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Physical Review Research

Trapped ions quantum logic gate with optical tweezers and the Magnus effect

M. Mazzanti, R. Gerritsma, R. J. C. Spreeuw, Arghavan Safavi-Naini

Published Jul 19, 2023• 13 citations
Publisher

Abstract

We consider the implementation of quantum logic gates in trapped ions using tightly focused optical tweezers. Strong polarization gradients near the tweezer focus lead to qubit-state-dependent forces on the ion. We show that these may be used to implement quantum logic gates on pairs of ion qubits in a crystal. The qubit-state-dependent forces generated by this effect are located on the plane perpendicular to the direction of propagation of the laser beams opening alternate ways of coupling to motional modes of an ion crystal. The proposed gate does not require ground-state cooling of the ions although the waist of the tightly focused beam needs to be comparable to its wavelength in order to achieve the needed field curvature. Furthermore, the gate can be implemented on both ground-state and magnetic-field-insensitive clock-state qubits without the need for counterpropagating laser fields. This simplifies the setup and eliminates errors due to phase instabilities between the gate laser beams. Finally, we show that imperfections in the gate execution, in particular, a 30-nm tweezer alignment error, lead to an infidelity of $\ensuremath{\sim}{10}^{\ensuremath{-}3}$. In the absence of experimental imperfections and within the limits of the gate model explored in this paper the fidelity is predicted to be $\ensuremath{\sim}0.999\phantom{\rule{0.16em}{0ex}}88$ when using a Laguerre-Gaussian beam to suppress photon scattering errors.

DOI
10.1103/physrevresearch.5.033036

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Ion traps and optical tweezers have emerged as highly promising technologies in the development of quantum computing, enabling precise control over qubits through electromagnetic and optical confinement. This paper explores the fundamental principles, advantages, and limitations of ion traps, including Paul and Penning configurations, and evaluates their role in modern quantum architectures. Particular emphasis is placed on coherence time, fidelity, and all-to-all connectivity, which make trapped ions a leading qubit candidate despite challenges in scalability and optical complexity. The work also examines optical tweezers, which use tightly focused laser beams to trap and manipulate ions and atoms with high precision, facilitating scalable arrays of qubits. Furthermore, hybrid traps that integrate optical tweezers with Paul traps are discussed as promising solutions to mitigate Radio-Frequency (RF) micromotion and enhance stability for cold ion–atom systems. Python-based simulations are presented to illustrate ion dynamics under Brownian motion, electric fields, and Gaussian laser traps, demonstrating how trap strength directly affects oscillation amplitude and confinement. Results confirm that stronger optical potentials reduce oscillation amplitude, while weaker traps lead to ion escape, aligning with theoretical predictions. Overall, this study highlights how the interplay of electromagnetic and optical techniques advances the frontier of quantum information science, with direct implications for computation, communication, and simulation.

