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arXiv:2503.11437 · Physical Review Applied

Stacked Josephson junctions for quantum circuit applications

Alex Kreuzer, Thilo Krumrey, Hossam Tohamy, Alexandru Ionita, Hannes Rotzinger, Alexey Vladimirovich Ustinov

Published Apr 14, 2026• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1103/klgx-jff9

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Quarton qubits with stacked Josephson junctions

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Superconducting quantum circuits rely on compact, low-loss inductive elements, strong anharmonicity, and robust flux biasing to realize coherent and controllable quantum bits. This thesis investigates how vertically stacked Josephson junction arrays can be employed to meet these requirements and enable compact flux qubits operated in the quarton regime. In the first part, stacked Al/AlOx/Al Josephson junctions are established as compact linear inductors. Their three-dimensional geometry reduces parasitic capacitance to ground while allowing multiple junctions to be integrated within a small footprint. A numerical modeling approach is used to quantify stray capacitances, Coulomb screening, and collective modes of extended stacked junction arrays. Cryogenic transport measurements confirm strongly underdamped junction dynamics with uniform junction characteristics, demonstrating their suitability as low-loss inductive elements in superconducting circuits. In the second part, these inductors are integrated into flux qubits operated in the quarton regime. In this regime, the qubit potential becomes nearly quartic around half-flux bias, resulting in positive anharmonicity and first-order insensitivity to flux noise at the operating point. Spectroscopy reveals qubit transition frequencies in the 3–5 GHz range and anharmonicities of 0.5–1.5 GHz, consistent with the expected quartic potential landscape. To distinguish intrinsic from externally induced decoherence, a persistent-current bias scheme is implemented, enabling stable and low-noise flux biasing over time scales of up to one week. A direct comparison between conventionally biased and persistently biased devices rules out external flux noise as the dominant coherence-limiting mechanism. High-resolution spectroscopy identifies avoided level crossings caused by microscopic two-level systems (TLS) in the amorphous tunnel barriers of the stacked junctions. A systematic cumulative analysis of splitting statistics across multiple devices shows that the spectral TLS density scales with the total tunnel-barrier area, while the array length determines the effective qubit–TLS coupling strength. The measured relaxation times follow scaling relations consistent with Fermi’s golden rule for a bath of weakly coupled TLS, demonstrating that TLS in the stacked junction arrays constitute the dominant intrinsic decoherence channel in quarton qubits. These results establish stacked Josephson junction arrays as compact superinductive elements and provide an understanding of coherence limitations in superconducting quantum circuits based on Josephson junction arrays, offering guidance for future device optimization.

