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IEICE Transactions on Electronics

Demonstration of Low-Power Shift-Register Based on Half-Flux-Quantum Logic

Masamitsu Tanaka, Toranosuke Nakayama, Shoma Tanemura, Masayuki Higashi, Feng Li, Akira Fujimaki

Published Feb 17, 2025• 3 citations
Publisher

Abstract

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.

DOI
10.1587/transele.2024sei0001

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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.
Abstract Half-flux-quantum (HFQ) circuits store and propagate half-flux quanta. The basic circuit element is a 0-π SQUID, which is a superconducting quantum interference device with a conventional Josephson junction (0-junction) and a π-shifted ferromagnetic junction (π-junction). A 0-π SQUID achieves a small critical current in the absence of an external magnetic field, thus reducing power consumption. It is easy to set up 0-0-π SQUIDs with two 0-junctions and a π-junction which serves as a π phase-shifter. We simulated 0-0-π SQUID-based HFQ circuits driven by low bias voltages, referred to as LV-HFQ circuits. In these circuits, shunt resistors are not required for switching junctions because there is no hysteresis in the current–voltage characteristics of 0-0-π SQUIDs. We estimated the power consumption and maximum operating frequency of an HFQ Josephson transmission line based on 0-0-π SQUIDs. When operating at 43.5 GHz, the power dissipation of a single element composed of a 0-0-π SQUID and a bias resistor fell to about 0.165 nW when biased at 60 μV. The LV-HFQ circuit is potentially more power-efficient than all other currently available superconducting logic circuits.
We report optimization of half-flux-quantum (HFQ) circuits composed of SQUIDs containing conventional Josephson junctions and π-shift magnetic Josephson junctions. The SQUID can act as a Josephson junction with an extremely small critical current and be easily switched by a weak driving force with the assistance of the circulating current that is induced due to the π-shift and quantization conditions. It leads to a drastic reduction of both static and dynamic power consumption. However, the parameter margins of the HFQ circuits obtained so far is narrow compared with conventional single-flux-quantum circuits. Since HFQ circuits use many circuit elements and require the two junctions in the SQUID to switch alternately and symmetrically, circuit parameter optimization is much more difficult. In this study, we developed an optimization tool for HFQ circuits, including operation judgment and margin calculation. We improved the critical margin of the HFQ Josephson transmission line to 39%. We also optimized the HFQ splitter, confluence buffer, and D flip-flop. We discuss design guidelines for HFQ circuits based on our systematic exploration of the optimized circuit parameter sets. We suggest that the optimized loop inductances are around 0.5 and 1.5 of Φ0/2 for data transmission and storage, respectively.
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.
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.
We demonstrated interface circuits between a half-flux-quantum (HFQ) circuit and a rapid single-flux-quantum (RSFQ) circuit to obtain SFQ/HFQ and HFQ/SFQ converters. These converters were created by simply inserting a resistor between an RSFQ circuit and the adjacent HFQ circuit, where both circuits are based on pulse logic. These converters enable us to create combinatory circuits that make the best use of the features of the two circuits. Using a DC/SFQ, SFQ/HFQ, HFQ/SFQ, and SFQ/DC converter, we measure an HFQ Josephson transmission line (JTL) composed of eight 0-0-π superconducting quantum interference devices (SQUIDs), which are the essential elements of an HFQ circuit. The 0-0-π SQUIDs are composed of two conventional Josephson junctions and a π-shifted ferromagnetic junction. The HFQ JTL demonstrated in this study is driven by a bias current 11-fold lower than that of a similar RSFQ JTL. These experimental results indicate that the HFQ circuit requires power that is two or more orders of magnitude lower than that of an RSFQ circuit.
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.