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Predicting Qubit Coherence Times from Geometric First Principles: Validation Against Published Data and Predictions for Novel Crystalline Superconductor Substrates

Stephen Cullor

Published Mar 14, 2026• 0 citations
Publisher

Abstract

I present a zero-parameter model for predicting the energy relaxation time (T₁) of superconducting transmon qubits derived from the Unified Structural Theory (UST). The model takes the form T₁ = 1/(ω × p_arch × tan δ_material), where the architecture participation ratio comes from published finite-element simulations and the oxide loss tangent comes from a UST-derived disorder model. Validated against 8 well-characterized published devices from four research groups (Yale, Princeton, Beijing, Fermilab/SQMS), the model achieves a mean absolute error of 9.5%, a maximum error of 20.4%, and a log-log correlation of r = 0.989 with zero fitted parameters. The oxide disorder model correctly identifies niobium oxide as the most lossy surface and explains the Fermilab observation that tantalum capping improves T₁ by 2–5×. The model predicts that crystalline superconductor surfaces — which terminate at ordered lattice planes rather than amorphous oxide layers — would reduce surface loss tangent by approximately 200×, yielding T₁ in the 100–200 ms range compared to the current record of 0.6 ms. Ten specific crystalline superconductor compounds satisfying these criteria have been identified by the UST materials prediction pipeline, which previously demonstrated 100% recall on known superconductors without training. Compound identities are protected under U.S. Provisional Patent #63/987,905. The UST framework derives 72 predictions across particle physics, cosmology, and condensed matter from four structural integers {5, 7, 24, 40} with a 93.1% pass rate and zero free parameters.

