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arXiv:2512.06895 · IEEE Transactions on Applied Superconductivity

Single Flux Quantum Circuit Operation at Millikelvin Temperatures

Jason Walter, Adam C. Weis, Kan-Ting Tsai, Meng-Ju Yu, Naveen Katam, Alex F. Kirichenko, Oleg A. Mukhanov, Shu-Jen Han, Igor V. Vernik

quant-phcond-mat.supr-conphysics.app-phSubmitted Dec 7, 2025• Announced Dec 9, 2025• 0 citations
arXivHTMLPDF

Abstract

As quantum computing processors increase in size, there is growing interest in developing cryogenic electronics to overcome significant challenges to system scaling. Single flux-quantum (SFQ) circuits offer a promising alternative to remote, bulky, and power-hungry room temperature electronics. To meet the need for digital qubit control, readout, and co-processing, SFQ circuits must be adapted to operate at millikelvin temperatures near quantum processors. SEEQC's SFQuClass digital quantum management approach proximally places energy-efficient SFQ (ERSFQ) circuits and qubits in a multi-chip module. This enables extremely low power dissipation, compatible with a typical dilution cryostat's limited cooling power, while maintaining high processing speed and low error rates. We report on systematic testing from 4 K to 10 mK of a comprehensive set of ERSFQ cells, as well as more complex circuits such as programmable counters and demultiplexers used in digital qubit control. We compare the operating margins and error rates of these circuits and find that, at millikelvin, bias margins decrease and the center of the margins (i.e., the optimal bias current value) increases by ~15%, compared to 4.2 K. The margins can be restored by thermal annealing by reducing Josephson junction (JJ) critical current Ic. To provide guidance for how circuit parameters vary from 4.2 K to millikelvin, relevant analog process control monitors (PCMs) were tested in the temperature range of interest. The measured JJ critical current (of the PCM JJ arrays) increases by ~15% when decreasing temperature from 4.2 K to millikelvin, in good agreement with both theory and the empirically measured change in the center of bias margins for the tested digital circuits.

Journal reference
IEEE Trans. Appl. Supercon., 36(5), 1700106, Aug. 2026
DOI
10.1109/TASC.2025.3639528
Comments
6 pages, 7 figures, presented at 17th European Conference on Applied Superconductivity, EUCAS 2025, 21-25 September 2025, Porto, Portugal. Accepted for publication in IEEE Trans. on Appl. Supercond

