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arXiv:2512.18156

Lattice-Renormalized Tunneling Models for Superconducting Qubit Materials

P. G. Pritchard, James M. Rondinelli

quant-phcond-mat.mtrl-sciSubmitted Dec 20, 2025• Announced Dec 23, 2025• 0 citations• Revised Mar 10, 2026 (v2)
v1 · Dec 20, 2025v2 · Mar 10, 2026
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Abstract

We present a lattice-renormalized formalism for configurational tunneling two-level systems (TLS) that overcomes limitations of minimum-energy-path and light-particle models. Derived from the nuclear Hamiltonian, our formulation introduces composite phonon coordinates to capture lattice distortions between degenerate potential wells. This approach resolves deficiencies in prior models and enables accurate computation of tunnel splittings and excitation spectra for hydrogen-based TLS in bcc Nb. Our results bound experimental tunnel splittings and reveal strong anharmonic couplings between tunneling atoms and lattice phonons, establishing a direct link between TLS dynamics and phonon-mediated strain interactions. The formalism further generalizes to multi-level systems (MLS), providing insight into defect-induced decoherence in superconducting qubits and guiding strategies for materials design to suppress TLS-related loss.

Comments
13 pages, 4 figures, 6 tables

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We present a lattice-renormalized formalism for configurational tunneling two-level systems (TLS) that overcomes limitations of minimum-energy-path and light-particle models. Derived from the nuclear Hamiltonian, our formulation introduces composite phonon coordinates to capture lattice distortions between degenerate potential wells. This approach resolves deficiencies in prior models and enables accurate computation of tunnel splittings and excitation spectra for hydrogen-based TLS in bcc Nb. Our results bound experimental tunnel splittings and reveal strong anharmonic couplings between tunneling atoms and lattice phonons, establishing a direct link between TLS dynamics and phonon-mediated strain interactions. The formalism further generalizes to multi-level systems (MLS), providing insight into defect-induced decoherence in superconducting qubits and guiding strategies for materials design to suppress TLS-related loss.
Interstitial hydrogen and deuterium in body-centered-cubic metals constitute archetypal quantum tunneling systems. Their relevance has been renewed by the connection between hydrogenic tunneling in Nb and defect-induced decoherence in superconducting qubits, motivating a predictive microscopic theory. Existing theoretical treatments invoke an adiabatic separation between the light interstitial and the host lattice, an assumption whose validity has not been rigorously established for hydrogenic species. Here, we show that the experimentally measured tunnel splittings of O-trapped H and D in bcc Nb are quantitatively well-described within a five-dimensional (5D) Lattice-Renormalized Born-Oppenheimer (LRBO) framework. This approach treats three interstitial modes and two judiciously selected lattice modes, which includes a transition-state mode, on equal quantum footing. By recasting nested Born-Oppenheimer hierarchies within this same formalism and benchmarking against modern \textit{ab initio} potential energy surfaces, we show that adiabatic separation of the light particle from lattice dynamics is satisfied only in the positive-muon (μ+μ^{+}μ+) mass limit. In contrast, tunneling for H and D is fundamentally a collective, nonadiabatic process mediated by anharmonic lattice couplings. Finally, we show that the breakdown of adiabaticity can be anticipated from simple energy estimates involving the ground-state light-particle energy evaluated at a small number of fixed lattice configurations, providing a practical criterion for assessing the validity of adiabatic tunneling theories in other systems.
Noise within solid-state systems at low temperatures can typically be traced back to material defects. In amorphous materials, these defects are broadly described by the tunneling two-level systems (TLSs) model. TLS have recently taken on further relevance in quantum computing because they dominate the coherence limit of superconducting quantum circuits. Efforts to mitigate TLS impacts have thus far focused on circuit design, material selection, and surface treatments. Our work takes an approach that directly modifies TLS properties. This is achieved by creating an acoustic bandgap that suppresses all microwave-frequency phonons around the operating frequency of a transmon qubit. For embedded TLS strongly coupled to the transmon qubit, we measure a pronounced increase in relaxation time by two orders of magnitude, with the longestT1time exceeding 5 milliseconds. Our work opens avenues for studying the physics of highly coherent TLS and methods for mitigating noise within solid-state quantum devices.
Two-level systems (TLSs) are the dominant source of decoherence in superconducting qubits, a leading platform for quantum computing. While TLSs are believed to arise from atomic-scale tunneling defects, their precise structural origins, particularly at complex and disordered interfaces in real devices, have remained elusive. Conventional structural characterization is extremely challenging because these interfaces are non-periodic, containing steps and roughness, and device-relevant TLS defects involve only atomic motions with small energy differences. We have determined the atomic character of candidate TLSs at the Al-Si interface of a superconducting qubit using aberration-corrected scanning transmission electron microscopy (STEM) combined with experiment-constrained 3D structure modeling and computational defect searching. High-angle annular dark-field (HAADF) STEM images were obtained from a disordered interface containing a prominent step defect and localized strain. Structure modeling started with 3D models created in the Ingrained framework to match the experimental projections, accounting for mistilt and uniform strain. These models were then refined using FANTASTX (Fully Automated Nanoscale To Atomistic Structure from Theory and eXperiments), a multi-objective optimizer that simultaneously minimizes disagreement with the experimental image via structural similarity and the ab initio (DFT) total system energy. Transition-state searches with the activation relaxation technique nouveau (ARTn) on the refined models identified many atomic configurations occupying double-well potentials corresponding to TLS. Statistical analysis of over 1500 TLSs shows that candidate TLS with tunneling energies and asymmetries in the range relevant to superconducting qubits (∼5 GHz) predominantly involve Al atoms located near the interface. These atoms exhibit smaller median tunneling displacements (∼0.44 Å) than the non-candidate TLS and reside in locally disordered environments with marginally longer and less dense first-neighbor shells than those of non-candidate TLSs. The most probable candidate TLSs feature cooperative motion of one or two Al atoms, and sometimes with Si, in directions largely parallel to the interface. This work provides the first direct atomic-scale insight into the structural defects that may be responsible for decoherence at a realistic, device-relevant interface. It also demonstrates a scalable, generalizable workflow for solving the atomic structure of complex, disordered interfaces by integrating aberration-corrected STEM with advanced computational refinement and defect searching. The methodology is directly applicable to other materials systems and heterointerfaces critical to quantum devices [5].
Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.
Material defects give rise to parasitic two-level systems (TLS) which present a major source of decoherence in superconducting qubits. Here, we study a strongly coupled TLS that resides in the tunnel barrier of transmon qubit. We use multi-photon spectroscopy and TLS strain tuning to explore the rich spectrum of the interacting three-partite system consisting of TLS, qubit, and its readout resonator. This reveals a strong effective resonant coupling between the TLS and the qubit's readout resonator which dresses the resonator states and results in a resonance frequency shift that spoils the readout signal. Our finding presents yet another way how material defects can interfere with qubit operation and hinder the realization of solid-state quantum processors.
Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.