Large-scale integration of single flux quantum (SFQ) circuits requires components as compact as possible. In this paper, we study the feasibility of integrating vertically stacked Josephson inductors (VSJIs) fabricated with self-shunted Josephson junctions into our SFQ-based circuits, and use both dc and RF electrical measurements to verify the performance of these junction stacks as compact inductors. The VSJIs consist of three Josephson junctions stacked vertically and are inserted into test structures to validate their potential as compact alternatives to geometrical inductors. The VSJIs are designed to be non-switching junctions and are combined with smaller area, switching Josephson junctions fabricated with the same junction barrier process. The VSJIs have a designed critical current of approximately 50% greater than that of the switching junctions, and their observed behavior can be modeled correctly by including the known nonlinearity of the Josephson inductance. To confirm that this nonlinearity does not degrade the expected bias margins, we simulate two common types of SFQ cells with the geometrical inductors replaced by VSJIs. The results verify that incorporating VSJIs in SFQ circuits would increase circuit density with minimal impact on circuit margins.Large-scale integration of single flux quantum (SFQ) circuits requires components as compact as possible. In this paper, we study the feasibility of integrating vertically stacked Josephson inductors (VSJIs) fabricated with self-shunted Josephson junctions into our SFQ-based circuits, and use both dc and RF electrical measurements to verify the performance of these junction stacks as compact inductors. The VSJIs consist of three Josephson junctions stacked vertically and are inserted into test structures to validate their potential as compact alternatives to geometrical inductors. The VSJIs are designed to be non-switching junctions and are combined with smaller area, switching Josephson junctions fabricated with the same junction barrier process. The VSJIs have a designed critical current of approximately 50% greater than that of the switching junctions, and their observed behavior can be modeled correctly by including the known nonlinearity of the Josephson inductance. To confirm that this nonlinearity does not degrade the expected bias margins, we simulate two common types of SFQ cells with the geometrical inductors replaced by VSJIs. The results verify that incorporating VSJIs in SFQ circuits would increase circuit density with minimal impact on circuit margins.

IEEE Transactions on Applied SuperconductivityFeb 27, 201920 citations

Detection of Low-Energy Fluxons From Discrete Long Josephson Junctions for Ballistic Computing

Han Cai, Liuqi Yu, Waltraut Wustmann +2 more

Single-flux quantum (SFQ) digital logic is typically energy efficient and fast, and logic that uses ballistic and reversible principles will provide a new platform for efficient computing. We are studying long Josephson junctions (LJJs), SFQs within them, and an SFQ detector, all intended for future ballistic logic gate experiments. Specifically, we launch low-energy SFQ into discrete LJJs, made from an array of 80 Josephson junctions (JJs) and connecting inductors. The component JJs have critical currents ( $I_{c}$ ) of only 7.5 $\mu \text{A}$ . Measurements of the discrete inductors from our LJJs indicate that the LJJ operates in the continuous regime of the Josephson transmission line, giving dynamics similar to continuous LJJs. The Josephson penetration depth is approximately 2.4 unit cells, and the rest energy of the SFQ in the LJJ is$\approx $47 zJ. While the SFQ launcher is fairly standard, the SFQ detector uses JJ critical currents of only$ \approx $16$ \mu \text{A}$. To understand the effects of noise in the circuit, we measured it in two systems: 1) at 4.2 K using a helium dunk probe; and 2) at 3.5 K in a cryogen-free refrigerator. Data show that SFQ detection events are synchronous with SFQ launch events in both systems. The additional jitter in one system over the other is predominantly attributed to noise in the detector. The traversal of the SFQ is consistent with ballistic propagation. This study shows the creation of low-energy SFQs in LJJs composed of discrete components and a method to detect these SFQs, as a step toward achieving ballistic reversible gates.Single-flux quantum (SFQ) digital logic is typically energy efficient and fast, and logic that uses ballistic and reversible principles will provide a new platform for efficient computing. We are studying long Josephson junctions (LJJs), SFQs within them, and an SFQ detector, all intended for future ballistic logic gate experiments. Specifically, we launch low-energy SFQ into discrete LJJs, made from an array of 80 Josephson junctions (JJs) and connecting inductors. The component JJs have critical currents ($I_{c}$) of only 7.5$\mu \text{A}$. Measurements of the discrete inductors from our LJJs indicate that the LJJ operates in the continuous regime of the Josephson transmission line, giving dynamics similar to continuous LJJs. The Josephson penetration depth is approximately 2.4 unit cells, and the rest energy of the SFQ in the LJJ is$\approx$47 zJ. While the SFQ launcher is fairly standard, the SFQ detector uses JJ critical currents of only$\approx$16$\mu \text{A}$. To understand the effects of noise in the circuit, we measured it in two systems: 1) at 4.2 K using a helium dunk probe; and 2) at 3.5 K in a cryogen-free refrigerator. Data show that SFQ detection events are synchronous with SFQ launch events in both systems. The additional jitter in one system over the other is predominantly attributed to noise in the detector. The traversal of the SFQ is consistent with ballistic propagation. This study shows the creation of low-energy SFQs in LJJs composed of discrete components and a method to detect these SFQs, as a step toward achieving ballistic reversible gates.

