Surface participation and dielectric loss in transmons

Short answer: Much of the energy loss in a superconducting qubit comes from thin lossy layers on the surfaces and interfaces of the metal. A 2015 Applied Physics Letters paper studied transmon relaxation against the calculated fraction of electric field energy in those layers, called the surface participation ratio, and found an approximately proportional relation. A 2022 npj Quantum Information paper provides formulas to predict surface loss for simple qubit geometries and finds a significant share comes from the small wire to the junction. These are experiments and calculations.

The idea of participation

The 2015 abstract defines the surface participation ratio as the fraction of electric field energy stored in a dissipative surface layer. If a qubit's energy sits partly in a lossy layer, it decays faster, and the more of its field energy that sits there, the shorter its relaxation time T1. The ratio can be calculated and changed by altering the qubit geometry.

2015: measured against geometry

The Yale authors study the energy relaxation times of transmon qubits in 3D cavities as a function of surface participation ratios. They compute the ratio with a two-step finite-element simulation and vary it experimentally through qubit geometry. With a clean electromagnetic environment and suppressed non-equilibrium quasiparticle density, they find an approximately proportional relation between relaxation rates and surface participation ratios. They suggest that dielectric dissipation from material interfaces is the major limiting factor for transmon T1 in 3D circuit QED, and that their analysis supports spatial discreteness of surface dielectric dissipation. Both statements are their conclusions from this set of devices.

2022: formulas for layout

The npj Quantum Information abstract presents analytical formulas for simplified but useful qubit geometries that predict surface dielectric loss when the layer thickness is much less than the metal thickness, which they call the limiting case needed for real devices. The authors say the formulas can be used to predict loss precisely and to optimize layout. They report that, surprisingly, a significant fraction of surface loss comes from the small wire connecting the Josephson junction to the qubit capacitor, and that tapering the wire significantly lowers its loss. They also predict the size and density of the two-level state spectrum from individual surface dissipation sites.

A third source

An arXiv copy of the 2015 paper was listed as a source and carries the same abstract, so it adds no independent evidence.

Limits

The 2015 relation is approximate and was measured for transmons in 3D cavities, so it may not carry over to planar qubits. The 2022 formulas are for simplified geometries and a thin-layer limit, and the abstract describes predictions, not measured improvements from tapering. Neither paper identifies which specific material is the lossy layer.

FAQ

What is surface participation?

The fraction of a qubit's electric field energy stored in a lossy surface layer.

How did relaxation depend on it?

Approximately proportionally, per the 2015 Yale authors.

What did the 2022 paper predict?

That a significant share of surface loss comes from the wire to the junction, and that tapering it lowers loss.

Does this show where the loss is?

It points to material interfaces in general, without identifying one material.

Can designers use this?

The 2022 authors say their formulas can be used to optimize qubit layout.