The effects of disorder in superconducting materials on qubit coherence

Introducing disorder in the superconducting materials has been considered promising to enhance the electromagnetic impedance and realize noise-resilient superconducting qubits. Despite a number of pioneering implementations, the understanding of the correlation between the material disorder and the qubit coherence is still developing. Here, we demonstrate a systematic characterization of fluxonium qubits with the superinductors made by spinodal titanium-aluminum-nitride with varied disorder. From qubit noise spectroscopy, the flux noise and the dielectric loss are extracted as a measure of the coherence properties. Our results reveal that the 1/f ^α flux noise dominates the qubit decoherence around the flux-frustration point, strongly correlated with the material disorder; while the dielectric loss are largely similar under a wide range of material properties. From the flux-noise amplitudes, the areal density (σ) of the phenomenological spin defects and material disorder are found to be approximately correlated by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>σ</mml:mi> <mml:mo>∝</mml:mo> <mml:msubsup><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow> <mml:mrow><mml:mi>x</mml:mi> <mml:mi>x</mml:mi></mml:mrow> <mml:mrow><mml:mn>3</mml:mn></mml:mrow> </mml:msubsup> </mml:math> , or effectively <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow><mml:mrow><mml:mo>(</mml:mo> <mml:mrow> <mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow> <mml:mrow><mml:mi>F</mml:mi></mml:mrow> </mml:msub> <mml:mi>l</mml:mi></mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:mrow> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>3</mml:mn></mml:mrow> </mml:msup> </mml:math> . This work has provided new insights on the origin of decoherence channels beyond surface defects and within the superconductors, and could serve as a useful guideline for material design and optimization.