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Applied Physics Letters

NbN-based half-flux-quantum element for integration with superconducting qubits

Naoki Takeuchi, Mikiya Naruse, Shigeyuki Miyajima, Duong Pham, Hirotaka Terai, Masamitsu Tanaka, Taro Yamashita

Published Apr 8, 2024• 3 citations
Publisher

Abstract

Half-flux-quantum (HFQ) logic is a superconductor logic family comprising conventional Josephson junctions (0-JJs) and π Josephson junctions (π-JJs). The energy scale of HFQ logic can be flexibly reduced by phase shifts owing to π-JJs; thus, HFQ circuits are a promising building block for qubit interface circuits. In this study, we demonstrate an NbN-based HFQ circuit element compatible with NbN-based superconducting qubits for all-NbN monolithic integration of qubits and HFQ circuits. The use of NbN is beneficial for both qubits and HFQ circuits owing to its high-quality junctions and high kinetic inductance. First, we developed a prototype of an NbN-based 0-JJ/π-JJ hybrid fabrication process for designing HFQ circuits. We evaluated 0-JJs and π-JJs fabricated through the hybrid process, which demonstrated that the 0-JJs had a small deviation with regard to critical current density and the π-JJs had a sufficiently high critical current density to work as π phase shifters. Furthermore, we fabricated an HFQ superconducting quantum interference device, which is one of the most fundamental elements in HFQ circuits, and observed clear HFQ-period modulation in the magnetic flux dependence of the maximum current at 4.2 K.

