Summary Table

EPR Analysis — Master Summary Table: All EPR output parameters consolidated — one

row per parameter, sorted by category

Core EPR

#	Category	Parameter	Symbol	Unit	Optimal Value	Good Range	Acceptable Range	Worst Value	Physical Significance	Improvement Strategy
1	Core EPR	Junction Participation Ratio	p_J	—	0.90–0.99	0.80–0.99	0.50–0.79	< 0.30	Sets anharmonicity & qubit nonlinearity	Increase pad size, reduce gap to substrate
2	Core EPR	Resonator Junction Participation	p_J^res	—	< 1×10⁻³	< 1×10⁻²	1×10⁻²–5×10⁻²	> 0.10	Determines Purcell T_1 limit	Increase qubit-resonator detuning
3	Core EPR	ZPF Voltage across Junction	V_zpf	µV	10–50 µV	5–100 µV	1–200 µV	< 0.5 µV	Governs qubit-photon coupling	Optimise mode volume and pad geometry
4	Core EPR	ZPF Phase	varphi_zpf	rad	0.1–0.5 rad	0.05–0.6 rad	0.6–0.9 rad	> 1.0 rad	Validity of dispersive approximation	Reduce anharmonicity target or redesign
5	Core EPR	Anharmonicity (EPR)	alpha / 2pi	MHz	150–350 MHz	100–400 MHz	50–99 MHz	< 30 MHz	Gate speed and leakage limit	Lower E_J / E_C ratio; smaller junction
6	Core EPR	Dispersive Shift chi	chi/2π	MHz	0.5–3 MHz	0.1–5 MHz	0.01–0.09 MHz	< 0.01 MHz	Readout contrast	Adjust g/|Δ| ratio via geometry
7	Core EPR	Cross-Kerr ZZ	zeta_ij / 2pi	MHz	< 0.01 MHz	< 0.10 MHz	0.10–0.50 MHz	> 1.0 MHz	Always-on 2Q gate error	Tunable coupler; echo sequences

Qubit Performance

#	Category	Parameter	Symbol	Unit	Optimal Value	Good Range	Acceptable Range	Worst Value	Physical Significance	Improvement Strategy
8	Qubit Performance	Energy Relaxation T_1	T_1	µs	> 500 µs	100–500 µs	10–99 µs	< 1 µs	Hard limit on gate fidelity	Reduce dominant loss channel from EPR
9	Qubit Performance	Coherence Time T2*	T2*	µs	> 300 µs	100–300 µs	20–99 µs	< 10 µs	Practical dephasing limit	Reduce flux/charge noise; surface cleaning
10	Qubit Performance	Qubit Quality Factor	Q_q	—	> 10⁷	10⁶–10⁷	10⁵–10⁶	< 10⁴	Universal figure of merit	Reduce all participation-weighted losses
11	Qubit Performance	Single-Qubit Gate Fidelity	F_1Q	%	> 99.9%	99.5–99.9%	99.0–99.4%	< 98%	Surface-code threshold	Increase T_1/T2; optimise DRAG pulses
12	Qubit Performance	Two-Qubit Gate Fidelity	F_2Q	%	> 99.5%	99.0–99.5%	97.0–98.9%	< 95%	2Q error correction threshold	Reduce ZZ via tunable coupler design
13	Qubit Performance	E_J / E_C Ratio	E_J / E_C	—	50–100	40–120	20–39	< 10	Charge noise protection	Increase shunt capacitance C_S

