Loss & Dissipation

Loss & Dissipation Parameters: Dielectric, surface, radiation, and junction loss

channels identified and weighted by EPR participations

1. Dielectric Loss (Bulk & Surface)

Parameter	Symbol	Unit	Description	Optimal / Best Value	Good Range	Acceptable Range	Poor / Worst Value	Physical Significance
Bulk Substrate Loss Tangent	tan delta_bulk	dimensionless	Intrinsic dielectric loss of the substrate material (Si, sapphire, SiO2); weighted by bulk EPR participation.	< 1×10⁻⁷ (Si, sapphire)	< 1×10⁻⁶	1×10⁻⁶ – 1×10⁻⁵	> 1×10⁻⁴	Silicon and sapphire are preferred substrates; amorphous SiO2 has tan δ ~ 10⁻³ (very poor).
Metal-Substrate Interface Loss	tan delta_MS	dimensionless	Effective loss tangent of metal–substrate (MS) two-level system (TLS) interface layer.	< 1×10⁻³	< 3×10⁻³	3×10⁻³ – 1×10⁻²	> 5×10⁻²	MS interface is typically 2–5 nm thick oxide layer; dominant loss in many planar qubits.
Substrate-Air Interface Loss	tan delta_SA	dimensionless	Effective loss tangent of substrate–air (SA) interface; due to adsorbed surface oxides and organics.	< 3×10⁻³	< 1×10⁻²	1×10⁻² – 5×10⁻²	> 0.1	Cleaning and surface passivation reduce SA loss; participation ratio from EPR isolates this channel.
Metal-Air Interface Loss	tan delta_MA	dimensionless	Effective loss tangent of metal–air (MA) interface; native oxide on superconducting film top surface.	< 3×10⁻³	< 1×10⁻²	1×10⁻² – 5×10⁻²	> 0.1	Nb and Al form native oxides; replacing top surface with clean metal reduces MA loss.
Surface Participation Ratio (MS)	p_MS	dimensionless	Fraction of electric field energy in metal-substrate interface region; computed from EPR E-field.	< 5×10⁻⁴	< 2×10⁻³	2×10⁻³ – 1×10⁻²	> 5×10⁻²	Thinner gaps increase p_MS; EPR identifies geometry changes to reduce interface participation.
TLS-Limited Quality Factor (1/f)	Q_TLS	dimensionless	Quality factor limited by two-level system (TLS) bath; power- and temperature-dependent.	> 3×10⁶	10⁶ – 3×10⁶	10⁵ – 10⁶	< 10⁴	Q_TLS improves with high drive power (TLS saturation); EPR participations give TLS contribution breakdown.

2. Radiation & Geometry Loss

Parameter	Symbol	Unit	Description	Optimal / Best Value	Good Range	Acceptable Range	Poor / Worst Value	Physical Significance
Radiation Loss Rate	gamma_rad / 2pi	kHz	Energy loss due to electromagnetic radiation from non-closed geometry; computed by EPR from far-field.	< 1 kHz	< 10 kHz	10 – 100 kHz	> 500 kHz	Open transmission line stubs or poorly designed ground planes lead to radiation loss.
Seam Loss (3D cavities)	gamma_seam / 2pi	kHz	Loss at mechanical seam between cavity halves; critical for 3D transmon and fluxonium devices.	< 1 kHz	< 5 kHz	5 – 50 kHz	> 200 kHz	EPR current participation at seam predicts seam loss; improved by indium bonding or tight tolerances.
Quasiparticle Loss Rate	gamma_qp / 2pi	kHz	Qubit decay due to nonequilibrium quasiparticles tunneling across junction.	< 2 kHz	< 20 kHz	20 – 100 kHz	> 500 kHz	Quasiparticle poisoning is stochastic; mitigated by gap engineering and quasiparticle traps.
Vortex Loss (in-field operation)	gamma_vortex / 2pi	kHz	Loss from magnetic vortices in superconducting film when operated in residual magnetic field.	< 1 kHz (< 1 µT shield)	< 10 kHz	10 – 100 kHz	> 500 kHz	Mitigated by magnetic shielding and moat structures; EPR current maps identify vortex-sensitive areas.
Conductor (Ohmic) Loss	gamma_ohm / 2pi	kHz	Residual ohmic loss from non-superconducting regions or above Tc contributions; usually negligible in Al.	< 0.1 kHz	< 1 kHz	1 – 10 kHz	> 100 kHz	Typically negligible at mK temperatures; relevant for normal-metal contacts or resistive wirebonds.