Loss & Dissipation
======================

Loss & Dissipation Parameters: Dielectric, surface, radiation, and junction loss
                channels identified and weighted by EPR participations

A. Dielectric Loss (Bulk & Surface)

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

   * - 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.

B. Radiation & Geometry Loss

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

   * - 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.