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As quantum computing processors increase in size, there is growing interest in developing cryogenic electronics to overcome significant challenges to system scaling. Single flux-quantum (SFQ) circuits offer a promising alternative to remote, bulky, and power-hungry room temperature electronics. To meet the need for digital qubit control, readout, and co-processing, SFQ circuits must be adapted to operate at millikelvin temperatures near quantum processors. SEEQC's SFQuClass digital quantum management approach proximally places energy-efficient SFQ (ERSFQ) circuits and qubits in a multi-chip module. This enables extremely low power dissipation, compatible with a typical dilution cryostat's limited cooling power, while maintaining high processing speed and low error rates. We report on systematic testing from 4 K to 10 mK of a comprehensive set of ERSFQ cells, as well as more complex circuits such as programmable counters and demultiplexers used in digital qubit control. We compare the operating margins and error rates of these circuits and find that, at millikelvin, bias margins decrease and the center of the margins (i.e., the optimal bias current value) increases by ~15%, compared to 4.2 K. The margins can be restored by thermal annealing by reducing Josephson junction (JJ) critical current Ic. To provide guidance for how circuit parameters vary from 4.2 K to millikelvin, relevant analog process control monitors (PCMs) were tested in the temperature range of interest. The measured JJ critical current (of the PCM JJ arrays) increases by ~15% when decreasing temperature from 4.2 K to millikelvin, in good agreement with both theory and the empirically measured change in the center of bias margins for the tested digital circuits.
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.
Superconducting single flux quantum (SFQ) technology is well known for digital logic operations below 4.2 K, which are compatible with the Josephson junction qubit. Operation speed and signal sensitivity of circuits in SFQ are also sufficient to control qubits. Therefore, the SFQ circuit is a candidate technology for multiple qubit control. However, the self-heating effect of the SFQ circuit is a potential barrier to development of an SFQ-supported multiple qubit system because the qubit operating temperature is lower than the conventional 4.2 K. The multi-chip approach is a possible solution because the qubit chip can be thermally isolated from the SFQ circuitry. We report on recent progress in SFQ circuit and packaging technology for operation at sub-Kelvin temperatures. As for multi-chip module technology, a test sample of the multi-chip module shows good reliability of electrical connections between chips, and each solder bump has a bandwidth wide enough for signal transmission. We have designed lower power SFQ circuits for sub-Kelvin temperatures. The critical currents of Josephson junctions were scaled down, inductances were scaled up, and bias voltage was reduced to make power consumption lower. Based on our fabrication technology, critical current densities were optimized by considering trade-off relations between fabrication availability and operation speed. We successfully confirmed its correct operations at around 0.35 K. The combination of the multi-chip module and optimized SFQ circuits is very effective way of controlling qubit.
Scaling superconducting quantum processors is increasingly constrained by the wiring, heat load, and calibration overhead associated with delivering high-resolution analog signals from room temperature to qubits at millikelvin temperature. Here we demonstrate a superconducting digital-to-analog converter (DAC) integrated with high-coherence fluxonium qubits in a multi-chip module architecture. The DACs generate persistent analog flux signals for tuning qubit parameters and are programmed deterministically using single-flux-quantum (SFQ) pulses, providing a digital interface compatible with established SFQ routing and demultiplexing technologies. Operating at millikelvin temperature, the DACs enable in-situ tuning of fluxonium qubits without measurable degradation of qubit coherence. The presented device provides a static control primitive for flux-tunable qubits, enabling parameter homogenization and eliminating the need for individual room-temperature DC bias lines. These results establish SFQ-programmable millikelvin DACs as a building block for digitally controlled superconducting quantum processors.
We implemented, optimized, and fully tested a superconducting Josephson junction fabrication process over multiple runs tailored for integrated digital circuits that are used for control and readout of superconducting qubits operating at millikelvin temperatures. This process was optimized for highly energy efficient rapid single flux quantum (ERSFQ) circuits with critical currents reduced by a factor of ∼10 as compared to those operated at 4.2 K. Specifically, it implemented Josephson junctions with 10 μA unit critical current fabricated with 10 μA/μm2 critical current density. In order to circumvent the substantial size increase in the SFQ circuit inductors, we employed an NbN high kinetic inductance layer with 8.5 pH/sq sheet inductance. Similarly, to maintain the small size of junction resistive shunts, we used a non-superconducting PdAu alloy with 4.0 Ω/sq sheet resistance. For integration with quantum circuits in a multi-chip module, 5 and 10 μm height bump processes were also optimized. To keep the fabrication process in check, we developed and thoroughly tested a comprehensive process control monitor chip set.
Current superconducting quantum computers (QC) rely on a brute-force scaling approach where quantum chips operating at the millikelvin stage inside dilution refrigerators are connected to room-temperature electronics via an ever-increasing number of signal wires. In order to drastically scale up such systems without facing refrigeration challenges, these quantum interface electronics need to be integrated at cryogenic temperatures, ideally at the same stage as qubits. In this paper, we show that, by employing energy-efficient digital superconducting microchips based on single flux quantum (SFQ) technology, all essential functions to operate a full stack quantum computer can be integrated at 10 mK. They include digital qubit charge control and magnetic flux control for single- and two-qubit gates, as well as digital qubit readout.
The digital circuits in a superconducting quantum computer must be cooled to cryogenic temperatures in a dilution refrigerator for control and information readout of the qubit information. Because the dilution refrigerator's heat capacity is limited, extremely low-power digital circuits are required. Single-flux-quantum (SFQ) circuits and Josephson photomultipliers (JPMs) are expected to serve as control and readout circuits for superconducting quantum computers. These circuits generate minimal heat, but further reductions in power consumption are required to make it possible to build larger, more scalable faulttolerant quantum computers (FTQC). In this paper, we propose a low-power and reliable peripheral circuit for JPM-based qubit readout utilizing an SFQ counter circuit. The counter performs majority voting across repeated readouts, significantly improving the reliability of the JPM readout process. Additionally, we quantitatively evaluate switching errors in SFQ circuits using Josephson junctions with low-critical current values. By integrating these circuit techniques and simulation results, we find that the proposed approach achieves a 90% reduction in power consumption while effectively suppressing the increase in readout error.