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arXiv:2511.15148 · Physical Review A

Radial Fast Entangling Gates Under Micromotion in Trapped-Ion Quantum Computers

Phoebe Grosser, Monica Gutierrez Galan, Isabelle Savill-Brown, Alexander K. Ratcliffe, Haonan Liu, Varun D. Vaidya, Simon A. Haine, C. Ricardo Viteri, Joseph J. Hope, Zain Mehdi

quant-phSubmitted Nov 19, 2025• Announced Nov 20, 2025• 0 citations
v1 · Nov 19, 2025v2 · Apr 28, 2026
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Abstract

Micromotion in radio-frequency ion traps is generally considered detrimental for quantum logic gates, and is typically minimized in state-of-the-art experiments. However, as a deterministic effect, it can be incorporated into quantum control frameworks aimed at designing high-fidelity quantum logic controls. In this work, we demonstrate that micromotion can be beneficial to the design of fast gates utilizing the radial modes of a two-ion crystal, particularly in the sub-trap-period regime where high-fidelity control sequences are identified with operation times ranging from hundreds of nanoseconds to microseconds. Through analysis of select fast gate solutions, we uncover the physical origin of micromotion enhancement and further study the induced gate error under experimental noises and control imperfections. This analysis establishes the feasibility of realising high-fidelity entangling gates in hundreds of nanoseconds using the micromotion-sensitive radial modes of trapped-ion crystals.

DOI
10.1103/zg69-17xc

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Micromotion in radio-frequency ion traps is generally considered detrimental for quantum logic gates, and is typically minimized in state-of-the-art experiments. However, as a deterministic effect, it can be incorporated into quantum control frameworks aimed at designing high-fidelity quantum logic controls. In this work, we demonstrate that micromotion can be beneficial to the design of fast gates utilizing the radial modes of a two-ion crystal, particularly in the sub-trap-period regime where high-fidelity control sequences are identified with operation times ranging from hundreds of nanoseconds to microseconds. Through analysis of select fast gate solutions, we uncover the physical origin of micromotion enhancement and further study the induced gate error under experimental noises and control imperfections. This analysis establishes the feasibility of realising high-fidelity entangling gates in hundreds of nanoseconds using the micromotion-sensitive radial modes of trapped-ion crystals.
Radio-frequency-induced micromotion in trapped ion systems is typically minimized or circumvented to avoid off-resonant couplings for adiabatic processes such as multi-ion gate operations. Nonadiabatic entangling gates (so-called ``fast gates'') do not require resolution of specific motional sidebands and are, therefore, not limited to time scales longer than the trapping period. We find that fast gates designed for micromotion-free environments have a significantly reduced fidelity in the presence of micromotion. We show that when fast gates are designed to account for the radio-frequency-induced micromotion, they can, in fact, outperform fast gates in the absence of micromotion. The state-dependent force due to the laser induces energy shifts that are amplified by the state-independent forces producing the micromotion. This enhancement is present for all trapping parameters and is robust to realistic sources of experimental error. This result paves the way for fast two-qubit entangling gates on scalable two-dimensional architectures, where micromotion is necessarily present on at least one interion axis.
The micromotion of ion crystals confined in Paul traps is usually considered an inconvenient nuisance, and is thus typically minimized in high-precision experiments such as high-fidelity quantum gates for quantum information processing (QIP). In this work, we introduce a particular scheme where this behavior can be reversed, making micromotion beneficial for QIP. We show that using laser-driven micromotion sidebands, it is possible to engineer state-dependent dipole forces with a reduced effect of off-resonant couplings to the carrier transition. This allows one, in a certain parameter regime, to devise entangling gate schemes based on geometric phase gates with both a higher speed and a lower error, which is attractive in light of current efforts towards fault-tolerant QIP. We discuss the prospects of reaching the parameters required to observe this micromotion-enabled improvement in experiments with current and future trap designs.
Non-adiabatic two-qubit gate proposals for trapped-ion systems offer superior performance and flexibility over adiabatic schemes at the cost of increased laser control requirements. Existing fast gate schemes are limited by single-qubit transition errors, which constrain the total number of pulses in high-fidelity solutions. We introduce an improved gate search scheme that enables both local and non-local two-qubit gates in chains containing tens of ions. These protocols use a multi-objective machine design approach that incorporates dominant sources of error in the design to ensure the solutions are compatible with existing fast laser controls. We also generalize previous schemes by allowing for unpaired pulses during the gate evolution. By imposing symmetries on the pulse sequences, we eliminate susceptibility to laser phase noise and further simplify the multi-mode control over the state-dependent motion of the ion crystal. We perform a comprehensive analysis of expected gate performance in the presence of random and systematic experimental errors to demonstrate the feasibility of performing microsecond two-qubit gates between arbitrary ion pairs in current linear ion-trap processors of up to 505050 ions with fidelities approaching 99.9%99.9\%99.9%.
An ion trap is one of the most promising candidates for quantum computing. Current schemes mainly focus on a linear chain of up to about 100 ions in a Paul trap. To further scale up the qubit number, one possible direction is to use 2D or 3D ion crystals (Wigner crystals). In these systems, ions are generally subjected to large micromotion due to the strong fast-oscillating electric field, which can significantly influence the performance of entangling gates. In this paper, we develop an efficient numerical method to design high-fidelity entangling gates in a general 3D ion crystal. We present numerical algorithms to solve the equilibrium configuration of the ions and their collective normal modes. We then give a mathematical description of the micromotion and use it to generalize the gate scheme for linear ion chains into a general 3D crystal. The involved time integral of highly oscillatory functions is expanded into a fast-converging series for accurate and efficient evaluation and optimization. As a numerical example, we show a high-fidelity entangling gate design between two ions in a 100-ion crystal, with a theoretical fidelity above 99.9%.
Quantum computers based on crystals of trapped ions are a prominent technology for quantum computation. A unique feature of trapped ions is their long-range Coulomb interactions, which can be exploited to realize large-scale multiqubit entanglement gates. However, scaling up the number of qubits, N , in these systems, while retaining high-fidelity and high-speed operations, is challenging. Specifically, designing multiqubit entanglement gates in long ion crystals of hundreds of ions involves an NP-hard optimization problem, rendering scale-up not only a technological challenge, but also a conceptual challenge. Here we introduce a method that mitigates this challenge, effectively allowing for a polynomial-time design of fast, robust, and programmable entanglement gates, acting on the entire ion-crystal. We show that while the number of simultaneous entanglement operations scales as N 2 , the gate duration scales as N , leading to a scaling advantage. We use our methods to investigate the drive-power requirements and susceptibility to noise and errors of these multiqubit gates. Our method delineates a path toward scaling up quantum computers based on ion-crystals with hundreds of qubits.
Trapped Rydberg ions are a novel platform for quantum information processing. This approach combines the advanced quantum control of trapped ions and the strong dipolar interaction of Rydberg atoms. In this thesis, a strong dipole-dipole interaction has been demonstrated and a sub-microsecond entangling gate has been implemented in a cold two-ion crystal. After minimizing the polarizability of the Rydberg state by microwave dressing and understanding the effect of the quadrupole radio-frequency trap,the entangling gate has been applied in a warm 12-ion crystal.