger than 6 µA, the output pulse train can be generated with correct frequency without the DC bias 25 , 26 . This provides the advantage of simpler control using the SFQ driver with low- I c junctions. Coherence properties of FBF flux qubit driven by SFQ driver Next, we proceeded with the time-domain characterization by using the SFQ driver. Figure 3 (c) shows the Rabi chevron pattern of the FBF flux qubit. In this experiment, the frequency of the pulse train was swept around the vicinity of the qubit transition frequency, while the number of the SFQ pulses was controlled by the duration of the trigger pulse. Consequently, the qubit was coherently driven back and forth between the ground and first excited states with an increasing number of SFQ pulses, revealing the characteristic Rabi chevron pattern. From the result, we found that the SFQ pulse train induces a π rotation at a duration of 30 ns and a frequency of 5.705 GHz. This implies that an SFQ-based π gate on the FBF flux qubit consists of 170 SFQ pulses. By applying this information to the equation: δθ = C c Φ 0 \(\:\sqrt{\left(2{\omega\:}_{01}\right)/\left(\hslash\:C\right)}\) , where δθ is the rotation angle induced by one SFQ pulse, C c is the coupling capacitance between the SFQ driver and qubit, C is total capacitance of qubit, and ω 01 is the qubit transition frequency 4 , 6 . We estimated 0.35 fF as the coupling capacitance between the SFQ driver and the qubit, which is around 65% of the designed value (0.54 fF). Consequently, we used the SFQ-based π gate to measure the energy relaxation time ( T 1 ). It is worth noting that, unlike the previous work used SFQ driver as a quasiparticle poisoning source for qubit and measured qubit coherence using the conventional microwave control scheme 6 , 28 , we directly drive the FBF flux qubit to the excited state using the SFQ-based π gate and measure its relaxation time. By comparing the coherence of FBF flux qubit driven by an SFQ-based π gate with that driven by the conventional microwave π-pulse, we can obtain intuitive information about the effect of the SFQ gate on qubit coherence. Figure 4 (a) shows the energy relaxation time ( T 1 ) of the FBF flux qubit. By fitting the relaxation data with an exponential decay function, we determined T 1 to be 1.4 µs. Notably, this value is orders of magnitude larger than that of the superconducting phase qubit with an SFS π-junction and is comparable to our previously reported T 1 for a FBF flux qubit embedded in a 3D cavity 21 , 29 . Next, we deduced that the SFQ-based π/2 gate (SFQ/2 gate) corresponds to 85 pulses and performed the Ramsey and spin-echo measurements. As shown in Fig. 3 (d), the Ramsey fringes pattern was obtained with various detuning frequencies. When the first SFQ-based π/2 pulse train frequency is detuned from the qubit transition frequency, it intentionally induces a phase accumulation on the qubit, resulting in a coherence driving between ground and excited state with increasing the delay time of the second SFQ-based π/2 pulse train. The fringes pattern is blurred around 200 ns, indicating that the energy relaxation may become dominant after a few (4–5) cycles of free evolution. To perform the spin-echo experiments, we used the technique described in ref. 6 for controlling rotations around orthogonal axes. In the SFQ control approach, the directions of state vectors on the equator of the Bloch sphere are determined by the relative timing of the SFQ pulse trains. Assuming the first pulse train rotates the qubit around the x -axis ( X SFQ ), if the second pulse train is delayed by a time τ = π/(2 ω 01 ), the qubit will be driven by a vector with a phase difference of φ = τω 01 = π/2 compared to the first pulse train. Thus, the relative timing is practically adjusted by the phase difference of the SFQ resonant trigger pulse ( ω d ). As shown in Fig. 4 (b), we found T 2E to be 2.3 µs, which is significantly longer than T 1 . This indicates that some of the loss is effectively recovered by the echo SFQ pulse train ( Y SFQ ). In a previous study using conventional microwave control methods, T 1 ​ of the capacitively-shunted FBF flux qubit with a π-junction was reduced to 1.4 µs, while that of the qubit without the π-junction was 16 µs 21,22 . Quantitative analysis indicated that the primary source of the decoherence in the FBF flux qubit might be the energy loss due to the quasiparticle in the metallic π-junction. In the present experiment, it is noted that T 1 of the FBF flux qubit driven by SFQ pulse trains on a monolithic chip was similar to that of the FBF flux qubit controlled by conventional microwave pulses. This suggests that the qubit's coherence on the monolithic chip is limited by quasiparticles generated in the metallic π-junction rather than those induced by the SFQ driver. Based on our advanced π-junction technology in this work, several approaches can be proposed to improve the qubit coherence in future work. One method is to use the π-junctions made from an isolating ferromagnetic, such as GdN 30 . Another approach involves incorporating an insulating layer to form a superconductor/insulator/ferromagnet/superconductor (SIFS) structure, which is expected to significantly improve coherence in the underdamped regime 31 , 32 . Methods The monolithic devices were fabricated on a 2-inch high-resistivity Si wafer with a 50 nm thick TiN buffer layer. The epitaxial TiN buffer layer provides excellent lattice matching for the growth of the epitaxial NbN-based junction on Si substrate 21 , 22 . Two types of junctions were utilized in the fabrication of the monolithic chip. The fully epitaxy NbN/AlN/NbN junctions with a critical current density of ~ 40 A/cm 2 were simultaneously used as SIS junctions for both qubit and SFQ drivers. These SIS junctions were fabricated using a standard lithography process. The other type of junction is a ferromagnetic NbN/PdNi/NbN (SFS) junction, which was fabricated on the same wafer using lift-off method and serves as the π-phase shifter for the flux qubit. The thickness of AlN insulating layer is 1.8 nm for achieving the critical current of ~ 40 A/cm 2 , while the PdNi ferromagnetic layer was set at 15 nm for obtaining of π-phase shift 24 . The critical current of π-junction is about 5 mA at 4.2 K. The fabrication process was shown in Supplementary