Post-Processing Derived Outputs

Derived outputs convert Q3D matrices into qubit design metrics such as Ec, Ej, g, chi, ZZ, and Purcell rate.

#	Parameter	Symbol / Unit	Extraction Method	Typical Q3D Value	Ideal / Optimal	Good Range	Worst Case	Why It Matters	Key Design Note
52	Charging Energy (Ec/h)	Ec / h·MHz	Ec = e²/(2C_Σ); C_Sigma from Q3D Maxwell matrix	200 – 350 MHz	200 – 350 MHz (transmon optimum)	150 – 400 MHz	< 50 or > 1 GHz	Sets charge sensitivity; Ej/Ec = 50–80 ideal for transmon; deviating worsens noise or anharmonicity	Ec/h = 200 MHz → C_Sigma = 91 fF; exact C_Sigma from Q3D is the critical input to Hamiltonian model
53	Josephson Energy (Ej/h)	Ej / h·GHz	Ej = Φ₀²/(2L_J) = Φ₀ I_c / 2π	10 – 30 GHz	10 – 30 GHz (Ej/Ec ~ 50–80)	5 – 50 GHz	< 2 or > 100 GHz	With Ec determines qubit frequency f₀₁ ≈ √(8EjEc)/h − Ec/h and anharmonicity α = −Ec/h	Ej is tunable via flux in split-junction transmons; Ej/Ec spread across chip sets yield
54	Qubit–Resonator Coupling (g / 2pi)	g / 2π / MHz	g = C_g/(C_Sigma) × √(ω_q ω_r)/2; C_g from Q3D off-diagonal	50 – 150 MHz	50 – 150 MHz (dispersive regime)	20 – 300 MHz	< 5 or > 500 MHz	Vacuum Rabi coupling; in dispersive regime (g ≪ Δ) enables QND readout without qubit decay	g/Δ < 0.1 ensures dispersive limit; Purcell rate Γ_P = (g/Δ)² × κ scales as g²
55	Dispersive Shift (chi/2π)	chi / 2π / MHz	chi = g²/Δ × α/(Δ+α); Δ = ω_q − ω_r; all from Q3D + junction params	1 – 5 MHz	1 – 5 MHz	0.5 – 10 MHz	< 0.1 or > 20 MHz	Qubit-state-dependent resonator shift; single-shot readout SNR ∝ chi/κ; larger chi → better fidelity	chi and Purcell rate trade off via g; Purcell filter allows larger g without excess Purcell loss
56	ZZ Coupling Rate (ζ/2π)	ζ / 2π / kHz	ζ = 2g²χ²/(Δ·α·(Δ+α)); derived from Q3D coupling capacitances	10 – 100 kHz	< 10 kHz	10 – 50 kHz	> 200 kHz	Always-on conditional phase rate between qubits; leads to leakage in spectator qubits during gates	ZZ suppression is the central challenge of transmon scaling; tunable coupler can push ζ < 1 kHz
57	Anharmonicity (alpha / 2pi)	α / 2π / MHz	α = −Ec/h; Ec from Q3D C_Sigma; or directly measured by two-tone spectroscopy	−200 to −300 MHz	−300 to −150 MHz	−350 to −100 MHz	|α|/2π < 50 MHz	Separates |0〉→|1〉 from |1〉→|2〉 transitions; sets minimum gate duration without leakage	Gate bandwidth BW < |α|/(2π) required to avoid leakage; |α| = 200 MHz → t_gate > 5 ns
58	Purcell Decay Rate (Γ_P/2π)	Γ_P / 2π / kHz	Γ_P = (g/Δ)² × κ; κ = ω_r/Q_ext from Q3D; g from coupling cap	1 – 10 kHz	< 1 kHz (with Purcell filter)	1 – 10 kHz	> 100 kHz	Resonator-induced qubit relaxation limiting T₁ even with long material T₁; mitigated by filter	Purcell filter (bandpass on resonator port) can reduce Γ_P by 10–100× without affecting readout