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:2504.06259 · IEEE Transactions on Quantum Engineering

Realization and Calibration of Continuously Parameterized Two-Qubit Gates on a Trapped-Ion Quantum Processor

Christopher G. Yale, Ashlyn D. Burch, Matthew N. H. Chow, Brandon Ruzic, Daniel Lobser, Brian McFarland, Melissa Revelle, Susan Clark

Published Jan 1, 2025• 2 citations
arXivHTMLPDF

Abstract

Continuously parameterized two-qubit gates are a key feature of state-of-the-art trapped-ion quantum processors as they have favorable error scalings and show distinct improvements in circuit performance over more restricted maximally entangling gatesets. In this work, we provide a comprehensive and pedagogical discussion on how to practically implement these continuously parameterized Mølmer Sørensen gates on the Quantum Scientific Computing Open User Testbed (QSCOUT), a low-level trappedion processor. To generate the arbitrary entangling angles, θ, we simply scale the amplitude of light used to generate the entanglement. However, doing so requires careful consideration of amplifier saturation as well as the variable light shifts that result. As such, we describe a method to calibrate and cancel the dominant fourth-order effects, followed by a dynamic virtual phase advance during the gate to cancel any residual light shifts, and find a linear scaling between θ and the residual light shift. Once, we have considered and calibrated these effects, we demonstrate performance improvement with decreasing θ. Finally, we describe nuances of hardware control to transform the XX-type interaction of the arbitraryangle Mølmer-Sørensen gate into a phase-agnostic and crosstalk-mitigating ZZ interaction.

DOI
10.1109/tqe.2025.3600216

Related papers

Noise-aware circuit compilations for a continuously parameterized two-qubit gateset

Christopher G. Yale, Rich Rines, Victory Omole +9 more

State-of-the-art noisy-intermediate-scale quantum processors are currently implemented across a variety of hardware platforms, each with their own distinct gatesets. As such, circuit compilation should not only be aware of but also deeply connect to the native gateset and noise properties of each. Trapped-ion processors are one such platform that provides a gateset that can be continuously parameterized across both one- and two-qubit gates. Here we use the Quantum Scientific Computing Open User Testbed to study noise-aware compilations focused on continuously parameterized two-qubit Z Z gates (based on the Mølmer-Sørensen interaction) using , a quantum software platform for hardware-aware circuit compiler optimizations. We discuss the realization of Z Z gates with arbitrary angle on the all-to-all connected trapped-ion system. Then we discuss a variety of different compiler optimizations that innately target these Z Z gates and their noise properties. These optimizations include moving from a restricted maximally entangling gateset to a continuously parameterized one, swap mirroring to further reduce the total entangling angle of the operations, focusing the heaviest Z Z angle participation on the best-performing gate pairs, and circuit approximation to remove the least impactful Z Z gates. We demonstrate these compilation approaches on the hardware with randomized quantum volume circuits, observing the potential to realize a larger quantum volume as a result of these optimizations. Using differing yet complementary analysis techniques, we observe the distinct improvements in system performance provided by these noise-aware compilations and study the role of stochastic and coherent error channels for each compilation choice.

arXiv:2411.01094•Physical Review Applied•Jul 14, 2025•3 citations

QSCOUT: Continuously parameterized Mølmer-Sørensen gates for quantum computing circuits (Part II)

Christopher G. Yale, Ashlyn D. Burch, Matthew N. H. Chow +11 more

Continuously Parameterized Mølmer-Sørensen Gates 2 • The MS gate has an entangling interaction of the form: 𝑀𝑆 𝜃, 𝜙 = exp -𝑖 𝜃 2 cos 𝜙 𝜎 𝑥 + sin 𝜙 𝜎 𝑦 ⊗2• 𝜃 is related to the amount of entanglement from the gate • Most quantum computers have not previously offered arbitrary 𝜃 for the two-qubit gate (IonQ only offers 𝑀𝑆( 𝜋 2 ), Quantinuum recently announced 𝑀𝑆(𝜃)) Enables: • Reduction in quantum circuit depth • Less error / more coherence per gate for smaller 𝜽 Key Elements of 𝑀𝑆(𝜃) 3• How do we realize an arbitrary-angle 𝑴𝑺(𝜽) gate?• Global tone and two individual tones to form the needed red-and blue-detuned Raman transition• All tones have a Gaussian pulse envelope to limit displacement errors [see B. Ruzic B67.00012 (this session)]• To set the angular enclosure, we adjust the global beam power Distortion correctionSources of Error:• 𝜹𝜽 (coherent rotation errors) → distortion/saturation in global beam control electronics• 𝜹𝝓 (coherent phase errors) → resulting AC Stark shifts

