Thermal & Loss Parameters
=========================

Loss and thermal checks for dielectric, conductor, substrate, TLS, radiation, and
                package-related dissipation.

.. list-table::
   :header-rows: 1

   * - #
     - 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.