Thermal & Loss Parameters

Loss and thermal checks for dielectric, conductor, substrate, TLS, radiation, and

package-related dissipation.

#	VER ID	Parameter	Severity	Design Rule / Constraint	Ideal / Optimal Value	Acceptable Range	Good	Bad	Why It Matters
41	HFSS-T-001	Dielectric Loss Tangent	Critical	tan δ < 10⁻⁶ (bulk substrate, Si or Al₂O₃)	< 10⁻⁶	10⁻⁷ – 10⁻⁵	< 10⁻⁶ (Si/sapphire): substrate contribution to T₁⁻¹ < 1 kHz; Q_i > 10⁶	> 10⁻³ (SiO₂, organics): dielectric loss dominates; T₁ < 1 µs; unacceptable	Bulk dielectric loss factor. Mandates high-resistivity Si or c-plane sapphire; amorphous oxides and organics are lossy.
43	HFSS-T-003	Dissipated Power P_sub	High	P_sub < 1 pW per qubit at design drive level	< 0.1 pW	0.1 – 100 pW	< 0.1 pW: quasiparticle generation rate negligible; T₁ not QP-limited	> 1 nW: significant quasiparticle poisoning; T₁ collapses in µs timescale	Power deposited in substrate at millikelvin temperatures. Excess heating raises quasiparticle population, reducing T₁.
44	HFSS-T-004	Thermal NEP	Medium	NEP < 10⁻²⁰ W/√Hz at qubit frequency (20 mK)	< 10⁻²⁰ W/√Hz	10⁻²⁰ – 10⁻¹⁸	< 10⁻²⁰: thermal photon occupancy n_th < 10⁻³; qubit not spuriously excited	> 10⁻¹⁶: near-classical noise floor; qubit excited multiple times per measurement cycle	Thermal noise equivalent power at qubit frequency. Drives spurious qubit excitation and sets fundamental measurement noise floor.
45	HFSS-T-005	TLS Loss Rate 1/T₁_TLS	Critical	1/T₁_TLS < 1 kHz (TLS contribution to decay)	< 0.5 kHz	0.5 – 10 kHz	< 0.5 kHz: TLS loss gives T₁_TLS > 2 ms; not limiting coherence budget	> 100 kHz: TLS dominates all other T₁ channels; requires redesign	Decay rate contribution from two-level system defects at metal–substrate, metal–air, and substrate–air interfaces.
46	HFSS-T-006	Conductor Loss α_c	Medium	α_c < 0.001 dB/m in SC resonator lines	< 0.0001 dB/m	0.0001 – 0.1 dB/m	< 0.0001 dB/m: ohmic loss negligible vs radiation and TLS loss in SC lines	> 1 dB/m: conductor loss dominates; normal-metal sections or damaged SC film	Ohmic attenuation per unit length. Negligible in good superconductors far below Tc; dominant in normal metal or granular films.
47	HFSS-T-007	Package Radiation Loss 1/Q_rad	High	1/Q_rad < 10⁻⁷ (shielded package)	< 10⁻⁷	10⁻⁷ – 10⁻⁵	< 10⁻⁷: radiation Q > 10⁷; package does not limit resonator or qubit Q	> 10⁻⁴: radiation loss comparable to TLS loss; package seams/vias must be redesigned	Inverse radiation Q. Power fraction radiated from chip to environment via package seams, slots, and via fields.