APS March Meeting Abstracts•Mar 1, 2023•0 citations

Analysis of the action of conventional trapped-ion entangling gates in qudit space

Pavel Kamenskikh, Nikita Semenin, Ilia Zalivako +4 more

Qudits, or multi-level quantum information carriers, present a promising path for scaling quantum computers. However, their use introduces increased complexity in quantum logic, necessitating careful control of relative phases between different qudit levels. In trapped-ion systems, entangling operations accumulate phases on specific levels that are no longer global, unlike in qubit architectures. Furthermore, the structure of multi-level gates becomes increasingly intricate with higher-dimensional Hilbert spaces. This work explores the theory of these additional local and nonlocal phases, accumulated in Mølmer--Sørensen and Light-shift gates. We propose methods to actively compensate for these phases, enhance gate robustness against parameter fluctuations, and simplify native gates for more efficient circuit decomposition. Our results pave the way toward the practical and scalable implementation of qudit-based quantum processors.

quant-pharXiv:2602.21886•Physical Review A•Feb 26, 2026•0 citations

Analytical and experimental study of center-line miscalibrations in Mølmer-Sørensen gates

Fernando Martínez-García, Lukas Gerster, Davide Vodola +4 more

A major challenge for the realization of useful universal quantum computers is achieving high fidelity two-qubit entangling gate operations. However, calibration errors can affect the quantum gate operations and limit their fidelity. To reduce such errors it is desirable to have an analytical understanding and quantitative predictions of the effects that miscalibrations of gate parameters have on the gate performance. In this work, we study a systematic perturbative expansion in miscalibrated parameters of the M\o{}lmer-S\o{}rensen entangling gate, which is widely used in trapped-ion quantum processors. Our analytical treatment particularly focuses on systematic center-line detuning miscalibrations. Via a unitary Magnus expansion, we compute the gate evolution operator, which allows us to obtain relevant key properties such as relative phases, electronic populations, quantum state purity and fidelities. These quantities, subsequently, are used to assess the performance of the gate using the fidelity of entangled states as performance metric. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor. The method and the results presented here can help design and calibrate high-fidelity gate operations of large-scale quantum computers.

arXiv:2112.05447•Physical Review A•Mar 23, 2022•9 citations

Closed-loop control for two-qubit gates with trapped ions

Eduardo J. Páez, Seyed Shakib Vedaie, Barry C. Sanders

State-of-the-art two-qubit gates with trapped ions employ open-loop control that rely on simplified models to precompute control sequences. Our aim is to introduce closed-loop control for two-qubit gates to correct disturbances as they occur during the gate implementation. We introduce a spectator ion into the ion chain used for quantum logic processing, where it couples with the other ions through collective motional modes. The spectator ion's position is continuously monitored by driving dipole transitions and detecting the resultant fluorescence. We show that incorporating a spectator ion is feasible for linear Paul trap implementations and is expected to reduce the two-qubit gate Bell-state preparation infidelity by an order of magnitude with the deleterious effects of position monitoring being negligible compared to the thermal effects that exist in the system, even in the absence of the spectator ions. Mathematically, we describe driven ion-trap dynamics, including the spectator ion, by a stochastic quantum master equation involving the amplitude-modulation multimode-motional coupling gate, motional drift, thermal effects, recoil from photon scattering, spontaneous decay, and light shift. Our on-the-fly control method employs reinforcement learning with the reward function based on the actual geometric phase of the spectator ion. A key advantage of our approach is that we introduce a control method that involves `learning' and correcting disturbances happening in the trap on-the-fly, thus achieving high-fidelity gates. Our approach will lead to a significantly higher two-qubit gate fidelity at a reduced calibration overhead owing to the small parameter drift in the control system.

