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arXiv:2410.24004 · npj Quantum Information

Kinetic-inductance-incorporated quantization for accurate Hamiltonian prediction in superconducting circuits

Seong Hyeon Park, Gahyun Choi, Eunjong Kim, Gwanyeol Park, Jisoo Choi, Jiman Choi, Yonuk Chong, Yongho Lee, Seungyong Hahn

Published Feb 25, 2026• 0 citations
arXivHTMLPDF

Abstract

We propose an improved method for quantizing superconducting circuits that incorporates material- and geometry-dependent kinetic inductance. Our approach models thin superconducting films as equivalent reactive boundary elements, seamlessly integrating into the conventional circuit quantization framework without adding significant computational complexity. As a proof of concept, we experimentally verify our method using planar superconducting quantum devices made of 35-nm-thick disordered niobium films, known to exhibit large kinetic inductance values. We demonstrate significantly improved accuracy in predicting the Hamiltonian based solely on the chip layout and material properties of superconducting films and Josephson junctions. Specifically, conventional methods exhibit average errors of 5.4% in mode frequencies and 41% in cross-Kerr shift frequencies, while our method reduces the errors to 1.1% and 11%, respectively. Our method enables systematic studies of superconducting devices based on disordered thin films or compact, fine-pitched elements and, more broadly, facilitates the precise engineering of superconducting quantum circuits at scale.

