General Amplitude Modulation for Robust Trapped-Ion Entangling Gates

Trapped-ion systems are a promising route toward the realization of both near-term and universal quantum computers. One of the remaining challenges is improving the fidelity of two-qubit entangling gates. These operations are implemented by addressing individual ions with laser pulses using the Molmer-Sorensen protocol. A well-studied extension of this protocol is amplitude modulation, where the amplitude of the laser pulses is controlled as a function of time. The current thinking is that this allows tradeoffs to be made between the laser power, gate time, and fidelity. We present an analytical study of amplitude modulation using a Fourier series expansion so that the laser amplitudes may be represented as any continuous function in principle. We specifically look to reduce gate-timing errors, and we have shown that the sensitivity of the fidelity to gate-timing errors can be improved without a significant increase in the laser power or the gate time.