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arXiv:2408.17218 · Communications Physics

Nonequilibrium regimes for quasiparticles in superconducting qubits with gap-asymmetric junctions

Giampiero Marchegiani, Gianluigi Catelani

Published Mar 27, 2025• 4 citations

Abstract

Superconducting qubits hold promise for quantum computing, but their operation is challenged by various sources of noise, including excitations known as quasiparticles. Qubits with gap asymmetry larger than their transition energy are less susceptible to quasiparticle decoherence as the quasiparticles are mostly trapped in the low-gap side of the junction. Because of this trapping, the gap asymmetry can contribute to maintaining the quasiparticles out of equilibrium. Here we address the temperature dependence of the quasiparticle densities in the two sides of the junction. We show that four qualitatively different regimes are possible with increasing temperature: (i) nonequilibrium, (ii) local quasiequilibrium, (iii) global quasiequilibrium, and (iv) full equilibrium. We identify shortcomings in assuming global quasiequilibrium when interpreting experimental data, highlighting how measurements in the presence of magnetic field can aid the accurate determination of the junction parameters, and hence the identification of the nonequilibrium regimes. Quasiparticle poisoning challenges the operation of superconducting qubits, but errors can be suppressed by engineering gap asymmetry between the electrodes of the qubit’s Josephson junction. The authors present a model of the qubit-quasiparticle system valid beyond the low-temperature limit and identify different nonequilibrium regimes, which can affect the interpretation of experimental data.

DOI: 10.1038/s42005-025-02052-x

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Superconducting qubits hold promise for quantum computing, but their operation is challenged by various sources of noise, including excitations known as quasiparticles. Qubits with gap asymmetry larger than their transition energy are less susceptible to quasiparticle decoherence as the quasiparticles are mostly trapped in the low-gap side of the junction. Because of this trapping, the gap asymmetry can contribute to maintaining the quasiparticles out of equilibrium. Here we address the temperature dependence of the quasiparticle densities in the two sides of the junction. We show that four qualitatively different regimes are possible with increasing temperature: (i) nonequilibrium, (ii) local quasiequilibrium, (iii) global quasiequilibrium, and (iv) full equilibrium. We identify shortcomings in assuming global quasiequilibrium when interpreting experimental data, highlighting how measurements in the presence of magnetic field can aid the accurate determination of the junction parameters, and hence the identification of the nonequilibrium regimes. Quasiparticle poisoning challenges the operation of superconducting qubits, but errors can be suppressed by engineering gap asymmetry between the electrodes of the qubit’s Josephson junction. The authors present a model of the qubit-quasiparticle system valid beyond the low-temperature limit and identify different nonequilibrium regimes, which can affect the interpretation of experimental data.

The quasiparticle density observed in low-temperature superconducting circuits is several orders of magnitude larger than the value expected at thermal equilibrium. The tunneling of this excess of quasiparticles across Josephson junctions is recognized as one of the main loss and decoherence mechanisms in superconducting qubits. Here we present a unified impedance theory that accounts for quasiparticle energy loss in circuit regions both far from and near to (across) junctions. Our theory leverages the recent experimental demonstration that the excess quasiparticles are in quasiequilibrium [Connolly et al., Phys. Rev. Lett. 132, 217001 (2024)] and uses a generalized fluctuation-dissipation theorem to predict the amount of charge and flux noise generated by them. We compute the resulting energy relaxation time

{T}_{1}

in transmon qubits with and without junction asymmetric gap engineering, and show that quasiparticles residing away from junctions can play a dominant role in the former case. They also may provide an upper limit for resonator quality factors if the density of amorphous two-level systems is reduced. In addition, we show that charge noise from quasiparticles leads to flux noise that is logarithmic in frequency, giving rise to a ``nearly white'' contribution that is comparable to the flux noise observed in flux qubits. This contrasts with amorphous two-level systems, whose associated flux noise is shown to be super-Ohmic. We discuss how this quasiparticle flux noise can limit ${T}_{2}^{\ensuremath{\ast}}$ coherence times in flux-tunable qubits. The final conclusion is that asymmetric gap engineering can greatly reduce noise and increase coherence times in superconducting qubits.

Designing the spatial profile of the superconducting gap-gap engineering-has long been recognized as an effective way of controlling quasiparticles in superconducting devices.In aluminum films, their thickness modulates the gap; therefore, standard fabrication of Al/AlO x /Al Josephson junctions, which relies on overlapping a thicker film on top of a thinner one, always results in gap-engineered devices.Here, we reconsider quasiparticle effects in superconducting qubits to explicitly account for the unavoidable asymmetry in the gap on the two sides of a Josephson junction.We find that different regimes can be encountered in which the quasiparticles have either similar densities in the two junction leads or are largely confined to the lower-gap lead.Qualitatively, for similar densities the qubit excited-state population is lower but its relaxation rate is higher than when the quasiparticles are confined; therefore, there is a potential trade-off between two desirable properties in a qubit.

The performance of various superconducting devices operating at ultra-low temperatures is impaired by the presence of non-equilibrium quasiparticles. Inelastic quasiparticle (QP) tunneling across Josephson junctions in superconducting qubits results in decoherence and spurious excitations and, notably, can trigger correlated errors that severely impede quantum error correction. In this work, we use "gap engineering" to suppress the tunneling of low-energy quasiparticles in Al-based transmon qubits, a leading building block for superconducting quantum processors. By implementing potential barriers for QP, we strongly suppress QP tunneling across the junction and preserve charge parity for over

10^3

seconds. The suppression of QP tunneling also results in a reduction in the qubit energy relaxation rates. The demonstrated approach to gap engineering can be easily implemented in all Al-based circuits with Josephson junctions.

Quasiparticles are a prominent decoherence source in superconducting qubits, but their effects are notoriously difficult to isolate in fluxonium. Unlike the transmon, fluxonium is insensitive to offset charge, precluding charge-parity detection of quasiparticle tunneling. We address this challenge by measuring the excitation and de-excitation rates in a fluxonium qubit under controlled on-chip quasiparticle injection and isolating the quasiparticle-induced contribution by subtracting the background transition rates. We show that to accurately model the external magnetic flux dependence of the quasiparticle-induced transition rates, it is necessary to account for the superconducting gap asymmetry across the Josephson junctions. A comparison between theory and experiment constrains the relative quasiparticle densities in the small junction and the junction array and helps explain previously reported discrepancies between the bounds on the quasiparticle densities inferred for these two circuit elements.

The density of quasiparticles typically observed in superconducting qubits exceeds the value expected in equilibrium by many orders of magnitude. Can this out-of-equilibrium quasiparticle density still possess an energy distribution in equilibrium with the phonon bath? Here, we answer this question affirmatively by measuring the thermal activation of charge-parity switching in a transmon qubit with a difference in superconducting gap on the two sides of the Josephson junction. We then demonstrate how the gap asymmetry of the device can be exploited to manipulate its parity.

Superconducting qubits probe environmental defects such as nonequilibrium quasiparticles, an important source of decoherence. We show that "hot" nonequilibrium quasiparticles, with energies above the superconducting gap, affect qubits differently from quasiparticles at the gap, implying qubits can probe the dynamic quasiparticle energy distribution. For hot quasiparticles, we predict a non-negligible increase in the qubit excited state probability Pe. By injecting hot quasiparticles into a qubit, we experimentally measure an increase of Pe in semiquantitative agreement with the model and rule out the typically assumed thermal distribution.