Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2109.04395 · Physical Review A

Entangling-gate error from coherently displaced motional modes of trapped ions

Brandon Ruzic, T. Barrick, J. D. Hunker, Ryan Law, Brian McFarland, Hayden McGuinness, Lambert Paul Parazzoli, Jonathan David Sterk, Jay Wesley Van Der Wall, Daniel Stick

Published May 5, 2022• 7 citations
arXivHTMLPDF

Abstract

Entangling gates in trapped-ion quantum computers are most often applied to stationary ions with initial motional distributions that are thermal and close to the ground state, while those demonstrations that involve transport generally use sympathetic cooling to reinitialize the motional state prior to applying a gate. Future systems with more ions, however, will face greater nonthermal excitation due to increased amounts of ion transport and exacerbated by longer operational times and variations over the trap array. In addition, pregate sympathetic cooling may be limited due to time costs and laser access constraints. In this paper, we analyze the impact of such coherent motional excitation on entangling-gate error by performing simulations of M\o{}lmer-S\o{}renson (MS) gates on a pair of trapped-ion qubits with both thermal and coherent excitation present in a shared motional mode at the start of the gate. We quantify how a small amount of coherent displacement erodes gate performance in the presence of experimental noise, and we demonstrate that adjusting the relative phase between the initial coherent displacement and the displacement induced by the gate or using Walsh modulation can suppress this error. We then use experimental data from transported ions to analyze the impact of coherent displacement on MS-gate error under realistic conditions.

DOI
10.1103/physreva.105.052409

Related papers

Leveraging motional-mode balancing and simply parametrized waveforms to perform frequency-robust entangling gates

Brandon Ruzic, Matthew N. H. Chow, Ashlyn D. Burch +5 more

Near-term quantum algorithms require high-performance entangling gates in a scalable quantum processor, and M\o{}lmer-S\o{}rensen (MS) gates on trapped ions have achieved some of the highest entanglement fidelities to date. However, technical noise that induces small changes in the motional frequencies of the ion chain is a dominant error source in these gates that limits scalability. Here, we report an improved MS-gate design that mitigates the impact of motional-frequency changes by using a class of laser waveforms with three salient features: a spectrally compact Fourier transform, a constant frequency that balances contributions to the MS-gate rotation angle from all motional modes, and a simple parameterization. Together, these features suppress residual coherent displacement of the motional modes, generate robustness to rotation-angle error, and provide low technical complexity and computational overhead. As a proof of concept, we implement this gate design on a four-ion chain, achieving a $<1\mathrm{%}$ fidelity reduction over a $\ifmmode\pm\else\textpm\fi{}10$ kHz range of frequency offset from the calibrated detuning. We also analyze the applicability of our gate design to longer ion chains through numerical simulations of our gate design on chains of up to 33 ions. This robustness to motional-frequency changes represents an order-of-magnitude improvement over the more complicated waveform-shaping techniques that currently dominate the robust-gate literature, and our simulations predict that a high level of robustness can be maintained in these systems for longer ion chains. In addition, the robustness and simplicity of our approach promises to accelerate the development of quantum architectures that invoke long algorithmic runtimes and frequent calibration.

Physical Review Applied•Jul 2, 2024•6 citations

Influence of fast and slow laser phase noise on the fidelity of the Mølmer-Sørensen trapped-ion gate

Nikita Semenin, Ksenia Khabarova, Nikolay Kolachevsky

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.

quant-pharXiv:2609.26912•Quantum Reports•Sep 24, 2026•0 citations

Ion-chain sympathetic cooling and gate dynamics

Aditya Paul, Crystal Noel

Sympathetic cooling is a technique often employed to mitigate motional heating in trapped-ion quantum computers. However, choosing system parameters such as number of coolants and cooling duty cycle for optimal gate performance requires evaluating trade-offs between motional errors and other slower errors such as qubit dephasing. The optimal parameters depend on cooling power, heating rate, and ion spacing in a particular system. In this study, we aim to analyze best practices for sympathetic cooling of long chains of trapped ions using analytical and computational methods. We use a case study to show that optimal cooling performance is achieved when coolants are placed at the center of the chain and provide a perturbative upper bound on the cooling limit of a mode given a particular set of cooling parameters. In addition, using computational tools, we analyze the trade-off between the number of coolant ions in a chain and the center-of-mass mode heating rate. We also show that cooling as often as possible when running a circuit is optimal when the qubit coherence time is otherwise long. These results provide a roadmap for how to choose sympathetic cooling parameters to maximize circuit performance in trapped-ion quantum computers using long chains of ions. Published by the American Physical Society 2024