arXiv:2406.15671IEEE Transactions on Applied SuperconductivitySep 9, 20250 citations

Development of highly integrated RSFQ circuits on the basis of intrinsically shunted Josephson junctions

F.-I. Buchholz, D Balashov, M. Khabipov +4 more

Physica C SuperconductivityFeb 1, 20014 citations

Stacked Josephson junctions for quantum circuit applications

Alex Kreuzer, Thilo Krumrey, Hossam Tohamy +3 more

Low-loss inductors are essential components in various superconducting circuits, such as qubits or digital electronics. In this study, we investigate highly compact inductors formed by vertically stacking Josephson junctions. Our implementation employs several layers of aluminum separated by tunnel barriers. Individual stacks are connected by suspended superconducting bridges, which are free of additional dielectric materials and, therefore, should not contribute significantly to losses. We present implementation details, fabrication results, and device characterization measurements.Low-loss inductors are essential components in various superconducting circuits, such as qubits or digital electronics. In this study, we investigate highly compact inductors formed by vertically stacking Josephson junctions. Our implementation employs several layers of aluminum separated by tunnel barriers. Individual stacks are connected by suspended superconducting bridges, which are free of additional dielectric materials and, therefore, should not contribute significantly to losses. We present implementation details, fabrication results, and device characterization measurements.

arXiv:2503.11437Physical Review AppliedApr 14, 20261 citation

Experimental analysis of a new generation of compact Josephson-inductance based RSFQ circuits

Th. Ortlepp, B. Dimov, Jürgen Kunert +3 more

Jun 10, 20070 citations

I_{c}

) of only 7.5

\mu \text{A}

. Measurements of the discrete inductors from our LJJs indicate that the LJJ operates in the continuous regime of the Josephson transmission line, giving dynamics similar to continuous LJJs. The Josephson penetration depth is approximately 2.4 unit cells, and the rest energy of the SFQ in the LJJ is$\approx

47 zJ. While the SFQ launcher is fairly standard, the SFQ detector uses JJ critical currents of only

\approx

16

\mu \text{A}$. To understand the effects of noise in the circuit, we measured it in two systems: 1) at 4.2 K using a helium dunk probe; and 2) at 3.5 K in a cryogen-free refrigerator. Data show that SFQ detection events are synchronous with SFQ launch events in both systems. The additional jitter in one system over the other is predominantly attributed to noise in the detector. The traversal of the SFQ is consistent with ballistic propagation. This study shows the creation of low-energy SFQs in LJJs composed of discrete components and a method to detect these SFQs, as a step toward achieving ballistic reversible gates.