Summary Table ============= EPR Analysis — Master Summary Table: All EPR output parameters consolidated — one row per parameter, sorted by category Core EPR .. list-table:: :header-rows: 1 * - # - 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 .. list-table:: :header-rows: 1 * - # - 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 .. list-table:: :header-rows: 1 * - # - 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 .. list-table:: :header-rows: 1 * - # - 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 .. list-table:: :header-rows: 1 * - # - 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 .. list-table:: :header-rows: 1 * - # - 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