Fig. 1 in the Supplementary Materials. The monolithic device was characterized at a base temperature of 15 mK in a dilution refrigerator. Resonator spectroscopy was performed using a vector network analyzer. For time domain measurements, the microwave trigger pulse for the SFQ circuit was generated via an IQ mixer using an arbitrary waveform generator and a microwave signal generator. Another IQ mixer setup was used to create the readout pulse, which was applied to the λ/2 CPWR for dispersive readout. The reflection signal from the CPWR, containing qubit information, was amplified twice: first by a high-electron-mobility transistor (HEMT) amplifier at 4 K and then by a low-noise amplifier at room temperature, before being processed by the analog-to-digital converter. Details of the measurement setup and wiring diagram are provided in Supplementary Fig. 2 in the Supplementary Materials. Conclusion In summary, we have demonstrated coherent control of a flux-bias-free (FBF) flux qubit using a low-power SFQ driver monolithically integrated on the same chip. The combination of a low-power SFQ driver and the FBF flux qubit provides several advantages for integration: the high anharmonicity of the FBF flux qubit is suitable for fast SFQ-based gate control, and the elimination of the external flux bias removes a potential source of magnetic noise in the integrated SFQ circuit. By using epitaxial NbN/AlN/NbN junctions with a critical current of only a few µA, we significantly reduced the energy dissipation of the SFQ driver. The low- I C design also creates SFQ pulses with broader temporal widths, reducing the quasiparticle poisoning to the qubit. As a result, we found that the coherence of the FBF flux qubit in the monolithic device was limited not by the SFQ driver but by quasiparticles generated from the metallic SFS π-junction. To further improve the qubit coherence in the monolithic SFQ-qubit chip, we proposed the use of an insulating ferromagnet π-junctions or an SIFS structure for future work. Declarations Data availability The data that support the findings of this study are available from the corresponding author upon reasonable request. Ethics approval Not applicable. Funding This work was partly supported by JSPS KAKENHI (JP19H05615 and JP18H05211). Acknowledgements DP and TY acknowledge Center for Heterogeneous Quantum/Material Fusion Technologies, Center for Key Interdisciplinary Research, Tohoku University. Author contributions D.P. wrote the manuscript, designed the qubit, fabricated the π-junctions, performed the main device measurements, and analyzed the data. T.U., M.T., and A.F. designed and simulated the SFQ circuits and measured the modulation patterns. S.M. and H.T. designed and fabricated the SFQ driver and the SIS junctions for the qubits. K.I. co-designed the qubit and provided consultation on the measurement setup. T.Y. conceived and supervised the project. Competing interests The authors declare no competing interests. Additional information Correspondence and requests for materials should be addressed to Duong Pham, Hirotaka Terai, or Taro Yamashita. References Arute F, et al. Quantum supremacy using a programmable superconducting processor. Nature. 2019;574:505–10. Kjaergaard M, et al. Superconducting qubits: current state of play. Annu Rev Condens Matter Phys. 2020;11:369–95. Gambetta JM, Chow JM, Steffen M. Building logical qubits in a superconducting quantum computing system. npj Quantum Inf. 2017;3:2. McDermott R, Vavilov MG. Accurate qubit control with single flux quantum pulses. Phys Rev Appl. 2014;2:014007. McDermott R, et al. Quantum–classical interface based on single flux quantum digital logic. Quantum Sci Technol. 2018;3:024004. Leonard E, et al. Digital coherent control of a superconducting qubit. 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Supplementary Files SupplementaryMaterials.docx Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 12 May, 2026 Reviews received at journal 11 May, 2026 Reviewers agreed at journal 06 May, 2026 Reviews received at journal 13 Apr, 2026 Reviewers agreed at journal 10 Apr, 2026 Reviewers agreed at journal 01 Apr, 2026 Reviewers invited by journal 30 Mar, 2026 Editor assigned by journal 26 Mar, 2026 Submission checks completed at journal 26 Mar, 2026 First submitted to journal 26 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9230218","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":614403763,"identity":"b8b8bda3-d009-4a5b-a504-ae8e6ae7e6cb","order_by":0,"name":"Duong Pham","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4UlEQVRIiWNgGAWjYDCCAzCSvQHKZmBIIFILzwEgmUCSFokEworBgO9G8rGHX3fckded+fbggZ8/GOz6GRiePcCnRfJGWrqx7Jlnhttu5yUc7ElgSJ7ZwJBugE+LwY0cM2nJtsOM227nGBwGOizZ4ABDmgQxWuy33TxDghbJj22HE7fd4AFrsSOoRfLMszRpxjOHk7edyTE42JMmkSDZTMAvfMeTj0n+3HHYdtvxM8YfftjY2POz96Q9wKcFBJh5G+BsicQGZp40QjoYGH8itDDYA5POMYJaRsEoGAWjYEQBAGBrVNucflKUAAAAAElFTkSuQmCC","orcid":"","institution":"Tohoku University","correspondingAuthor":true,"prefix":"","firstName":"Duong","middleName":"","lastName":"Pham","suffix":""},{"id":614403764,"identity":"5cefe19f-904d-4954-abfc-512ea913ba22","order_by":1,"name":"Tomoharu Ueda","email":"","orcid":"","institution":"Nagoya University","correspondingAuthor":false,"prefix":"","firstName":"Tomoharu","middleName":"","lastName":"Ueda","suffix":""},{"id":614403765,"identity":"2579fab4-73e9-4cda-8847-2243ba1cd710","order_by":2,"name":"Shigeyuki Miyajima","email":"","orcid":"","institution":"National Institute of Information and Communications Technology (NICT)","correspondingAuthor":false,"prefix":"","firstName":"Shigeyuki","middleName":"","lastName":"Miyajima","suffix":""},{"id":614403766,"identity":"c15e1357-346e-4c2d-8293-be3ae79ad4ba","order_by":3,"name":"Hirotaka Terai","email":"","orcid":"","institution":"National Institute of Information and Communications Technology (NICT)","correspondingAuthor":false,"prefix":"","firstName":"Hirotaka","middleName":"","lastName":"Terai","suffix":""},{"id":614403767,"identity":"8714b7f6-43ff-43c9-b692-c527131d9f63","order_by":4,"name":"Kunihiro Inomata","email":"","orcid":"","institution":"National Institute of Advanced Industrial Science and Technology (AIST)","correspondingAuthor":false,"prefix":"","firstName":"Kunihiro","middleName":"","lastName":"Inomata","suffix":""},{"id":614403768,"identity":"3cb1350e-701b-46a4-ad71-9d05ddab0ac2","order_by":5,"name":"Masamitsu