Resonator & Coupling

#	Category	Parameter	Symbol	Unit	Optimal Value	Good Range	Acceptable Range	Worst Value	Physical Significance	Improvement Strategy
14	Resonator & Coupling	Resonator Frequency	omega_r / 2pi	GHz	6.5–8.5 GHz	5–10 GHz	3–5 GHz	< 2 GHz	Dispersive regime requirement	Adjust resonator length/capacitance
15	Resonator & Coupling	Resonator Internal Q	Q_int	—	> 10⁵	10⁴–10⁵	10³–10⁴	< 500	Readout SNR and back-action	Improve substrate and metal quality
16	Resonator & Coupling	Coupling Strength g / 2pi	g / 2pi	MHz	50–150 MHz	20–200 MHz	5–19 MHz	< 2 MHz	Sets chi and readout bandwidth	Adjust coupling capacitor geometry
17	Resonator & Coupling	Purcell Decay Rate	γ_P/2π	kHz	< 1 kHz	1–10 kHz	10–100 kHz	> 500 kHz	T_1 limit via resonator	Add Purcell filter; increase detuning
18	Resonator & Coupling	Residual ZZ Static	zeta_ZZ / 2pi	kHz	< 10 kHz	< 100 kHz	100–500 kHz	> 1 MHz	Conditional phase error	Tunable coupler; frequency detuning

Loss & Dissipation

#	Category	Parameter	Symbol	Unit	Optimal Value	Good Range	Acceptable Range	Worst Value	Physical Significance	Improvement Strategy
19	Loss & Dissipation	Bulk Substrate Loss Tangent	tan delta_bulk	—	< 1×10⁻⁷	< 1×10⁻⁶	1×10⁻⁶–1×10⁻⁵	> 1×10⁻⁴	Bulk energy dissipation	Use float-zone Si or sapphire
20	Loss & Dissipation	Metal-Substrate Interface Loss	tan delta_MS	—	< 1×10⁻³	< 3×10⁻³	3×10⁻³–1×10⁻²	> 5×10⁻²	Dominant TLS loss channel	Ion mill before deposition; clean surfaces
21	Loss & Dissipation	Surface Participation (MS)	p_MS	—	< 5×10⁻⁴	< 2×10⁻³	2×10⁻³–1×10⁻²	> 5×10⁻²	Weights MS interface loss to T_1	Wider gaps; ground plane design
22	Loss & Dissipation	TLS-Limited Q	Q_TLS	—	> 3×10⁶	10⁶–3×10⁶	10⁵–10⁶	< 10⁴	TLS bath limitation	Surface treatment; new barrier materials
23	Loss & Dissipation	Seam Loss Rate (3D)	gamma_seam / 2pi	kHz	< 1 kHz	< 5 kHz	5–50 kHz	> 200 kHz	3D cavity assembly limit	Indium sealing; tighter tolerances

Junction Parameters

#	Category	Parameter	Symbol	Unit	Optimal Value	Good Range	Acceptable Range	Worst Value	Physical Significance	Improvement Strategy
24	Junction Parameters	Josephson Inductance	L_J	nH	5–20 nH	2–50 nH	50–200 nH	> 500 nH	Sets qubit frequency	Junction area and J_c control
25	Junction Parameters	Josephson Energy	E_J / h	GHz	10–50 GHz	5–100 GHz	100–500 GHz	> 1 THz	Qubit spectrum with EC	Barrier thickness and area
26	Junction Parameters	Charging Energy	E_C / h	MHz	150–350 MHz	100–500 MHz	500–1000 MHz	> 2 GHz	Anharmonicity and charge sensitivity	Shunt capacitor area tuning
27	Junction Parameters	Junction Loss Tangent	tan delta_J	—	< 3×10⁻⁶	< 1×10⁻⁵	1×10⁻⁵–1×10⁻⁴	> 1×10⁻³	Intrinsic junction T_1 limit	ALD AlOx; crystalline barriers

Simulation

#	Category	Parameter	Symbol	Unit	Optimal Value	Good Range	Acceptable Range	Worst Value	Physical Significance	Improvement Strategy
28	Simulation	Eigenfrequency Convergence	Delta f / f	ppm	< 5 ppm	< 50 ppm	50–500 ppm	> 1000 ppm	Accuracy of all extracted parameters	More refinement passes; finer mesh
29	Simulation	Energy Error	Delta U / U	%	< 0.1%	< 0.5%	0.5–2%	> 5%	Bounds participation ratio error	Increase mesh density at interfaces
30	Simulation	Participation Sum Check	sum p	—	0.99–1.01	0.97–1.03	0.93–1.07	< 0.90 or > 1.10	Simulation completeness check	Include all eigenmodes up to 20 GHz

Total Parameters: 30