DOI
10.1063/5.0203046

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Half-flux-quantum (HFQ) logic is a superconductor logic family comprising conventional Josephson junctions (0-JJs) and π Josephson junctions (π-JJs). The energy scale of HFQ logic can be flexibly reduced by phase shifts owing to π-JJs; thus, HFQ circuits are a promising building block for qubit interface circuits. In this study, we demonstrate an NbN-based HFQ circuit element compatible with NbN-based superconducting qubits for all-NbN monolithic integration of qubits and HFQ circuits. The use of NbN is beneficial for both qubits and HFQ circuits owing to its high-quality junctions and high kinetic inductance. First, we developed a prototype of an NbN-based 0-JJ/π-JJ hybrid fabrication process for designing HFQ circuits. We evaluated 0-JJs and π-JJs fabricated through the hybrid process, which demonstrated that the 0-JJs had a small deviation with regard to critical current density and the π-JJs had a sufficiently high critical current density to work as π phase shifters. Furthermore, we fabricated an HFQ superconducting quantum interference device, which is one of the most fundamental elements in HFQ circuits, and observed clear HFQ-period modulation in the magnetic flux dependence of the maximum current at 4.2 K.
Abstract We have developed half-flux-quantum (HFQ) circuits using all-π-junctions formed from an NbN/AlN/PdNi/NbN (SIFS) structure. The circuits were fabricated using a novel process that incorporated a ground plane on top of the chip, enabling the epitaxial growth of NbN-based junctions from the substrate. The π-state of the junctions was demonstrated through a HFQ shift. Notably, these π-junctions exhibited self-overdamped current-voltage characteristics, enabling them to function as switching components without the need for shunt resistors. The elimination of shunt resistors and the high sheet inductance of NbN are expected to enhance the density of HFQ circuits. To evaluate the performance and power consumption of the all-π-junctions HFQ circuits, we designed and fabricated an HFQ toggle flip-flop (HFQ-TFF) circuit utilizing π-π-π SQUIDs as the fundamental components. Our findings reveal that the NbN-based HFQ-TFF circuit correctly operates as a frequency divider while consuming only around 30% of the power compared to single-flux-quantum TFF (SFQ-TFF) circuits. These results suggest that the HFQ circuit using SIFS-π-junctions has promising potential for integrated circuits requiring low-power consumption at cryogenic temperatures, such as qubit control.
Abstract Half-flux-quantum (HFQ) circuits are based on 0–π superconducting quantum interference devices (SQUIDs) and is one of the energy-efficient superconductor digital circuits. The bit energy is determined by the critical current I cn of 0–π SQUID, which can be easily tuned with the loop inductance and junction critical current. In this work, an alternative π–π–π SQUID is adopted to demonstrate HFQ circuits to simplify the fabrication process and enhance circuit energy efficiency. The properties of superconductor/ferromagnet/insulator/superconductor Josephson junctions (π-JJs) are measured with temperature dependence from 4.2 K down to 10 mK. HFQ toggle flip-flops (TFFs) are successfully demonstrated at frequencies of up to 6.7 GHz and 44.5 GHz at temperatures of 4.2 K and 10 mK, respectively. Comparing the HFQ TFF with its rapid single-flux quantum counterpart under the same fabrication process, it is anticipated that the HFQ TFF will exhibit approximately 70% reduction in both static and dynamic energy dissipation. This research establishes the foundation for developing cryogenic interface control and readout circuits for large-scale quantum computing in the future.
We adopt superconductor/ferromagnet/insulator/superconductor (SFIS) Josephson junctions (JJs) as both switching JJs and intrinsic π phase shifters in superconductor digital circuits. The critical current density (Jc) and characteristic voltage (Vc) of the SFIS junctions are about 22 A/cm2 and 22 μV, respectively. The intrinsic π phase shift is confirmed by measuring the suppressed nominal critical current Icn and half-period-shifted modulation pattern of a π–π–π superconducting quantum interference device (SQUID) that contains three π-JJs in a superconducting loop. A single-flux-quantum (SFQ) circuit composed of a DC/SFQ, Josephson transmission line (JTL), and SFQ/DC converter based on SFIS JJs alone is demonstrated at 4.2 K. The energy dissipation of the SFQ/DC converter decreases by 80% because some JJs are self-biased by the π phase shifter. The intrinsic circulating currents induced by the π phase shifters lead to a narrow bias margin (±5%) and even error function, which can be solved by parameters optimization or circuit initialization in the future. The half-modulation period (Φ0/2) of a half-flux-quantum (HFQ) SQUID (a partial HFQ JTL) exhibits propagation of HFQ between π–π–π SQUIDs, indicating that more complex HFQ circuits can be developed with π-JJs alone in the future.
We successfully fabricated magnetic Josephson junctions integrated on a Nb four-layer superconducting structure for demonstrating half flux quantum (HFQ) circuits. In the developed process, we adopted a 0-0-π SQUID instead of the 0-π SQUID as the basic element of the HFQ circuits. In this work, we characterized the Nb/PdNi/Nb magnetic Josephson junctions on the Nb four-layer structures fabricated by two different processes. We measured the I-V characteristics of junctions in liquid helium at 4.2 K. The results showed that the fabricated junctions had properties comparable to conventional ones on Si wafers.
We report on low-power operation of the half-flux-quantum (HFQ) shift-register circuit. We used a superconducting quantum interference device composed of two conventional switching junctions (0-junctions) and one π-shifted non-switching magnetic Josephson junction (π-junction) as a switching element, called 0-0-π SQUID. Because the π-shift assists switching by inducing a spontaneous current, the 0-0-π SQUID shows a nominal small critical current value and is easily switched by a weak driving force. This feature allows us to significantly reduce static and dynamic power consumption at junctions and bias-feeding resistors. We carefully designed the HFQ circuit elements using a circuit parameter optimization tool and introducing additional non-switching 0-0-π SQUIDs to compensate for superconductor phase shifts. We fabricated the test circuit of the 4-bit shift-register by forming Nb/PdNi/Nb π-junctions on the Nb four-layer, 10-kA/cm2 device. We successfully obtained correct operation with measured power consumption of 0.12-0.18 μW/bit, which was about 1/10 of the conventional single-flux-quantum shift-register designed with the 0-junctions of the same critical currents and the standard bias voltage.
We developed a process for fabricating nitride superconductor-based superconducting qubits monolithically integrated with a single flux quantum (SFQ)-based readout and control circuits. Since we used a Josephson junction (JJ) made of an NbN/AlN/NbN tri-layer, including a critical current density (Jc) of 50 A/cm2as the suitable material for superconducting qubits and SFQ readout/control circuits operating at 20 mK, the JJs for both the qubits and the SFQ circuits could simultaneously be fabricated. The device structure was also composed of three superconductive layers, comprising two superconductive layers as wiring layers and other layers as the top ground plane. Then, we used a Pd film as the resistive layer, which is required as the shunt resistors and the bias resistors for the SFQ control circuits, followed by an investigation of the properties of NbN/AlN/NbN epitaxial junctions and evaluation of the sheet inductance of the base NbN and wiring NbTiN layer. Our results showed the successful fabrication of a JJ with a sufficiently low leakage current and aJcof around 50 A/cm2, which was close to the target value. Furthermore, the evaluated sheet inductance exceeded 1 pH, which was several times larger than the values obtained for Nb-integrated circuits.