Toolchain for shuttling trapped-ion qubits in segmented traps

TL;DR

The paper tackles the challenge of fast, low-excitation shuttling of trapped-ion qubits through complex, segmented RF traps. It introduces a hardware-informed numerical toolchain that combines an electrostatics solver with a spherical-harmonic multipole expansion, penalty-based unconstrained quadratic optimization, and postprocessing to generate voltage waveforms compatible with multi-channel AWGs. The framework is validated against measured secular frequencies and demonstrated on linear shuttling and junction traversal, with detailed assessments of accuracy and performance. By enabling rapid prototyping and design optimization of trap geometries and transport protocols, this work provides a scalable foundation for advancing trapped-ion quantum processors toward larger registers and practical fault-tolerant operation.

Abstract

Scalable trapped-ion quantum computing requires fast and reliable transport of ions through complex, segmented radiofrequency trap architectures without inducing excessive motional excitation. We present a numerical toolchain for the systematic generation of time-dependent electrode voltages enabling fast, low-excitation ion shuttling in segmented radiofrequency traps. Based on a model of the trap electrode geometry, the framework combines an electrostatic field solver, efficient unconstrained optimization, waveform postprocessing, and dynamical simulations of ion motion to compute voltage waveforms that realize prescribed transport trajectories while respecting experimental constraints such as voltage limits and bandwidth. The toolchain supports arbitrary trap geometries, including junctions and multi-zone layouts, and allows for the flexible incorporation of optimization objectives. We provide a detailed assessment of the accuracy of the framework by investigating its numerical stability and by comparing measured and predicted secular frequencies. The framework is optimized for numerical performance, enabling rapid numerical prototyping of trap architectures of increasing complexity. As application examples, we apply the framework to the transport of a potential well along a linear, uniformly segmented trap, and we compute a solution for shuttling a potential well around the corner of an X-type trap junction. The presented approach provides an extensible and highly efficient numerical foundation for designing and validating transport protocols in current and next-generation trapped-ion processors.

Figures (11)

• Figure 1: Schematic overview of the numerical shuttling toolchain presented in this work. An electrostatics solver is used for computing potential values near support points of a shuttling path. The trap electrode potentials are used to determine efficient multipole expansions. Based on these, optimal voltage set sequences are computed for realization of the shuttling operation. Several postprocessing steps are employed to generate voltage waveforms which can be generated a multichannel arbitrary waveform generator. Shuttling solutions can also be analyzed to e.g. perform parametric trap design studies of for closed-loop optimization of trap geometries.
• Figure 2: Trap potential evaluation: The trap geometry is defined within coordinate system $\hat{x},\hat{y},\hat{z}$, as well as a shuttling path (dotted line with green end points). A primed coordinate system is attached to each support point $\boldsymbol{\mathsf{p}}$ along the shuttling path. Furthermore, an expansion sphere with radius $\kappa$ is set up for each support point, the surface which hosts the set of $\mathcal{P}$ of $K$ design points $\boldsymbol{\mathsf{r}}_k$ defined in a coordinate system $x,y,z$ and shown on the right end. For each support point $\boldsymbol{\mathsf{p}}$ of the shuttling path, the design points are transformed to the trap coordinate system by $\mathcal{R}(\boldsymbol{\mathsf{p}})$, such that the rotated axes of the sphere coincide with the ones of the primed coordinate system centered at $\boldsymbol{\mathsf{p}}$ (see Eq. \ref{['eq:designPointsTransform']}). Evaluating the electrode potentials at the transformed design points allows for an accurate and efficient representation of the trap potentials.
• Figure 3: Reconstruction of an example unit potential $\phi=0.3\;R_{2,0}+0.7\;R_{2,2}+1.0\;R_{4,-2}$ with a Fibonacci grid of $K=25$ points. a) shows the Gram matrix $G$ Eq. \ref{['eq:gramMatrix']} prior to orthogonalization. b) shows the difference (modulus) of the Gram matrix for the orthogonalized basis vectors and the unit matrix.
• Figure 4: Secular frequencies versus expansion sphere size: The top panel shows the computed secular frequencies versus the relative expansion sphere size $\kappa/d$, with $d$ being the minimum ion-electrode distance used as characteristic length scale. The dashed lines indicate measurement results obtained with identical trapping parameters (see text). The bottom panel shows the deviations between measured and computed secular frequencies, referenced to the values obtained for the expansion radius marked by the arrow. The dashed lines indicate the relative accuracies of the spectroscopy measurements. The expansion sphere radii are indicated as normalized to a characteristic length of the trap geometry.
• Figure 5: Anharmonic terms: The reconstructed solid harmonic coefficients for $l=4$ are shown for $L=4$ and $K=25$ (left) and $K=1000$ (right) expansion points, versus the relative expansion sphere size $\kappa/d$ (see Fig. \ref{['fig:expansion_sphere_radius_scan_secular_frequency']}). The inset shows the moduli of the relative differences between the two cases.