Tanaka","email":"","orcid":"","institution":"Nagoya University","correspondingAuthor":false,"prefix":"","firstName":"Masamitsu","middleName":"","lastName":"Tanaka","suffix":""},{"id":614403769,"identity":"9665c29a-1091-4cbc-b676-741e51c75c16","order_by":6,"name":"Akira Fujimaki","email":"","orcid":"","institution":"Nagoya University","correspondingAuthor":false,"prefix":"","firstName":"Akira","middleName":"","lastName":"Fujimaki","suffix":""},{"id":614403770,"identity":"fdf57787-30fa-4b27-9282-e905373b2f77","order_by":7,"name":"Taro Yamashita","email":"","orcid":"","institution":"Tohoku University","correspondingAuthor":false,"prefix":"","firstName":"Taro","middleName":"","lastName":"Yamashita","suffix":""}],"badges":[],"createdAt":"2026-03-26 06:53:43","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9230218/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9230218/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105840494,"identity":"ad74396c-9319-41b2-b3bd-dd2187f25c8c","added_by":"auto","created_at":"2026-03-31 16:25:29","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":789227,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCircuit diagram and device.\u003c/strong\u003e \u003cstrong\u003e(a)\u003c/strong\u003e The circuit diagram of the monolithic quantum-classical device. \u003cstrong\u003e(b)\u003c/strong\u003e Microscope image of the fabricated monolithic chip. The black dashed line represents the coupling strip line from SFQ circuit to the qubit. \u003cstrong\u003e(c)\u003c/strong\u003e Microscope image of FBF flux qubit with a shunt capacitor. \u003cstrong\u003e(d)\u003c/strong\u003e Microscope image of the qubit’s loop with a π-junction.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-9230218/v1/03c4759aff07c8611d981e5f.png"},{"id":105840495,"identity":"f5bb9a7c-7eb3-460e-8094-58f6becbcfc7","added_by":"auto","created_at":"2026-03-31 16:25:29","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":126539,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSFQ Driver\u003c/strong\u003e. \u003cstrong\u003e(a)\u003c/strong\u003e Circuit diagram of the SFQ driver. \u003cstrong\u003e(b)\u003c/strong\u003e Simulation results for the circuit at an input frequency of \u003cem\u003eω\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e/2π = 6.057 GHz.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-9230218/v1/26e494ba3181d8a3c615a675.png"},{"id":105840515,"identity":"e81ad9a5-83ce-46e0-b5ba-822ff6593d9a","added_by":"auto","created_at":"2026-03-31 16:25:38","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":554000,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSpectroscopy measurement\u003c/strong\u003e. \u003cstrong\u003e(a)\u003c/strong\u003eThe resonator spectroscopy shows the flux dependence periods of the FBF flux qubit. \u003cstrong\u003e(b)\u003c/strong\u003e Two-tone spectroscopy of FBF flux qubit driven by SFQ driver at zero magnetic bias. \u003cstrong\u003e(c)\u003c/strong\u003e The Rabi chevron pattern and \u003cstrong\u003e(d)\u003c/strong\u003e the Ramsey fringe pattern of FBF flux qubit driven by SFQ driver.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-9230218/v1/64af505b18c4a10e0a42f29f.png"},{"id":105840504,"identity":"6ebd7c09-b531-4f3f-9e84-c8f172228f28","added_by":"auto","created_at":"2026-03-31 16:25:33","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":116314,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCoherence of flux-bias-free flux qubit driven by SFQ circuit\u003c/strong\u003e. \u003cstrong\u003e(a)\u003c/strong\u003e Energy relaxation time \u003cem\u003eT\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e­. \u003cstrong\u003e(b)\u003c/strong\u003e Spin-echo coherence time \u003cem\u003eT\u003c/em\u003e\u003csub\u003e2E\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-9230218/v1/8921e3db4e72b29788a9afcf.png"},{"id":105840554,"identity":"093e9056-c2ad-4e0f-a79f-0386bd51ff79","added_by":"auto","created_at":"2026-03-31 16:25:47","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2184148,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9230218/v1/76988ec6-a13c-4f50-9af8-833bb7ebfd20.pdf"},{"id":105840517,"identity":"845efd90-66f1-4cac-a3f1-9e32a1eaf20b","added_by":"auto","created_at":"2026-03-31 16:25:38","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":496415,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryMaterials.docx","url":"https://assets-eu.researchsquare.com/files/rs-9230218/v1/286fffba5cdcf49a73075730.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Flux-bias-free flux qubit driven by low-power single-flux-quantum driver on monolithically integrated circuit","fulltext":[{"header":"Introduction","content":"\u003cp\u003eSuperconducting quantum circuits have emerged as a leading platform in the race to develop scalable quantum computers\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Advances in microwave pulse techniques and fabrication processes have enabled gate and measurement fidelities of superconducting qubits to reach a criterion for fault-tolerant quantum computing\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. However, the conventional qubit control using electric devices operating at room temperature requires a large number of coaxial cables between the room temperature environment and the sample stage at millikelvin, as well as bulky microwave components. This approach has clear scalability limitations due to the thermal load and the physical space inside the dilution refrigerator\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. A promising approach to overcome this challenge is to employ a cryogenic control system, such as single-flux-quantum (SFQ) circuits operating in the cryogenic environment\u003csup\u003e\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. SFQ circuits are extremely low-power digital circuits that operate at clock frequencies exceeding 40 GHz, and a systematic design methodology has already been established for the foundry process based on Nb/Al/AlO\u003csub\u003ex\u003c/sub\u003e/Nb junctions\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. By distributing the control signals to the qubits using SFQ circuits that operate at the millikelvin stage of the dilution refrigerator, the number of coaxial cables connected to the millikelvin stage can be significantly reduced.