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Synopsis

Efficient and noise-robust two-qubit gates are essential for scalable trapped-ion quantum computing. This thesis extends existing power-optimal methods for robust multitone Mølmer–Sørensen gate design and develops tone-number-efficient optimization methods to reduce the number of frequency tones required to implement gates on arbitrary ion pairs. Using a quadrature approximation of the motional infidelity, we derive a quadratic formulation of the robustness constraint that enables both spectral and gradient-based optimization. The eigenspectrum of the resulting motional-infidelity matrix, together with an infidelity-based eigenvalue cutoff, provides a geometric interpretation of existing power-optimal AMFM and ENS solutions and the design trade-offs between optical power and gate duration, robustness, ion number, and ion-pair separation. Building on this framework, we obtain tone-numberefficient (TNE) gate solutions using gradient-based ℓ1-norm optimization of the frequencytone amplitudes, subject to the gate and robustness constraints, followed by post-processing to remove residual low-amplitude tones. Compared with direct amplitude thresholding of poweroptimal ℓ2-norm solutions, the resulting TNE solutions require substantially fewer tones, achieve experimentally practical tone numbers over the parameter ranges considered, and retain optical powers and robustness comparable to those of the corresponding power-optimal solutions. Furthermore, an effective constraint bound derived from the ENS eigenspectrum and target infidelity provides a useful estimate of the required tone number.

For Zoom link info, please contact Lindiwe Coyne at physgrad@sfu.ca.