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arXiv:2602.11326 · Physical Review A

Multi-ion entangling gates mediated by spectrally unresolved modes

Modesto Orozco-Ruiz, Florian Mintert

quant-phSubmitted Feb 11, 2026• Announced Feb 13, 2026• 0 citations
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Abstract

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.

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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.
A central challenge in developing practical quantum processors is maintaining low control complexity while scaling to large numbers of qubits. Trapped-ion systems excel in small-scale operations and support rapid qubit scaling via long-chain architectures. However, their performance in larger systems is hindered by spectral crowding in radial motional modes, a problem that forces reliance on intricate pulse-shaping techniques to maintain gate fidelities. Here, we overcome this challenge by developing a novel trapped-ion processor with an individual-addressing system that generates steerable Hermite-Gaussian beam arrays. The transverse gradient of these beams couples qubits selectively to sparse axial motional modes, enabling to isolate a single mode as entanglement mediator. Leveraging this capability, we demonstrate addressable two-qubit entangling gates in chains up to six ions with fidelities consistently around 0.97, achieved without complex pulse shaping. Our method significantly reduces control overhead while preserving scalability, providing a crucial advance toward practical large-scale trapped-ion quantum computing.
Spectral crowding of collective motional modes limits the fidelity of entangling interactions in trapped-ion quantum processors by inducing off-resonant coupling to spectator modes. We introduce a geometric-phase entangling interaction driven by a transverse, time-dependent structured-light force. By applying the force in a plane orthogonal to the optical propagation direction, we reduce the effects of spectral crowding while preserving single-ion addressing. The scheme is compatible with arbitrary qubit encodings, provided that the qubit states experience a differential AC Stark shift. We experimentally realise high-fidelity two-qubit gates with error rates below 5×10−35\times10^{-3}5×10−3 in ion crystals containing up to 12 ions confined within a single potential well. These results establish gradient-field light-shift gates as a scalable approach to high-fidelity entangling generation in spectrally crowded trapped-ion systems.
A central challenge in developing practical quantum processors is maintaining low control complexity while scaling to large numbers of qubits. Trapped-ion systems excel in small-scale operations and support rapid qubit scaling via long-chain architectures. However, their performance in larger systems is hindered by spectral crowding in radial motional modes, a problem that forces reliance on intricate pulse-shaping techniques to maintain gate fidelities. Here, we overcome this challenge by developing a trapped-ion processor with an individual-addressing system that generates steerable Hermite-Gaussian beam arrays. The transversal gradient of these beams couples qubits selectively to sparse axial motional modes, enabling to isolate a single or few modes as entanglement mediator. Leveraging this capability, we demonstrate addressable two-qubit entangling gates in chains up to six ions, with Bell-state preparation fidelities consistently around 0.97, achieved without complex pulse shaping. Our method substantially reduces control overhead while preserving scalability, providing a crucial advance toward practical large-scale trapped-ion quantum computing.
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.
The construction of entangling gates with individual addressing capability represents a crucial approach for implementing quantum computation in trapped-ion crystals. Conventional entangling gate schemes typically rely on laser beam wave vectors to couple the ions' spin and motional degrees of freedom. Here, we experimentally demonstrate an alternative method that employs a polarization gradient field generated by a tightly focused laser beam-an approach theoretically proposed as the Magnus effect for quantum logic gate design [Mazzanti et al., Phys. Rev. Res. 5, 033036 (2023)PPRHAI2643-156410.1103/PhysRevResearch.5.033036]. Using this technique, we perform Raman operations on hyperfine qubits encoded in ^{171}Yb^{+} ions, generating spin-dependent forces along axial motional modes in a linear trap. By utilizing an acousto-optic deflector to create arbitrary spot pairs for individual ion addressing in two-ion (four-ion) chains, we achieve Mølmer-Sørensen gates with Bell-state fidelities exceeding 98.7(1)% [and 97.2(4)%]. Further improvements in numerical aperture (NA) and laser power could reduce gate durations while enhancing fidelity by orders of magnitude. This method is compatible with-and can significantly simplify-optical tweezer gate proposals, where motional mode engineering enables scalable trapped-ion quantum computation. The technique can be readily extended to two-dimensional ion crystals, representing a key advancement toward large-scale trapped-ion quantum processors.
Abstract We propose and study ways speeding up of the entangling operations in the trapped ions system with high fidelity. First, we find a scheme to increase the speed of a two-qubit gate without the limitation of trap frequency, which was considered as the fundamental limit. Second, we study the fast gate scheme for entangling more than two qubits simultaneously. We apply the method of applying multiple frequency components on laser beams for the gate operations. In particular, in order to avoid infinite terms from the coupling to carrier transition, we focus on the phase-insensitive gate scheme here. We carefully study the effect of large excitation of motional mode beyond the limit of Lamb–Dicke approximation by including up to second order terms of the Lamb–Dicke parameter. We study the speed limit of multi-qubit global entangling gates without individual addressing requirements. Furthermore, our gates can be made insensitive to the fluctuation of initial motional phases which are difficult to stabilise in the phase-insensitive gate scheme.