arXiv:2405.13851•Physical Review Applied•Oct 15, 2024•1 citation

Resilient Entangling Gates for Trapped Ions

A. E. Webb, S. C. Webster, Sam C. Collingbourne +5 more

Constructing a large-scale ion trap quantum processor will require entangling gate operations that are robust in the presence of noise and experimental imperfection. We experimentally demonstrate how a new type of Mølmer-Sørensen gate protects against infidelity caused by heating of the motional mode used during the gate. Furthermore, we show how the same technique simultaneously provides significant protection against slow fluctuations and mis-sets in the secular frequency. Since this parameter sensitivity is worsened in cases where the ions are not ground-state cooled, our method provides a path towards relaxing ion cooling requirements in practical realizations of quantum computing and simulation.

arXiv:1805.07351•Physical Review Letters•Nov 1, 2018•80 citations

Dual-Isotope Sympathetic Cooling in a Long Ion Chain

Tianyi Wang, Marko Cetina

Owing to their high controllability and connectivity, one-dimensional ion chains are attractive building blocks for near-term quantum computers. However, long ion chains are susceptible to motional heating caused by fluctuating external electric fields. To enable deep computations, this source of noise must be suppressed without inducing qubit decoherence or degrading qubit connectivity. We demonstrate steady-state mid-circuit sympathetic cooling of all computationally-relevant motional modes of a 23-ion chain consisting of \qubit qubit and \coolant coolant ions without using any qubit operations. In a room-temperature system, our cooling scheme preserves the mean phonon occupations of the long-wavelength axial and radial modes near their values following state preparation, while keeping the modes used to implement entangling gates near their ground states throughout a 56-ms circuit. Crucially, we show that our cooling sequence preserves qubit coherence, and evaluate its impact on single- and two-qubit gate operations. Additionally, we demonstrate a parallel qubit reset protocol leveraging the shared radial mode coupling between species. Our sympathetic cooling scheme represents a critical step toward reducing gate errors in individually-addressed long ion chains and establishes a versatile platform for simulating open quantum systems.

quant-pharXiv:2608.23386•Aug 25, 2026•0 citations

Batch Optimization of Frequency-Modulated Pulses for Robust Two-Qubit Gates in Ion Chains

Mingyu Kang, Qiyao Liang, Bichen Zhang +5 more

Two-qubit gates in trapped-ion quantum computers are generated by applying spin-dependent forces that temporarily entangle the internal state of the ion with its motion. Laser pulses are carefully designed to generate a maximally entangling gate between the ions while minimizing any residual entanglement between the motion and the ion. The quality of the gates suffers when the actual experimental parameters differ from the ideal case. Here, we improve the robustness of frequency-modulated M\o{}lmer-S\o{}rensen gates to motional mode-frequency offsets by optimizing the average performance over a range of systematic errors using batch optimization. We then compare this method with frequency-modulated gates optimized for ideal parameters that include an analytic robustness condition. Numerical simulations show good performance up to 12 ions, and the method is experimentally demonstrated on a two-ion chain.