\u003c/p\u003e \u003cp\u003eMany attempts have been made to control qubits by SFQ circuits\u003csup\u003e\u003cspan additionalcitationids=\"CR10 CR11 CR12 CR13 CR14 CR15\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, and Al-based transmons have been successfully operated by using SFQ circuits made of Nb/Al/AlO\u003csub\u003ex\u003c/sub\u003e/Nb junctions with the critical current density (\u003cem\u003eJ\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e) of 1 kA/cm\u003csup\u003e2\u003c/sup\u003e integrated on the same chip or as a multi-chip module\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. In these works, it was revealed that a large critical current (\u003cem\u003eI\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e) of the Josephson junctions could result in the nonequilibrium quasiparticle poisoning in the qubit due to local heating from the SFQ circuit\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. A smaller \u003cem\u003eI\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e would be preferable not only to suppress the quasiparticle poisoning but also to allow the integration of a larger number of control circuits within the limited cooling capacity at the millikelvin stage. Furthermore, the high-bandwidth SFQ pulses can generate quasiparticles in the superconducting electrode of the qubits, which can limit the gate fidelity\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Therefore, SFQ circuits with lower \u003cem\u003eI\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e would be desirable because they can yield SFQ pulses with broader temporal widths.\u003c/p\u003e \u003cp\u003eIn this paper, we demonstrate coherent qubit control using an SFQ driver with an \u003cem\u003eI\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e of a few \u0026micro;A. As the superconducting qubit, we adopted a flux-bias-free (FBF) flux qubit instead of the transmon. The concept of the FBF flux qubit was proposed in refs. 19, 20, and the coherence time in the microsecond range has been demonstrated recently\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Using the FBF flux qubits in combination with SFQ drivers offers several advantages. First, the FBF flux qubits exhibit anharmonicity on the order of GHz, significantly larger than the few hundred MHz of transmons, making them suitable for high-speed gate control\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Second, conventional flux qubits and tunable transmons generally require an external flux bias for operation. In an SFQ-qubit integrated circuit, this flux bias is undesirable because it can induce flux noise into the SFQ loop. Therefore, the elimination of the external flux bias in the FBF flux qubit is beneficial for the stable operation of the SFQ driver. In this demonstration, we used epitaxial NbN/AlN/NbN junctions with a \u003cem\u003eJ\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e of 40 A/cm\u003csup\u003e2\u003c/sup\u003e for both the SFQ circuits and the FBF flux qubits, allowing simple monolithic integration on the same chip. Furthermore, employing niobium nitride (NbN) as the electrode material for SFQ circuits, which has a larger superconducting gap than niobium (Nb), is expected to reduce the quasiparticle excitation to the qubit.\u003c/p\u003e\n\u003ch3\u003eMonolithic chip with SFQ circuit and FBF flux qubit\u003c/h3\u003e\n\u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a) shows the circuit diagram of the monolithic SFQ-qubit device, with the upper part for the SFQ driver and the lower part for the FBF flux qubit. Figures\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b), 1(c), and 1(d) show the microscope images of the fabricated chip. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(d), our flux qubit consists of three superconductor-insulator-superconductor (SIS) Josephson junctions made from an epitaxial NbN/AlN/NbN structure. Two of these junctions have the same critical current, \u003cem\u003eI\u003c/em\u003e\u003csub\u003eC0\u003c/sub\u003e​, while the third, smaller junction (\u003cem\u003eα\u003c/em\u003e junction) has a critical current of \u003cem\u003eαI\u003c/em\u003e\u003csub\u003eC0\u003c/sub\u003e​. The smaller SIS junction is shunted by a cross-shaped capacitor to reduce the charge noise. A half-wave (λ/2) coplanar waveguide resonator (CPWR) with a frequency of \u003cem\u003eω\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e/2π\u0026thinsp;=\u0026thinsp;8.265 GHz is coupled to the shunt capacitor for reading the qubit state.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe difference from the conventional flux qubit is the addition of a π-junction made from a NbN/PdNi/NbN structure, which acts as a half-flux-quantum bias\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. To confirm that the superconductor-ferromagnetic-superconductor (SFS) junction works properly as a π-phase shifter on the qubit, we fabricated a superconducting quantum interference device (SQUID) that includes two SIS junctions and an SFS junction on the same wafer as the monolithic SFQ-qubit chip. We measured the magnetic field dependence of its critical currents at 15 mK and observed a π-phase shift in the modulation pattern of the SQUID, indicating the π-state of the SFS junction. The modulation pattern and the Hamiltonian of the FBF flux qubit were presented in Supplementary Fig.\u0026nbsp;3 in the Supplementary Materials of this work and ref. 21, respectively.