DOI
10.5281/zenodo.19024536

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I present a zero-parameter model for predicting the energy relaxation time (T₁) of superconducting transmon qubits derived from the Unified Structural Theory (UST). The model takes the form T₁ = 1/(ω × p_arch × tan δ_material), where the architecture participation ratio comes from published finite-element simulations and the oxide loss tangent comes from a UST-derived disorder model. Validated against 8 well-characterized published devices from four research groups (Yale, Princeton, Beijing, Fermilab/SQMS), the model achieves a mean absolute error of 9.5%, a maximum error of 20.4%, and a log-log correlation of r = 0.989 with zero fitted parameters. The oxide disorder model correctly identifies niobium oxide as the most lossy surface and explains the Fermilab observation that tantalum capping improves T₁ by 2–5×. The model predicts that crystalline superconductor surfaces — which terminate at ordered lattice planes rather than amorphous oxide layers — would reduce surface loss tangent by approximately 200×, yielding T₁ in the 100–200 ms range compared to the current record of 0.6 ms. Ten specific crystalline superconductor compounds satisfying these criteria have been identified by the UST materials prediction pipeline, which previously demonstrated 100% recall on known superconductors without training. Compound identities are protected under U.S. Provisional Patent #63/987,905. The UST framework derives 72 predictions across particle physics, cosmology, and condensed matter from four structural integers {5, 7, 24, 40} with a 93.1% pass rate and zero free parameters.
Abstract We present a transmon qubit fabrication technique that yields systematic improvements in T 1 relaxation times. We encapsulate the surface of niobium and prevent the formation of its lossy surface oxide. By maintaining the same superconducting metal and only varying the surface, this comparative investigation examining different capping materials, such as tantalum, aluminum, titanium nitride, and gold, as well as substrates across different qubit foundries demonstrates the detrimental impact that niobium oxides have on coherence times of superconducting qubits, compared to native oxides of tantalum, aluminum or titanium nitride. Our surface-encapsulated niobium qubit devices exhibit T 1 relaxation times 2–5 times longer than baseline qubit devices with native niobium oxides. When capping niobium with tantalum, we obtain median qubit lifetimes above 300 μs, with maximum values up to 600 μs. Our comparative structural and chemical analysis provides insight into why amorphous niobium oxides may induce higher losses compared to other amorphous oxides.
times 2 to 5 times longer than baseline niobium qubit devices with native niobium oxides. When capping niobium with tantalum, we obtain median qubit lifetimes above 200 microseconds. Our comparative structural and chemical analysis suggests that amorphous niobium oxides may induce higher losses compared to other amorphous oxides. These results are in line with high-accuracy measurements of the niobium oxide loss tangent obtained with ultra-high Q superconducting radiofrequency (SRF) cavities. This new surface encapsulation strategy enables even further reduction of dielectric losses via passivation with ambient-stable materials, while preserving fabrication and scalable manufacturability thanks to the compatibility with silicon processes.
Improving qubit lifetime is essential for fault-tolerant quantum computing. It is widely acknowledged that intricate processing techniques introduce defects at the interfaces and surfaces of superconducting quantum circuits, which can create sources of decoherence. Therefore, a precise understanding of how a material's structure contributes to decoherence is critical for enhancing the performance of superconducting qubits. This talk highlights our recent advancements in understanding surface oxides in resonators and ultrathin aluminum oxide barriers in Josephson junctions (JJs) using transmission electron microscopy and spectroscopy techniques [1-4]. The Superconducting Quantum Materials & Systems Center (SQMS) demonstrated that encapsulating niobium surfaces with a ∼10nm tantalum layer results in 2-5x longer T1​ than bare niobium [2]. Our collaborative investigation shows that this improvement is attributed to tantalum's less lossy surface oxide, which contains fewer sub-oxides than niobium oxide. Moreover, the amorphous Ta2O5 shows a bonding nature closer to crystalline form than amorphous Nb2O5, potentially reducing hydrogen diffusion toward the oxide/metal interface [1, 2]. Moreover, we will briefly discuss our preliminary study of the thin film structure under cryogenic conditions down to 20K, conducted using a liquid helium TEM holder in a Thermo Cs-corrected Titan. We also explored the effect of aluminum deposition rates on aluminum oxide microstructure and qubit lifetime. Although increasing the deposition rate from 0.5 Å/s to 5 Å/s significantly improved oxide layer roughness and thickness variation, the qubits’ coherence remained unchanged. This is likely due to Cooper pairs only tunneling through the thinnest parts of the barrier, making them less affected by the grain boundaries in the thin aluminum films. Additionally, we uncovered a stress-induced grain boundary sliding mechanism, which contributes to short-circuit failures in JJs [4]. Our discovery provides vital insight into oxide microstructure and superconducting qubits’ functionality [5].
times 2 to 5 times longer than baseline niobium qubit devices with native niobium oxides. When capping niobium with tantalum, we obtain median qubit lifetimes above 200 microseconds. Our comparative structural and chemical analysis suggests that amorphous niobium oxides may induce higher losses compared to other amorphous oxides. These results are in line with high-accuracy measurements of the niobium oxide loss tangent obtained with ultra-high Q superconducting radiofrequency (SRF) cavities. This new surface encapsulation strategy enables even further reduction of dielectric losses via passivation with ambient-stable materials, while preserving fabrication and scalable manufacturability thanks to the compatibility with silicon processes.
The performance of superconducting quantum circuits for quantum computing has advanced tremendously in recent decades; however, a comprehensive understanding of relaxation mechanisms does not yet exist. In this work, we utilize a multimode approach to characterizing energy losses in superconducting quantum circuits, with the goals of predicting device performance and improving coherence through materials, process, and circuit design optimization. Using this approach, we measure significant reductions in surface and bulk dielectric losses by employing a tantalum-based materials platform and annealed sapphire substrates. With this knowledge we predict the relaxation times of aluminum- and tantalum-based transmon qubits, and find that they are consistent with experimental results. We additionally optimize device geometry to maximize coherence within a coaxial tunnel architecture, and realize on-chip quantum memories with single-photon Ramsey times of 2.0 - 2.7 ms, limited by their energy relaxation times of 1.0 - 1.4 ms. These results demonstrate an advancement towards a more modular and compact coaxial circuit architecture for bosonic qubits with reproducibly high coherence.
State-of-the-art transmon qubits rely on large capacitors, which systematically improve their coherence due to reduced surface-loss participation. However, this approach increases both the footprint and the parasitic cross-coupling and is ultimately limited by radiation losses---a potential roadblock for scaling up quantum processors to millions of qubits. In this work we present transmon qubits with sizes as low as $36\phantom{\rule{0.2em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.2em}{0ex}}39\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{m}}^{2}$ with $\ensuremath{\gtrsim}100$-nm-wide vacuum-gap capacitors that are micromachined from commercial silicon-on-insulator wafers and shadow evaporated with aluminum. We achieve a vacuum participation ratio up to 99.6% in an in-plane design that is compatible with standard coplanar circuits. Qubit relaxation-time measurements for small gaps with high zero-point electric field variance of up to 22 V/m reveal a double exponential decay indicating comparably strong qubit interaction with long-lived two-level systems. The exceptionally high selectivity of up to 20 dB to the superconductor-vacuum interface allows us to precisely back out the sub-single-photon dielectric loss tangent of aluminum oxide previously exposed to ambient conditions. In terms of future scaling potential, we achieve a ratio of qubit quality factor to a footprint area equal to $20\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{m}}^{\ensuremath{-}2}$, which is comparable with the highest T1{T}_{1}T1​ devices relying on larger geometries, a value that could improve substantially for lower surface-loss superconductors.