ION HEIGHT TRADE-OFF WITH PSEUDOPOTENTIAL STRENGTH: IMPLICATIONS FOR MOTIONAL HEATING, OPTICAL ACCESS, AND SCALABILITY IN LARGE-SCALE ION-TRAP ARRAYS

Abstract

Scaling surface-electrode ion traps to hundreds of qubits requires a careful balance between competing geometric constraints. Reducing the ion height above the electrode plane deepens the radiofrequency pseudopotential and stiffens confinement, yet it simultaneously enhances anomalous motional heating and restricts the numerical aperture available for laser addressing and fluorescence collection. This study quantifies these trade-offs across an ion-height range of 30 to 200 micrometres using a simulated dataset of 18 configurations and ten derived performance metrics. Power-law, exponential, and polynomial regression models were applied to characterize heating-rate scaling, pseudopotential decay, and array performance. The motional heating rate followed an inverse power-law in ion height with exponent α = 2.02 (nonlinear least-squares fit, R² = 0.988), while the pseudopotential depth decayed exponentially with a decay constant of 0.0269 µm⁻¹ (R² = 0.990). A composite figure of merit combining trap stability, gate fidelity, optical access, and array capacity peaked at 132 µm (FOM = 0.969, R² = 0.999), identifying this height as the optimal design point for balancing trapping strength against decoherence. Pearson correlation analysis revealed near-perfect positive coupling between ion height and trap stability (r = 1.00) and near-perfect negative coupling with radial secular frequency (r = −0.95). These results provide quantitative design guidance for next-generation quantum charge-coupled device architectures and support the growing consensus that mid-range ion heights offer the most favourable operating regime for scalable trapped-ion quantum computing.

Keywords : ion trap, pseudopotential, motional heating, anomalous heating, quantum computing, surface-electrode trap, optical access, quantum charge-coupled device.