Power-optimized amplitude modulation for robust trapped-ion entangling gates: a study of gate-timing errors

TL;DR

This paper develops an analytical amplitude modulation method for trapped-ion entangling gates, significantly enhancing robustness against gate-timing errors by increasing error insensitivity order with minimal power increase.

Contribution

It introduces a Fourier series-based amplitude modulation technique that improves gate-timing error robustness from quadratic to tenth order, with linear constraints and minimal power increase.

Findings

Error sensitivity improved from D7D0D2 to D7D0D6 and D7D0D10

Linear constraints enable high-order error insensitivity

Minimal power increase with more Fourier coefficients

Abstract

Trapped-ion systems are a promising route toward the realization of both near-term and universal quantum computers. However, one of the pressing challenges is improving the fidelity of two-qubit entangling gates. These operations are often implemented by addressing individual ions with laser pulses using the Molmer-Sorensen (MS) protocol. Amplitude modulation (AM) is a well-studied extension of this protocol, where the amplitude of the laser pulses is controlled as a function of time. We present an analytical study of AM, using a Fourier series expansion to maintain the generality of the laser amplitude's functional form. We then apply this general AM method to gate-timing errors by imposing conditions on these Fourier coefficients, producing trade-offs between the laser power and fidelity at a fixed gate time. The conditions derived here are linear and can be used, in principle, to achieve arbitrarily high orders of insensitivity to gate-timing errors. Numerical optimization is then employed to identify the minimum-power pulse satisfying these constraints. Our central result is that the leading order dependence on gate timing errors is improved from $\mathcal{O}(\Delta t^2)$ to $\mathcal{O}(\Delta t^6)$ with the addition of one linear constraint on the Fourier coefficients and to $\mathcal{O}(\Delta t^{10})$ with two linear constraints without a significant increase in the average laser power. The increase approaches zero as more Fourier coefficients are included. In further studies, this protocol can be applied to other error sources and used in conjunction with other error-mitigation techniques to improve two-qubit gates.