arXiv:2104.06887•Physical Review Applied•Aug 24, 2021•37 citations
Entangling gates in trapped-ion quantum computers are most often applied to stationary ions with initial motional distributions that are thermal and close to the ground state, while those demonstrations that involve transport generally use sympathetic cooling to reinitialize the motional state prior to applying a gate. Future systems with more ions, however, will face greater nonthermal excitation due to increased amounts of ion transport and exacerbated by longer operational times and variations over the trap array. In addition, pregate sympathetic cooling may be limited due to time costs and laser access constraints. In this paper, we analyze the impact of such coherent motional excitation on entangling-gate error by performing simulations of M\o{}lmer-S\o{}renson (MS) gates on a pair of trapped-ion qubits with both thermal and coherent excitation present in a shared motional mode at the start of the gate. We quantify how a small amount of coherent displacement erodes gate performance in the presence of experimental noise, and we demonstrate that adjusting the relative phase between the initial coherent displacement and the displacement induced by the gate or using Walsh modulation can suppress this error. We then use experimental data from transported ions to analyze the impact of coherent displacement on MS-gate error under realistic conditions.
Near-term quantum algorithms require high-performance entangling gates in a scalable quantum processor, and M\o{}lmer-S\o{}rensen (MS) gates on trapped ions have achieved some of the highest entanglement fidelities to date. However, technical noise that induces small changes in the motional frequencies of the ion chain is a dominant error source in these gates that limits scalability. Here, we report an improved MS-gate design that mitigates the impact of motional-frequency changes by using a class of laser waveforms with three salient features: a spectrally compact Fourier transform, a constant frequency that balances contributions to the MS-gate rotation angle from all motional modes, and a simple parameterization. Together, these features suppress residual coherent displacement of the motional modes, generate robustness to rotation-angle error, and provide low technical complexity and computational overhead. As a proof of concept, we implement this gate design on a four-ion chain, achieving a $<1\mathrm{%}$ fidelity reduction over a $\ifmmode\pm\else\textpm\fi{}10$ kHz range of frequency offset from the calibrated detuning. We also analyze the applicability of our gate design to longer ion chains through numerical simulations of our gate design on chains of up to 33 ions. This robustness to motional-frequency changes represents an order-of-magnitude improvement over the more complicated waveform-shaping techniques that currently dominate the robust-gate literature, and our simulations predict that a high level of robustness can be maintained in these systems for longer ion chains. In addition, the robustness and simplicity of our approach promises to accelerate the development of quantum architectures that invoke long algorithmic runtimes and frequent calibration.
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.
Sympathetic cooling is a technique often employed to mitigate motional heating in trapped-ion quantum computers. However, choosing system parameters such as number of coolants and cooling duty cycle for optimal gate performance requires evaluating trade-offs between motional errors and other slower errors such as qubit dephasing. The optimal parameters depend on cooling power, heating rate, and ion spacing in a particular system. In this study, we aim to analyze best practices for sympathetic cooling of long chains of trapped ions using analytical and computational methods. We use a case study to show that optimal cooling performance is achieved when coolants are placed at the center of the chain and provide a perturbative upper bound on the cooling limit of a mode given a particular set of cooling parameters. In addition, using computational tools, we analyze the trade-off between the number of coolant ions in a chain and the center-of-mass mode heating rate. We also show that cooling as often as possible when running a circuit is optimal when the qubit coherence time is otherwise long. These results provide a roadmap for how to choose sympathetic cooling parameters to maximize circuit performance in trapped-ion quantum computers using long chains of ions. Published by the American Physical Society 2024
Constructing a large-scale ion trap quantum processor will require entangling gate operations that are robust in the presence of noise and experimental imperfection. We experimentally demonstrate how a new type of Mølmer-Sørensen gate protects against infidelity caused by heating of the motional mode used during the gate. Furthermore, we show how the same technique simultaneously provides significant protection against slow fluctuations and mis-sets in the secular frequency. Since this parameter sensitivity is worsened in cases where the ions are not ground-state cooled, our method provides a path towards relaxing ion cooling requirements in practical realizations of quantum computing and simulation.
Owing to their high controllability and connectivity, one-dimensional ion chains are attractive building blocks for near-term quantum computers. However, long ion chains are susceptible to motional heating caused by fluctuating external electric fields. To enable deep computations, this source of noise must be suppressed without inducing qubit decoherence or degrading qubit connectivity. We demonstrate steady-state mid-circuit sympathetic cooling of all computationally-relevant motional modes of a 23-ion chain consisting of \qubit qubit and \coolant coolant ions without using any qubit operations. In a room-temperature system, our cooling scheme preserves the mean phonon occupations of the long-wavelength axial and radial modes near their values following state preparation, while keeping the modes used to implement entangling gates near their ground states throughout a 56-ms circuit. Crucially, we show that our cooling sequence preserves qubit coherence, and evaluate its impact on single- and two-qubit gate operations. Additionally, we demonstrate a parallel qubit reset protocol leveraging the shared radial mode coupling between species. Our sympathetic cooling scheme represents a critical step toward reducing gate errors in individually-addressed long ion chains and establishes a versatile platform for simulating open quantum systems.
Two-qubit gates in trapped-ion quantum computers are generated by applying spin-dependent forces that temporarily entangle the internal state of the ion with its motion. Laser pulses are carefully designed to generate a maximally entangling gate between the ions while minimizing any residual entanglement between the motion and the ion. The quality of the gates suffers when the actual experimental parameters differ from the ideal case. Here, we improve the robustness of frequency-modulated M\o{}lmer-S\o{}rensen gates to motional mode-frequency offsets by optimizing the average performance over a range of systematic errors using batch optimization. We then compare this method with frequency-modulated gates optimized for ideal parameters that include an analytic robustness condition. Numerical simulations show good performance up to 12 ions, and the method is experimentally demonstrated on a two-ion chain.