[Paper Review] Closed-loop optimization of fast trapped-ion shuttling with sub-quanta excitation

Jonathan David Sterk, Henry Coakley+8 more|arXiv (Cornell University)|Jan 18, 2022

Quantum Information and Cryptography46 references24 citations

TL;DR

This paper presents a closed-loop optimization of voltage waveforms for fast, low-excitation shuttling of trapped ions in segmented Paul traps. By iteratively refining waveforms based on experimental feedback using sideband spectroscopy and a Nelder–Mead optimizer, the method achieves 0.36 ± 0.08 quanta of motional excitation during 3-electrode transport at 0.5 electrodes/µs (35 m/s), with sub-quanta performance independent of axial motion phase.

ABSTRACT

Shuttling ions at high speed and with low motional excitation is essential for realizing fast and high-fidelity algorithms in many trapped-ion based quantum computing architectures. Achieving such performance is challenging due to the sensitivity of an ion to electric fields and the unknown and imperfect environmental and control variables that create them. Here we implement a closed-loop optimization of the voltage waveforms that control the trajectory and axial frequency of an ion during transport in order to minimize the final motional excitation. The resulting waveforms realize fast round-trip transport of a trapped ion across multiple electrodes at speeds of $0.5$ electrodes/$\mu$s ($35 ext{m/s}$) with a maximum of $0.36\pm0.08$ quanta gain. This sub-quanta gain is independent of the phase of the secular motion at the distal location, obviating the need for an electric field impulse or time delay to eliminate the coherent motion

Motivation & Objective

• To minimize motional excitation during fast ion shuttling in trapped-ion quantum computing architectures.
• To overcome experimental imperfections such as fabrication variations, background electric fields, and waveform distortion without relying on precise theoretical models.
• To develop a model-agnostic, experimentally driven optimization framework for high-fidelity ion transport.
• To achieve transport speeds sufficient for scalable quantum algorithms while maintaining coherence.
• To eliminate the need for phase-locked electric field impulses or time delays to correct coherent motion.

Proposed method

• A closed-loop optimization framework uses experimental feedback to refine voltage waveforms for ion transport.
• The loss function is derived from integrated red sideband spectra of the |0⟩↔|1⟩ transition, serving as a proxy for mean motional quanta.
• The Nelder–Mead derivative-free algorithm optimizes the waveform by minimizing the maximum loss across multiple hold-time offsets at the destination.
• Waveforms are synthesized in real time from a precomputed set of 211 voltage solutions along a 210 µm path, each maintaining a fixed 2.5 MHz axial frequency.
• Sideband probing with variable hold times at the distal site reveals phase-dependent excitation, enabling optimization over the full phase cycle.
• Two-stage optimization is employed: initial short probe times to avoid saturation, followed by longer probes from the converged initial state.

Experimental results

Research questions

• RQ1 Can experimental feedback be used to optimize ion transport waveforms without relying on accurate physical models?
• RQ2 What is the minimum achievable motional excitation during fast ion shuttling in the presence of experimental imperfections?
• RQ3 Can sub-quanta excitation be achieved independently of the phase of axial motion at the destination?
• RQ4 How does closed-loop optimization compare to theoretically derived protocols in real-world conditions with unknown system deviations?
• RQ5 Can this method be generalized to tune other quantum control protocols in trapped-ion and neutral-atom systems?

Key findings

• The optimized waveform achieved a maximum motional excitation of 0.36 ± 0.08 quanta during 3-electrode transport at 0.5 electrodes/µs (35 m/s).
• The sub-quanta excitation is independent of the phase of the axial motion at the distal location, eliminating the need for phase-correction pulses or time delays.
• The optimization converged after 150 function evaluations, with the loss function becoming insensitive to further improvement.
• The method successfully compensated for experimental imperfections such as fabrication deviations, background electric fields, and waveform filtering effects.
• The use of sideband integral loss as a proxy for motional excitation enabled fast, reliable, and quantitative feedback during optimization.
• The approach is generalizable and could be applied to tune other quantum control protocols in trapped-ion, neutral-atom, and atom interferometry platforms.