DOI
10.1038/s41534-026-01187-1

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We propose an improved method for quantizing superconducting circuits that incorporates material- and geometry-dependent kinetic inductance. Our approach models thin superconducting films as equivalent reactive boundary elements, seamlessly integrating into the conventional circuit quantization framework without adding significant computational complexity. As a proof of concept, we experimentally verify our method using planar superconducting quantum devices made of 35-nm-thick disordered niobium films, known to exhibit large kinetic inductance values. We demonstrate significantly improved accuracy in predicting the Hamiltonian based solely on the chip layout and material properties of superconducting films and Josephson junctions. Specifically, conventional methods exhibit average errors of 5.4% in mode frequencies and 41% in cross-Kerr shift frequencies, while our method reduces the errors to 1.1% and 11%, respectively. Our method enables systematic studies of superconducting devices based on disordered thin films or compact, fine-pitched elements and, more broadly, facilitates the precise engineering of superconducting quantum circuits at scale.
Disordered superconducting materials with high kinetic inductance are an important resource for generating nonlinearity in quantum circuits and creating high-impedance environments. In thin films fabricated from these materials, the combination of disorder and low effective dimensionality leads to increased order parameter fluctuations and enhanced kinetic inductance values. Among the challenges of harnessing these compounds in coherent devices are their proximity to the superconductor-insulator phase transition and the two-level systems located in the disordered structure. Here, we fabricate tungsten silicide wires from quasi-two-dimensional films and embed them into microwave resonators and fluxonium qubits, where the kinetic inductance provides the inductive part of the circuits. In this work, we study the dependence of loss on the frequency, disorder, and geometry of the devices, and find that the loss increases with the level of disorder and is dominated by the localized quasiparticles trapped in the spatial variations of the superconducting gap. High kinetic inductance materials are widely used in superconducting circuits, yet their loss mechanisms are not fully understood. Here the authors study quantum circuits incorporating nanowires made of quasi-2D disordered superconductor WSi and identify localized quasiparticles as the dominant source of loss.
Parametric amplification is essential for quantum measurement, enabling the amplification of weak microwave signals with minimal added noise. While Josephson-junction-based amplifiers have become standard in superconducting quantum circuits, their magnetic sensitivity, limited saturation power, and sub-kelvin operating requirements motivate the development of alternative nonlinear platforms. Here we demonstrate a two-mode kinetic-inductance parametric amplifier based on a pair of capacitively coupled Kerr-nonlinear resonators fabricated from NbTiN and NbN thin films. The distributed Kerr nonlinearity of these materials enables nondegenerate four-wave-mixing amplification with gains approaching 40 dB, gain-bandwidth products up to 6.9 MHz, and 1-dB compression powers two to three orders of magnitude higher than those of state-of-the-art Josephson amplifiers. A coupled-mode theoretical model accurately captures the pump-induced modification of the hybridized modes and quantitatively reproduces the observed signal and idler responses. The NbN device exhibits a significantly larger Kerr coefficient and superior gain-bandwidth performance, highlighting the advantages of high-kinetic-inductance materials. Our results establish coupled kinetic-inductance resonators as a robust platform for broadband, high-power, and magnetically resilient quantum-limited amplification, offering a scalable route for advanced readout in superconducting qubits, spin ensembles, quantum dots, and other microwave-quantum technologies.
We characterize inductors fabricated from ultra-thin, approximately 100 nm wide strips of niobium (Nb) and niobium nitride (NbN). These nanowires have a large kinetic inductance in the superconducting state. The kinetic inductance scales linearly with the nanowire length, with a typical value of 1 nH µm(-1) for NbN and 44 pH µm(-1) for Nb at a temperature of 2.5 K. We measure the temperature and current dependence of the kinetic inductance and compare our results to theoretical predictions. We also simulate the self-resonant frequencies of these nanowires in a compact meander geometry. These nanowire inductive elements have applications in a variety of microwave frequency superconducting circuits.
Advancements in the fabrication of superconducting quantum devices have highlighted tantalum as a promising material, owing to its low surface oxidation microwave loss at low temperatures. However, tantalum films exhibit significantly larger kinetic inductances compared to materials such as aluminum or niobium. Given the inevitable variations in film thickness, this increased kinetic inductance leads to considerable, uncontrolled frequency variances and shifts in components like superconducting coplanar waveguide (SCPW) resonators. Achieving high precision in resonator frequencies is crucial, particularly when multiple resonators share a common Purcell filter with limited bandwidth in superconducting quantum information processors. Here, we tackle this challenge from both fabrication and design perspectives, achieving a reduction in resonator frequency fluctuation by a factor of more than 100. Concurrently, the internal quality factor of the SCPW resonator remains at high level. Our findings open up new avenues for the enhanced utilization of tantalum in large-scale superconducting chips.
Niobium nitride (NbN\mathrm{Nb}\mathrm{N}NbN) is a particularly promising material for quantum technology applications, as it shows the degree of reproducibility necessary for large-scale superconducting circuits. We demonstrate that resonators based on NbN\mathrm{Nb}\mathrm{N}NbN thin films present a one-photon internal quality factor above 105{10}^{5}105 maintaining a high impedance (larger than $2\mathrm{k}\mathrm{\ensuremath{\Omega}}$), with a footprint of approximately $50\ifmmode\times\else\texttimes\fi{}100\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{m}}^{2}$ and a Kerr nonlinearity of few tenths of a hertz. These quality factors, mostly limited by losses induced by the coupling to two-level systems, have been maintained for kinetic inductances ranging from tenths to hundreds of picoHenry per square. We also demonstrate minimal variations in the performance of the resonators during multiple cooldowns over more than nine months. Our work proves the versatility of niobium nitride high-kinetic-inductance resonators, opening perspectives towards the fabrication of compact, high-impedance, and high-quality multimode circuits, with sizable interactions.
Research on spatially inhomogeneous weakly coupled superconductors has recently received a boost of interest because of the experimental observation of a dramatic enhancement of the kinetic inductance with relatively low losses. Here, we study the kinetic inductance and the quality factor of a strongly disordered, weakly coupled superconducting thin film. We employ a gauge-invariant random-phase approximation capable of describing collective excitations and other fluctuations. In line with the experimental findings, we have found that in the range of frequencies of interest, and for sufficiently low temperatures, an exponential increase of the kinetic inductance with disorder coexists with a still large quality factor of ∼10^{4}. More interestingly, on the metallic side of the superconductor-insulator transition, we have identified a range of frequencies and temperatures, T∼0.1T_{c}, where quantum coherence effects induce a broad statistical distribution of the quality factor with an average value that increases with disorder. We expect these findings to further stimulate experimental research on the design and optimization of superinductors for a better performance and miniaturization of quantum devices such as qubit circuits and microwave detectors.