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eDesign of SFQ driver circuit\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a) shows the circuit design of the SFQ driver, which consists of a DC-to-SFQ converter (comprising JJ1 and JJ2) and a Josephson transmission line (JTL) (comprising JJ3 and JJ4). The designed parameters for the SFQ circuit are listed in Table I. The shunt resistor for JJ1 is 36.3 Ω, while those for JJ2, JJ3, and JJ4 are 44.6 Ω, designed to achieve the McCumber parameters (\u003cem\u003eβ\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2π\u003cem\u003eI\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003cem\u003eC\u003c/em\u003e/Φ\u003csub\u003e0\u003c/sub\u003e) of approximately 1. In this SFQ driver, we used junctions with critical currents approximately 100 times smaller than those in conventional SFQ circuits to reduce power consumption. Consequently, the operating speed, determined by the time constant \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eR\u003c/em\u003e\u0026thinsp;~\u0026thinsp;1/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{{I}_{C}}\\)\u003c/span\u003e\u003c/span\u003e, is 10 times slower than that of conventional SFQ circuits. To generate a train of SFQ pulses, a microwave trigger tone (\u003cem\u003eω\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e) is applied to the input of the DC-to-SFQ converter, while the direct currents (DC1 and DC2) serve as biases for the converter and JTL. When the total currents induced by the microwave trigger and DC biases exceed the critical current of the junctions, SFQ pulses are generated and transferred to the qubit. Under the coherence driving conditions, where \u003cem\u003eω\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eω\u003c/em\u003e\u003csub\u003e01\u003c/sub\u003e/\u003cem\u003en\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1, 2, 3, \u0026hellip;), the qubit is coherently driven by the SFQ pulses. In the simulation, the maximum current induced by the trigger signal is 6 \u0026micro;A, and the total DC bias currents are approximately 5.7 \u0026micro;A. The SFQ pulses generation begins at a trigger current of 3 \u0026micro;A. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b), the SFQ driver operates correctly at the input frequency up to 6.057 GHz\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. The generated SFQ pulse train is transmitted to the qubit via a passive transmission line (PTL), designed with an impedance of 50 Ω to match the coplanar waveguide connected to the qubit. By using NbN with a \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e of ~\u0026thinsp;16 K as the electrode material, it is expected that the generation of quasiparticles to the qubits due to the high-bandwidth SFQ pulses can be mitigated. SFQ circuits consisting of Josephson junctions with small \u003cem\u003eI\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e require large circuit inductances \u003cem\u003eL\u003c/em\u003e to maintain the \u003cem\u003eLI\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e product approximately equal to the single flux quantum Φ\u003csub\u003e0\u003c/sub\u003e, which increases the circuit footprint. To suppress this increase, we use polycrystalline NbTiN with the large kinetic inductance as a wiring, which allows the compact circuit design.\u003c/p\u003e \u003cp\u003eTable I. The designed parameters for the SFQ circuit. Unit: \u003cem\u003eR\u003c/em\u003e (Ω), \u003cem\u003eL\u003c/em\u003e (pH), JJ (\u0026micro;A)\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"15\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e5\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e7\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eJJ1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eJJ2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c14\"\u003e \u003cp\u003eJJ3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c15\"\u003e \u003cp\u003eJJ4\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e33.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e408\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e193\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e1.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe microscope image of the entire monolithic device is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb. The upper area houses the SFQ driver, which is covered by an NbN ground plane (GP), while the lower area contains the FBF flux qubit coupled to λ/2 CPWR. The on-top ground plane not only acts as a common ground for the chip but also prevents the direct crosstalk from the trigger tone of SFQ driver to the qubit. The SiO\u003csub\u003e2\u003c/sub\u003e was used as an isolating layer for junctions on the devices. In the final step of the fabrication process, this SiO\u003csub\u003e2\u003c/sub\u003e layer was removed from the qubit part using the buffered hydrofluoric (BHF) wet etching method to reduce the two-level system (TLS) on the qubit. To ensure the wet etching did not induce any damage to the SFQ driver, an NbN wall was prepared between the SFQ part and the qubit part. The details of the fabrication flow process can be found in Supplementary Fig.\u0026nbsp;1 in the Supplementary Materials, and ref. 27.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eSpectroscopy measurements of FBF flux qubit\u003c/h3\u003e\n\u003cp\u003eTo demonstrate that the π-junction works as a half-flux quantum bias on the qubit, we performed resonator spectroscopy at 15 mK. The \u003cem\u003eλ\u003c/em\u003e/2 resonator has a fundamental frequency of \u003cem\u003eω\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e/2π\u0026thinsp;=\u0026thinsp;8.265 GHz, a loaded quality factor of \u003cem\u003eQ\u003c/em\u003e\u003csub\u003eL\u003c/sub\u003e = 0.83 \u0026times; 10\u003csup\u003e4\u003c/sup\u003e, and an internal quality factor of \u003cem\u003eQ\u003c/em\u003e\u003csub\u003eint\u003c/sub\u003e = 0.23 \u0026times; 10\u003csup\u003e5\u003c/sup\u003e. A continuous wave (CW) microwave signal with a frequency range of 8.21\u0026ndash;8.30 GHz was applied to the resonator at the coil currents from \u0026minus;\u0026thinsp;500 to 500 \u0026micro;A for the external magnetic flux bias. The power applied to the resonator was approximately\u0026thinsp;\u0026minus;\u0026thinsp;140 dBm, corresponding to a single photon level. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a), the resonator spectroscopy exhibits spectra with a 2π periodicity, corresponding to Φ\u003csub\u003e0\u003c/sub\u003e of the external flux bias. Notably, our qubit shows a minimum frequency at zero coil current, indicating that it was tuned to the flux-insensitive point without any external flux bias. This feature is different from the conventional flux qubit, which requires a half-flux quantum bias to achieve the flux-insensitive point. To verify that the π-phase shift in the qubit originates from the SFS π-junction and is not affected by trapped flux noise, we warmed the operation temperature to above \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e of NbN and then re-cooled the system to de-flux it. The same spectrum was observed across different cooling cycles, indicating that the SFS π-junction robustly serves as a half-flux quantum bias for the qubit\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b) shows the two-tone spectroscopy of the FBF flux qubit driven by SFQ circuit, measured at zero magnetic flux bias. In this measurement, microwave pulses with the frequency of \u003cem\u003eω\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e/2π ranging from 1\u0026ndash;7 GHz were applied as trigger signals for the DC-to-SFQ converter. Another microwave tone at a frequency of \u003cem\u003eω\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e/2π was applied to the resonator to read the qubit state using the dispersive readout technique. As a result, we found that the FBF flux qubit had a qubit frequency (\u003cem\u003eω\u003c/em\u003e\u003csub\u003e01\u003c/sub\u003e/2π) of 5.705 GHz. Notably, also at the subharmonic frequencies (\u003cem\u003eω\u003c/em\u003e\u003csub\u003e01\u003c/sub\u003e/2π\u003cem\u003en\u003c/em\u003e) with \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2\u0026ndash;5, the resonances were observed in the qubit spectrum, providing evidence for the coherent control of the qubit by the SFQ driver\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eTo generate the SFQ pulse train, the total currents induced by the trigger signal and DC bias must exceed the critical current of JJ2 in the DC-to-SFQ converter. In our circuit, a low junction critical current of 1.9 \u0026micro;A was designed to reduce power consumption, which is approximately two orders of magnitude smaller than that of a typical SFQ circuit. According to previous studies, the power consumption could be reduced by a similar factor\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. Since the critical current is low, we expected that the SFQ pulse train could be generated even without the DC bias currents if the current induced from the trigger tone is sufficient to switch the junction. In our experiments, the driver actually worked either by applying a large-amplitude trigger pulse alone or by combining a reduced-amplitude pulse with DC bias currents. The simulation results using JSIM program confirmed that if the current induced by the trigger signal is larger than 6 \u0026micro;A, the output pulse train can be generated with correct frequency without the DC bias\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. This provides the advantage of simpler control using the SFQ driver with low-\u003cem\u003eI\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e junctions.\u003c/p\u003e\n\u003ch3\u003eCoherence properties of FBF flux qubit driven by SFQ driver\u003c/h3\u003e\n\u003cp\u003eNext, we proceeded with the time-domain characterization by using the SFQ driver. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(c) shows the Rabi chevron pattern of the FBF flux qubit. In this experiment, the frequency of the pulse train was swept around the vicinity of the qubit transition frequency, while the number of the SFQ pulses was controlled by the duration of the trigger pulse. Consequently, the qubit was coherently driven back and forth between the ground and first excited states with an increasing number of SFQ pulses, revealing the characteristic Rabi chevron pattern. From the result, we found that the SFQ pulse train induces a π rotation at a duration of 30 ns and a frequency of 5.705 GHz. This implies that an SFQ-based π gate on the FBF flux qubit consists of 170 SFQ pulses. By applying this information to the equation: \u003cem\u003eδθ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eC\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e Φ\u003csub\u003e0\u003c/sub\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{\\left(2{\\omega\\:}_{01}\\right)/\\left(\\hslash\\:C\\right)}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cem\u003eδθ\u003c/em\u003e is the rotation angle induced by one SFQ pulse, \u003cem\u003eC\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e is the coupling capacitance between the SFQ driver and qubit, \u003cem\u003eC\u003c/em\u003e is total capacitance of qubit, and \u003cem\u003eω\u003c/em\u003e\u003csub\u003e01\u003c/sub\u003e is the qubit transition frequency\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. We estimated 0.35 fF as the coupling capacitance between the SFQ driver and the qubit, which is around 65% of the designed value (0.54 fF).\u003c/p\u003e \u003cp\u003eConsequently, we used the SFQ-based π gate to measure the energy relaxation time (\u003cem\u003eT\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e). It is worth noting that, unlike the previous work used SFQ driver as a quasiparticle poisoning source for qubit and measured qubit coherence using the conventional microwave control scheme\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e, we directly drive the FBF flux qubit to the excited state using the SFQ-based π gate and measure its relaxation time. By comparing the coherence of FBF flux qubit driven by an SFQ-based π gate with that driven by the conventional microwave π-pulse, we can obtain intuitive information about the effect of the SFQ gate on qubit coherence. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a) shows the energy relaxation time (\u003cem\u003eT\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e) of the FBF flux qubit. By fitting the relaxation data with an exponential decay function, we determined \u003cem\u003eT\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e to be 1.4 \u0026micro;s. Notably, this value is orders of magnitude larger than that of the superconducting phase qubit with an SFS π-junction and is comparable to our previously reported \u003cem\u003eT\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e for a FBF flux qubit embedded in a 3D cavity\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eNext, we deduced that the SFQ-based π/2 gate (SFQ/2 gate) corresponds to 85 pulses and performed the Ramsey and spin-echo measurements. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(d), the Ramsey fringes pattern was obtained with various detuning frequencies. When the first SFQ-based π/2 pulse train frequency is detuned from the qubit transition frequency, it intentionally induces a phase accumulation on the qubit, resulting in a coherence driving between ground and excited state with increasing the delay time of the second SFQ-based π/2 pulse train. The fringes pattern is blurred around 200 ns, indicating that the energy relaxation may become dominant after a few (4\u0026ndash;5) cycles of free evolution. To perform the spin-echo experiments, we used the technique described in ref. 6 for controlling rotations around orthogonal axes. In the SFQ control approach, the directions of state vectors on the equator of the Bloch sphere are determined by the relative timing of the SFQ pulse trains. Assuming the first pulse train rotates the qubit around the \u003cem\u003ex\u003c/em\u003e-axis (\u003cem\u003eX\u003c/em\u003e\u003csub\u003eSFQ\u003c/sub\u003e), if the second pulse train is delayed by a time \u003cem\u003eτ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;π/(2\u003cem\u003eω\u003c/em\u003e\u003csub\u003e01\u003c/sub\u003e), the qubit will be driven by a vector with a phase difference of \u003cem\u003eφ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eτω\u003c/em\u003e\u003csub\u003e01\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;π/2 compared to the first pulse train. Thus, the relative timing is practically adjusted by the phase difference of the SFQ resonant trigger pulse (\u003cem\u003eω\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e). As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b), we found \u003cem\u003eT\u003c/em\u003e\u003csub\u003e2E\u003c/sub\u003e to be 2.3 \u0026micro;s, which is significantly longer than \u003cem\u003eT\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e. This indicates that some of the loss is effectively recovered by the echo SFQ pulse train (\u003cem\u003eY\u003c/em\u003e\u003csub\u003eSFQ\u003c/sub\u003e).\u003c/p\u003e \u003cp\u003eIn a previous study using conventional microwave control methods, \u003cem\u003eT\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e​ of the capacitively-shunted FBF flux qubit with a π-junction was reduced to 1.4 \u0026micro;s, while that of the qubit without the π-junction was 16 \u0026micro;s\u003csup\u003e21,22\u003c/sup\u003e. Quantitative analysis indicated that the primary source of the decoherence in the FBF flux qubit might be the energy loss due to the quasiparticle in the metallic π-junction. In the present experiment, it is noted that \u003cem\u003eT\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e of the FBF flux qubit driven by SFQ pulse trains on a monolithic chip was similar to that of the FBF flux qubit controlled by conventional microwave pulses. This suggests that the qubit's coherence on the monolithic chip is limited by quasiparticles generated in the metallic π-junction rather than those induced by the SFQ driver.\u003c/p\u003e \u003cp\u003eBased on our advanced π-junction technology in this work, several approaches can be proposed to improve the qubit coherence in future work. One method is to use the π-junctions made from an isolating ferromagnetic, such as GdN\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. Another approach involves incorporating an insulating layer to form a superconductor/insulator/ferromagnet/superconductor (SIFS) structure, which is expected to significantly improve coherence in the underdamped regime\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e,\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eThe monolithic devices were fabricated on a 2-inch high-resistivity Si wafer with a 50 nm thick TiN buffer layer. The epitaxial TiN buffer layer provides excellent lattice matching for the growth of the epitaxial NbN-based junction on Si substrate\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. Two types of junctions were utilized in the fabrication of the monolithic chip. The fully epitaxy NbN/AlN/NbN junctions with a critical current density of ~\u0026thinsp;40 A/cm\u003csup\u003e2\u003c/sup\u003e were simultaneously used as SIS junctions for both qubit and SFQ drivers. These SIS junctions were fabricated using a standard lithography process. The other type of junction is a ferromagnetic NbN/PdNi/NbN (SFS) junction, which was fabricated on the same wafer using lift-off method and serves as the π-phase shifter for the flux qubit. The thickness of AlN insulating layer is 1.8 nm for achieving the critical current of ~\u0026thinsp;40 A/cm\u003csup\u003e2\u003c/sup\u003e, while the PdNi ferromagnetic layer was set at 15 nm for obtaining of π-phase shift\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. The critical current of π-junction is about 5 mA at 4.2 K. The fabrication process was shown in Supplementary Fig.\u0026nbsp;1 in the Supplementary Materials.\u003c/p\u003e \u003cp\u003eThe monolithic device was characterized at a base temperature of 15 mK in a dilution refrigerator. Resonator spectroscopy was performed using a vector network analyzer. For time domain measurements, the microwave trigger pulse for the SFQ circuit was generated via an IQ mixer using an arbitrary waveform generator and a microwave signal generator. Another IQ mixer setup was used to create the readout pulse, which was applied to the λ/2 CPWR for dispersive readout. The reflection signal from the CPWR, containing qubit information, was amplified twice: first by a high-electron-mobility transistor (HEMT) amplifier at 4 K and then by a low-noise amplifier at room temperature, before being processed by the analog-to-digital converter. Details of the measurement setup and wiring diagram are provided in Supplementary Fig.\u0026nbsp;2 in the Supplementary Materials.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn summary, we have demonstrated coherent control of a flux-bias-free (FBF) flux qubit using a low-power SFQ driver monolithically integrated on the same chip. The combination of a low-power SFQ driver and the FBF flux qubit provides several advantages for integration: the high anharmonicity of the FBF flux qubit is suitable for fast SFQ-based gate control, and the elimination of the external flux bias removes a potential source of magnetic noise in the integrated SFQ circuit.