Scholarly review .•Oct 3, 2025•0 citations
We consider the implementation of quantum logic gates in trapped ions using tightly focused optical tweezers. Strong polarization gradients near the tweezer focus lead to qubit-state-dependent forces on the ion. We show that these may be used to implement quantum logic gates on pairs of ion qubits in a crystal. The qubit-state-dependent forces generated by this effect are located on the plane perpendicular to the direction of propagation of the laser beams opening alternate ways of coupling to motional modes of an ion crystal. The proposed gate does not require ground-state cooling of the ions although the waist of the tightly focused beam needs to be comparable to its wavelength in order to achieve the needed field curvature. Furthermore, the gate can be implemented on both ground-state and magnetic-field-insensitive clock-state qubits without the need for counterpropagating laser fields. This simplifies the setup and eliminates errors due to phase instabilities between the gate laser beams. Finally, we show that imperfections in the gate execution, in particular, a 30-nm tweezer alignment error, lead to an infidelity of \ensuremath∼10\ensuremath−3\ensuremath{\sim}{10}^{\ensuremath{-}3}\ensuremath∼10\ensuremath−3. In the absence of experimental imperfections and within the limits of the gate model explored in this paper the fidelity is predicted to be \ensuremath∼0.99988\ensuremath{\sim}0.999\phantom{\rule{0.16em}{0ex}}88\ensuremath∼0.99988 when using a Laguerre-Gaussian beam to suppress photon scattering errors.
We consider the implementation of quantum logic gates in trapped ions using tightly focused optical tweezers. Strong polarization gradients near the tweezer focus lead to qubit-state dependent forces on the ion. We show that these may be used to implement quantum logic gates on pairs of ion qubits in a crystal. The qubit-state dependent forces generated by this effect live on the plane perpendicular to the direction of propagation of the laser beams opening new ways of coupling to motional modes of an ion crystal. The proposed gate does not require ground state cooling of the ions and does not rely on the Lamb-Dicke approximation, although the waist of the tightly focused beam needs to be comparable with its wavelength in order to achieve the needed field curvature. Furthermore, the gate can be performed on both ground state and magnetic field insensitive clock state qubits without the need for counter-propagating laser fields. This simplifies the setup and eliminates errors due to phase instabilities between the gate laser beams. Finally, we show that imperfections in the gate execution, in particular pointing errors <30<30<30 nm in the tweezers reduce the gate fidelity from F≳0.99998\mathcal F\gtrsim 0.99998F≳0.99998 to ≳0.999\gtrsim 0.999≳0.999.
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.
We propose a new scalable architecture for trapped ion quantum computing that combines optical tweezers delivering qubit state-dependent local potentials with oscillating electric fields. Since the electric field allows for long-range qubit-qubit interactions mediated by the center-of-mass motion of the ion crystal alone, it is inherently scalable to large ion crystals. Furthermore, our proposed scheme does not rely on either ground-state cooling or the Lamb-Dicke approximation. We study the effects of imperfect cooling of the ion crystal, as well as the role of unwanted qubit-motion entanglement, and discuss the prospects of implementing the state-dependent tweezers in the laboratory.
Geometric phase gates with addressed laser radiation are widely used in trapped-ion quantum computers to drive high-fidelity entangling gates on an arbitrary qubit pair of a larger ion chain. Such programmable connectivity exploits the collective phonons to mediate the desired interaction, while simultaneously achieving robustness to their thermal fluctuations by a careful calibration of the gate time with respect to the laser and vibrational-mode frequencies. Crosstalk errors can arise when the spectator qubits, which should ideally remain idle during the gate, are partially driven by the laser fields. The minimal crosstalk, which is set by the laser beam size on the spectator ions, can be achieved when the addressing beams propagate perpendicular to the ion chain. However, this results in exciting the radial phonons, and can complicate achieving high-fidelities as the ion chain grows due to the so-called spectral mode crowding. In this work, we present the theoretical description of a scheme recently implemented by Faorlin et al.al.al.. This scheme overcomes these complications by engineering addressable state-dependent forces along the ion-chain with laser beams that propagate perpendicular to it through the use of structured light gradients. In this way, one can excite the axial phonons and avoid the spectral mode crowding, while simultaneously minimizing the crosstalk. We present a detailed derivation of the entangling gate scheme, together with analytical closed-form expressions for the leading contribution to the gate error caused by thermal motional fluctuations and dephasing noise. Our results confirm that such fluctuations account for up to 93%\%% of the error budget under the operating conditions of the gate implemented by Faorlin et al.al.al.. We identify target parameters to reduce the motional error from the reported 10−310^{-3}10−3 to the 10−510^{-5}10−5 level.
Ion traps and optical tweezers have emerged as highly promising technologies in the development of quantum computing, enabling precise control over qubits through electromagnetic and optical confinement. This paper explores the fundamental principles, advantages, and limitations of ion traps, including Paul and Penning configurations, and evaluates their role in modern quantum architectures. Particular emphasis is placed on coherence time, fidelity, and all-to-all connectivity, which make trapped ions a leading qubit candidate despite challenges in scalability and optical complexity. The work also examines optical tweezers, which use tightly focused laser beams to trap and manipulate ions and atoms with high precision, facilitating scalable arrays of qubits. Furthermore, hybrid traps that integrate optical tweezers with Paul traps are discussed as promising solutions to mitigate Radio-Frequency (RF) micromotion and enhance stability for cold ion–atom systems. Python-based simulations are presented to illustrate ion dynamics under Brownian motion, electric fields, and Gaussian laser traps, demonstrating how trap strength directly affects oscillation amplitude and confinement. Results confirm that stronger optical potentials reduce oscillation amplitude, while weaker traps lead to ion escape, aligning with theoretical predictions. Overall, this study highlights how the interplay of electromagnetic and optical techniques advances the frontier of quantum information science, with direct implications for computation, communication, and simulation.