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arXiv:2607.13166

Robust Nonperturbative Trapped-Ion Quantum Logic

Luca Stefanescu, Florian Mintert

quant-phSubmitted Jul 14, 2026• Announced Jul 16, 2026• 0 citations
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Abstract

Entangling gates of trapped ions are typically mediated by collective motional degrees of freedom. Weak coupling between qubit and motional degrees of freedom and the resulting harmonic dynamics give access to a broad range of gate schemes, but also impose strict limitations on achievable gate times. In this paper, we devise optimally designed driving schemes for the realization of fast, high-fidelity entangling gates mediated by anharmonic dynamics. The driving can also be optimized to achieve resilience to multiple system imperfections, and the anharmonicity in the motional dynamics can be used to enhance such resilience.

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Entangling gates of trapped ions are typically mediated by collective motional degrees of freedom. Weak coupling between qubit and motional degrees of freedom and the resulting harmonic dynamics give access to a broad range of gate schemes, but also impose strict limitations on achievable gate times. In this paper, we devise optimally designed driving schemes for the realization of fast, high-fidelity entangling gates mediated by anharmonic dynamics. The driving can also be optimized to achieve resilience to multiple system imperfections, and the anharmonicity in the motional dynamics can be used to enhance such resilience.
We introduce a scheme that combines phonon-mediated quantum logic gates in trapped ions with the benefits of continuous dynamical decoupling. We demonstrate theoretically that a strong driving of the qubit decouples it from external magnetic-field noise, enhancing the fidelity of two-qubit quantum gates. Moreover, the scheme does not require ground-state cooling, and is inherently robust to undesired ac Stark shifts. The underlying mechanism can be extended to a variety of other systems where a strong driving protects the quantum coherence of the qubits without compromising the two-qubit couplings.
Abstract We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors. The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and, unlike the state of the art, requires neither weak-coupling Lamb–Dicke approximation nor perturbation treatment. With the application of gradient-based optimal control, it enables finding amplitude- and phase-modulated laser control protocols that work without the Lamb–Dicke approximation, promising gate speeds on the order of microseconds comparable to the characteristic trap frequencies. Also, robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections. Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation, and thus can find applications in near-future experiments.
Entangling interactions between distant qubits can be mediated via an additional degree of freedom. In conventional trapped-ion schemes, realizing a well-defined, coherent gate typically requires spectrally addressing a specific bus mode. As the ion number increases, the coupling to each individual motional mode becomes weaker, so gates on large ion strings mediated by a single mode are necessarily slow. Moreover, addressing a large number of modes demands complex driving schemes, and the fundamentally perturbative character of these approaches imposes constraints on achievable gate speed and fidelity. Here, we introduce a scheme for entangling trapped-ion qubits using a time-dependent magnetic-field gradient, in which all axial motional modes participate in mediating the interaction and the gate construction is nonperturbative. The framework can be used to implement both multi-qubit gates and two-qubit gates between arbitrary pairs in a linear ion string. Through several explicit examples, we highlight the advantages over existing magnetic-gradient schemes and show how gates on multiple ion pairs can be carried out simultaneously.
We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors. The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and, unlike the state of the art, requires neither weak-coupling Lamb-Dicke approximation nor perturbation treatment. With the application of gradient-based optimal control, it enables finding amplitude- and phase-modulated laser control protocols that work beyond the Lamb-Dicke regime, promising gate speed at the order of microseconds comparable to the characteristic trap frequencies. Also, robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections. Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation, and thus can find applications in near-future experiments.