\u003c/p\u003e \u003cp\u003eBy using epitaxial NbN/AlN/NbN junctions with a critical current of only a few \u0026micro;A, we significantly reduced the energy dissipation of the SFQ driver. The low-\u003cem\u003eI\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e design also creates SFQ pulses with broader temporal widths, reducing the quasiparticle poisoning to the qubit. As a result, we found that the coherence of the FBF flux qubit in the monolithic device was limited not by the SFQ driver but by quasiparticles generated from the metallic SFS π-junction. To further improve the qubit coherence in the monolithic SFQ-qubit chip, we proposed the use of an insulating ferromagnet π-junctions or an SIFS structure for future work.\u003c/p\u003e "},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was partly supported by JSPS KAKENHI (JP19H05615 and JP18H05211).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDP and\u0026nbsp;TY acknowledge Center for Heterogeneous Quantum/Material Fusion Technologies, Center for Key Interdisciplinary Research, Tohoku University.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eD.P. wrote the manuscript, designed the qubit, fabricated the \u0026pi;-junctions, performed the main device measurements, and analyzed the data. T.U., M.T., and A.F. designed and simulated the SFQ circuits and measured the modulation patterns. S.M. and H.T. designed and fabricated the SFQ driver and the SIS junctions for the qubits. K.I. co-designed the qubit and provided consultation on the measurement setup. T.Y. conceived and supervised the project.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCorrespondence and requests for materials should be addressed to Duong Pham, Hirotaka Terai, or Taro Yamashita.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eArute F, et al. Quantum supremacy using a programmable superconducting processor. Nature. 2019;574:505\u0026ndash;10.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKjaergaard M, et al. 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Nat Phys. 2010;6:593\u0026ndash;7.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSharma PK, Pal A. Shunt-free cryogenic memory using ferromagnetic insulator-based Josephson junctions. Appl Phys Lett. 2024;125:052601.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKato T, Golubov AA, Nakamura Y. Decoherence in a superconducting flux qubit with a π-junction. Phys Rev B. 2007;76:172502.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePham D, et al. NbN-based tunnel-type π-junctions for low-power half-flux-quantum circuits. Supercond Sci Technol. 2024;37:055004.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"epj-quantum-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epjq","sideBox":"Learn more about [EPJ Quantum Technology](http://epjquantumtechnology.springeropen.com)","snPcode":"40507","submissionUrl":"https://submission.nature.com/new-submission/40507/3","title":"EPJ Quantum Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9230218/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9230218/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eControlling a large number of superconducting qubits is a key challenge for realizing a fault-tolerant quantum computer. Implementing a qubit control system operating at the proximal millikelvin stage of the dilution refrigerator is a promising approach to reduce the number of coaxial cables required for qubit control. Single-flux-quantum (SFQ) logic circuits are one candidate for realizing such cryogenic control systems; however, their power dissipation must be minimized to avoid any negative impact on qubit performance. In this study, we demonstrate the operation of a flux-bias-free (FBF) flux qubit controlled by an SFQ driver on a monolithic chip. Here, the critical current (\u003cem\u003eI\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e) of the Josephson junctions in the SFQ driver was set to a few \u0026micro;A, which is two orders of magnitude smaller than that in a typical SFQ circuit operating at 4 K, significantly reducing power consumption. Using this low-power SFQ driver, we successfully demonstrate single-qubit operation without any reduction of the energy relaxation time of the FBF qubit.\u003c/p\u003e","manuscriptTitle":"Flux-bias-free flux qubit driven by low-power single-flux-quantum driver on monolithically integrated circuit","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-31 16:25:01","doi":"10.21203/rs.3.rs-9230218/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-05-12T09:40:41+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-11T09:44:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"253983309775832277279558660774890377252","date":"2026-05-07T00:47:24+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-13T06:15:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"261032252933514241523844684957342530163","date":"2026-04-10T06:39:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"278418494326255199302694308321964782926","date":"2026-04-01T10:49:21+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-30T08:39:11+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-27T03:32:44+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-27T03:32:42+00:00","index":"","fulltext":""},{"type":"submitted","content":"EPJ Quantum Technology","date":"2026-03-26T06:47:30+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"epj-quantum-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epjq","sideBox":"Learn more about [EPJ Quantum Technology](http://epjquantumtechnology.springeropen.com)","snPcode":"40507","submissionUrl":"https://submission.nature.com/new-submission/40507/3","title":"EPJ Quantum Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1198c425-c0d4-40f4-843c-b23efa97d9ca","owner":[],"postedDate":"March 31st, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-12T09:40:41+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-11T09:44:44+00:00","index":28,"fulltext":""},{"type":"reviewerAgreed","content":"253983309775832277279558660774890377252","date":"2026-05-07T00:47:24+00:00","index":27,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[],"tags":[],"updatedAt":"2026-05-12T10:37:06+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-31 16:25:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9230218","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9230218","identity":"rs-9230218","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}