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arXiv:2606.23951

Mølmer-Sørensen gates in trapped-ions chains in the presence of correlated noise

D. V. Donchenko, E. A. Anikin, O. Lakhmanskaya, K. Lakhmanskiy

quant-phSubmitted Jun 22, 2026• Announced Jun 24, 2026• 0 citations
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Abstract

We analyze the impact of correlated laser frequency noise on Mølmer-Sørensen gates in qubit registers based on trapped-ion chains. Using perturbation theory, we calculate gate fidelities in the presence of noise with arbitrary power spectral density for different chain lengths and ion positions in the chain. With our approach, we account for simultaneous excitation of multiple phonon modes during gate operation. We find out that the impact of medium-frequency laser noise depends considerably on the positions of the ions in the chain. In contrast, low-frequency noise has similar effect for different chain lengths and ion positions.

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We analyze the impact of correlated laser frequency noise on Mølmer-Sørensen gates in qubit registers based on trapped-ion chains. Using perturbation theory, we calculate gate fidelities in the presence of noise with arbitrary power spectral density for different chain lengths and ion positions in the chain. With our approach, we account for simultaneous excitation of multiple phonon modes during gate operation. We find out that the impact of medium-frequency laser noise depends considerably on the positions of the ions in the chain. In contrast, low-frequency noise has similar effect for different chain lengths and ion positions.
High-fidelity two-qubit entangling gates are essential for the realization of useful quantum algorithms on quantum processors. The Mølmer-Sørensen (MS) gate has become a common choice for trapped-ion quantum computing due to its resilience to ion temperature and its demonstrated record fidelities. However, the spectral impurity of the driving laser field impacts gate performance, with phase noise influencing the qubit dynamics through mechanisms operating on different timescales. In this work, we present a comprehensive theoretical analysis of laser phase noise in the MS gate, identifying two spectral ranges which influence the gate fidelity the most: "fast" noise at frequencies near the motional mode spectrum, and "slow" noise at frequencies on the order of the inverse gate time. We derive the noise Hamiltonians for two common laser beam geometries and obtain analytical expressions for the average gate error in terms of the laser noise power spectral density and gate parameters. For slowly varying noise spectra, we provide simplified error estimates. In addition, we validate our findings against previously published numerical simulations.
In this work, we design and implement frequency-robust Molmer-Sorensen gates on a linear chain of trapped ions, using Gaussian amplitude modulation and a constant laser frequency. We select this frequency to balance the entanglement accumulation of all motional modes during the gate to produce a strong robustness to frequency error, even for long ion chains. We demonstrate this technique on a three-ion chain, achieving < 1%<\,1\%<1% reduction from peak fidelity over a 20 20\,20kHz range of frequency offset, and we analyze the performance of this gate design through numerical simulations on chains of two to 33 ions.
Carrier transition is one of the major factors hindering the high-speed implementation of the Mølmer-Sørensen gates in trapped-ion quantum processors. We present an approach to design laser pulse shapes for the Mølmer-Sørensen gate in ion chains which accounts for the effect of carrier transition on qubit-phonon dynamics. We show that the fast-oscillating carrier term effectively modifies the spin-dependent forces acting on ions, and this can be compensated by a simple nonlinear transformation of a laser pulse. Using numerical simulations for short ion chains and perturbation theory for longer chains up to 202020 ions, we demonstrate that our approach allows to reach the infidelity below 10−410^{-4}10−4 while keeping the gate duration of the order of tens of microseconds.
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.
High-fidelity two-qubit gates in quantum computers are often hampered by fluctuating experimental parameters. The effects of time-varying parameter fluctuations lead to coherent noise on the qubits, which can be suppressed by designing control signals with appropriate filter functions. Here, we develop filter functions for M\o{}lmer-S\o{}rensen gates of trapped-ion quantum computers that accurately predict the change in gate error due to small parameter fluctuations at any frequency. We then design the filter functions of frequency-modulated laser pulses, and compare this method with pulses that are robust to static offsets of the motional-mode frequencies. Experimentally, we measure the noise spectrum of the motional modes and use it for designing the filter functions, which improves the gate fidelity from 99.23(7)% to 99.55(7)% in a five-ion chain.
High-fidelity single- and multiqubit operations compose the backbone of quantum information processing. This fidelity is based on the ability to couple single- or two-qubit levels in an extremely coherent and precise manner. A necessary condition for coherent quantum evolution is a highly stable local oscillator driving these transitions. Here we study the effect of fast noise, that is, noise at frequencies much higher than the local oscillator linewidth, on the fidelity of one- and two-qubit gates in a trapped-ion system. We analyze and measure the effect of fast noise on single-qubit operations, including resonant $\ensuremath{\pi}$ rotations and off-resonant sideband transitions. We further numerically analyze the effect of fast phase noise on the M\o{}lmer-S\o{}rensen two-qubit gate. We find a unified and simple way to estimate the performance of all of these operations through a single parameter given by the noise power spectral density at the qubit response frequency. While our analysis focuses on phase noise and on trapped-ion systems, it is relevant for other sources of fast noise as well as for other qubit systems in which spinlike qubits are coupled by a common bosonic field. Our analysis can help in guiding the design of quantum hardware platforms and gates, improving their fidelity towards fault-tolerant quantum computing.