Qubit–Feedline T1 Estimator

Qubit–Feedline T₁ Estimator

C_mf and C_gnd are read from simulation lookup tables and log-linearly interpolated. T₁ is calculated with input-output theory.

BEM simulation

Method: Boundary-element method (BEM), Maxwell capacitance matrix
Substrate: Half silicon / half vacuum — ε_eff = (1 + ε_Si)/2 = 6.35
Feedline: Length 1.98 mm, centre-conductor width 10 μm, gap 5.5 μm each side
Boundary box: 2 mm × 2 mm
Grid: R ∈ … μm · D ∈ … μm · s ∈ … μm

Interpolation: Trilinear log-space (geometric mean in each dimension)

ⓘ Accuracy note: Capacitances from this calculator are more likely to be underestimated than overestimated, typically by ~20 %. Two reasons: (1) the BEM solves for charge distribution in 2D rather than full 3D field lines — mathematically equivalent only under idealised assumptions; (2) for large islands or wide centre-to-centre distances the feedline segment can no longer be treated as infinitely long, reducing the effective coupling captured by the simulation.

Simulation source

BEM FEM Both

⚠ FEM data not yet available — qubit-feedline-t1-fem.csv not found. Showing BEM results only.

⚠ Parameter combination is outside or near the edge of the lookup grid — result involves extrapolation and may be less accurate.

Geometry Island radius R (μm): —

Centre-to-centre distance D (μm): —

Island gap width s (μm): —

T₁ calculation parameters Qubit frequency f_q (GHz):

Total qubit capacitance C_Σ (fF):

Feedline impedance Z₀ (Ω):

Results at current D

—

C_mf (aF) — feedline coupling

—

T₁ (μs) — feedline decay

—

C_gnd (fF) — island to ground

—

C_self (fF) — island total cap

C_mf (aF) — log

Centre-to-centre distance D (μm)

T₁ (μs) — log

Centre-to-centre distance D (μm)

Formulas

Quantity	Formula / Note
C_mf, C_gnd, C_self	Log-linearly interpolated from simulation table in (R, D, s). C_mf = \|C_{feedline,island}\|, C_gnd = \|C_GND,island\|, C_self = C_{island,island} (Maxwell matrix diagonal).
Angular frequency	ω = 2πf_q
T₁ (input-output theory)	T₁ = C_Σ / (2ω² C_mf² Z₀)
Factor of 2	Two ports of an infinite matched feedline (power radiated both ways)
Validity	ω C_mf Z₀ ≪ 1 (weak coupling; typically ~10⁻⁴)

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