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quant-pharXiv:2606.06951•Jun 8, 2026•0 citations
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.
Superconducting quantum circuits rely on compact, low-loss inductive elements, strong anharmonicity, and robust flux biasing to realize coherent and controllable quantum bits. This thesis investigates how vertically stacked Josephson junction arrays can be employed to meet these requirements and enable compact flux qubits operated in the quarton regime. In the first part, stacked Al/AlOx/Al Josephson junctions are established as compact linear inductors. Their three-dimensional geometry reduces parasitic capacitance to ground while allowing multiple junctions to be integrated within a small footprint. A numerical modeling approach is used to quantify stray capacitances, Coulomb screening, and collective modes of extended stacked junction arrays. Cryogenic transport measurements confirm strongly underdamped junction dynamics with uniform junction characteristics, demonstrating their suitability as low-loss inductive elements in superconducting circuits. In the second part, these inductors are integrated into flux qubits operated in the quarton regime. In this regime, the qubit potential becomes nearly quartic around half-flux bias, resulting in positive anharmonicity and first-order insensitivity to flux noise at the operating point. Spectroscopy reveals qubit transition frequencies in the 3–5 GHz range and anharmonicities of 0.5–1.5 GHz, consistent with the expected quartic potential landscape. To distinguish intrinsic from externally induced decoherence, a persistent-current bias scheme is implemented, enabling stable and low-noise flux biasing over time scales of up to one week. A direct comparison between conventionally biased and persistently biased devices rules out external flux noise as the dominant coherence-limiting mechanism. High-resolution spectroscopy identifies avoided level crossings caused by microscopic two-level systems (TLS) in the amorphous tunnel barriers of the stacked junctions. A systematic cumulative analysis of splitting statistics across multiple devices shows that the spectral TLS density scales with the total tunnel-barrier area, while the array length determines the effective qubit–TLS coupling strength. The measured relaxation times follow scaling relations consistent with Fermi’s golden rule for a bath of weakly coupled TLS, demonstrating that TLS in the stacked junction arrays constitute the dominant intrinsic decoherence channel in quarton qubits. These results establish stacked Josephson junction arrays as compact superinductive elements and provide an understanding of coherence limitations in superconducting quantum circuits based on Josephson junction arrays, offering guidance for future device optimization.
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.
Quantum computing based on superconducting qubits requires the understanding and control of the materials, device architecture, and operation. However, the materials for the central circuit element, the Josephson junction, have mostly been focused on using the AlO x tunnel barrier. Here, we demonstrate Josephson junctions and superconducting qubits employing two-dimensional materials as the tunnel barrier. We batch-fabricate and design the critical Josephson current of these devices via layer-by-layer stacking N layers of MoS 2 on the large scale. Based on such junctions, MoS 2 transmon qubits are engineered and characterized in a bulk superconducting microwave resonator for the first time. Our work allows Josephson junctions to access the diverse material properties of two-dimensional materials that include a wide range of electrical and magnetic properties, which can be used to study the effects of different material properties in superconducting qubits and to engineer novel quantum circuit elements in the future.
Flux quantum logic and memory circuits using superconducting Josephson tunnel junctions have high-speed switching times (approximately 1 ps), low power dissipation (< 1 (mu) W per circuit) and low levels of thermally induced electrical noise. Current designs of such circuits employ single trilayer junctions, which impose circuit size and logic threshold limitations. A new design component, the multilayered tunnel junction, consists of a vertically stacked array (a 1D superlattice) of Josephson tunnel junctions. The introduction of multilayered junctions into superconducting electronic circuitry offers a reduction in the current device size, fault tolerances, and new device applications. We present numerical simulations of simple circuits employing multilayered Josephson junctions as design components. Comparison with conventional single flux quantum circuitry is discussed. We also present preliminary measurements of multilayered Josephson junctions fabricated for use in flux quantum devices.
Abstract Decoherence in quantum bits (qubits) is a major challenge for realizing scalable quantum computing. One of the primary causes of decoherence in qubits and quantum circuits based on superconducting Josephson junctions is the critical current fluctuation. Many efforts have been devoted to suppressing the critical current fluctuation in Josephson junctions. Nonetheless, the efforts have been hindered by the defect-induced trapping states in oxide-based tunnel barriers and the interfaces with superconductors in the traditional Josephson junctions. Motivated by this, along with the recent demonstration of 2D insulator h -BN with exceptional crystallinity and low defect density, we fabricated a vertical NbSe 2 / h -BN/Nb Josephson junction consisting of a bottom NbSe 2 superconductor thin layer and a top Nb superconductor spaced by an atomically thin h -BN layer. We further characterized the superconducting current and voltage ( I – V ) relationships and Fraunhofer pattern of the NbSe 2 / h -BN/Nb junction. Notably, we demonstrated the critical current noise (1/ f noise power) in the h -BN-based Josephson device is at least a factor of four lower than that of the previously studied aluminum oxide-based Josephson junctions. Our work offers a strong promise of h -BN as a novel tunnel barrier for high-quality Josephson junctions and qubit applications.
Superconducting circuit devices require electrical interconnects between different circuit elements on the chip, for which conventional device architectures use a combination of two structural elements: \textit{airbridges} to connect non-adjacent elements in the base layer, and \textit{bandages} to connect the electrodes forming the Josephson junctions to the base layer. Bandages introduce unwanted parasitic material interfaces and increase the manufacturing complexity. Here, we overcome the limitations imposed by \emph{bandages} by establishing \textit{all} electrical interconnects with airbridges of varying size fabricated in a single step. The airbridges show a high yield and mechanical stability over a wide range of sizes from 0.5 μm0.5\,μ\mathrm{m}0.5μm to 4 μm4\,μ\mathrm{m}4μm in width and from 5 μm5\,μ\mathrm{m}5μm to 40 μm40\,μ\mathrm{m}40μm in length, and show low loss when integrated in coplanar waveguide resonators and transmon qubits. Measured relaxation times up to more than 250 μs250\,μ\mathrm{s}250μs in standard transmon geometries show that the process achieves high coherence while substantially easing and accelerating device fabrication.