quant-pharXiv:2607.00462•Jul 2, 2026•0 citations

Experimental Bayesian Calibration of Trapped-Ion Entangling Operations

Lukas Gerster, Fernando Martínez-García, Pavel Hrmo +7 more

The performance of quantum gate operations is experimentally determined by how correctly operational parameters can be determined and set, and how stable these parameters can be maintained.In addition, gates acting on different sets of qubits require unique sets of control parameters.Thus, an efficient multidimensional parameter estimation procedure is crucial to calibrate even medium-sized quantum processors.Here, we develop and characterize an efficient calibration protocol to automatically estimate and adjust experimental parameters of the widely used two-qubit Mølmer-Sørensen entangling gate operation in a trapped-ion quantum information processor.The protocol exploits Bayesian parameter estimation methods that include a stopping criterion based on a desired gate infidelity.We experimentally demonstrate a tune-up procedure that leads to a residual median gate infidelity due to miscalibration of 1.3(1) × 10 -3 , requiring 1200 ± 500 experimental cycles, while completing the entire gate calibration procedure in less than one minute, which provides a significant speedup over commonly used manual tune-up routines.This approach is applicable to other quantum information processor architectures with known or sufficiently characterized theoretical models.

arXiv:2112.01411•PRX Quantum•Jun 8, 2022•24 citations
Continuously parameterized two-qubit gates are a key feature of state-of-the-art trapped-ion quantum processors as they have favorable error scalings and show distinct improvements in circuit performance over more restricted maximally entangling gatesets. In this work, we provide a comprehensive and pedagogical discussion on how to practically implement these continuously parameterized Mølmer Sørensen gates on the Quantum Scientific Computing Open User Testbed (QSCOUT), a low-level trappedion processor. To generate the arbitrary entangling angles, θ, we simply scale the amplitude of light used to generate the entanglement. However, doing so requires careful consideration of amplifier saturation as well as the variable light shifts that result. As such, we describe a method to calibrate and cancel the dominant fourth-order effects, followed by a dynamic virtual phase advance during the gate to cancel any residual light shifts, and find a linear scaling between θ and the residual light shift. Once, we have considered and calibrated these effects, we demonstrate performance improvement with decreasing θ. Finally, we describe nuances of hardware control to transform the XX-type interaction of the arbitraryangle Mølmer-Sørensen gate into a phase-agnostic and crosstalk-mitigating ZZ interaction.
State-of-the-art noisy-intermediate-scale quantum processors are currently implemented across a variety of hardware platforms, each with their own distinct gatesets. As such, circuit compilation should not only be aware of but also deeply connect to the native gateset and noise properties of each. Trapped-ion processors are one such platform that provides a gateset that can be continuously parameterized across both one- and two-qubit gates. Here we use the Quantum Scientific Computing Open User Testbed to study noise-aware compilations focused on continuously parameterized two-qubit Z Z gates (based on the Mølmer-Sørensen interaction) using , a quantum software platform for hardware-aware circuit compiler optimizations. We discuss the realization of Z Z gates with arbitrary angle on the all-to-all connected trapped-ion system. Then we discuss a variety of different compiler optimizations that innately target these Z Z gates and their noise properties. These optimizations include moving from a restricted maximally entangling gateset to a continuously parameterized one, swap mirroring to further reduce the total entangling angle of the operations, focusing the heaviest Z Z angle participation on the best-performing gate pairs, and circuit approximation to remove the least impactful Z Z gates. We demonstrate these compilation approaches on the hardware with randomized quantum volume circuits, observing the potential to realize a larger quantum volume as a result of these optimizations. Using differing yet complementary analysis techniques, we observe the distinct improvements in system performance provided by these noise-aware compilations and study the role of stochastic and coherent error channels for each compilation choice.
Continuously Parameterized Mølmer-Sørensen Gates 2 • The MS gate has an entangling interaction of the form: 𝑀𝑆 𝜃, 𝜙 = exp -𝑖 𝜃 2 cos 𝜙 𝜎 𝑥 + sin 𝜙 𝜎 𝑦 ⊗2• 𝜃 is related to the amount of entanglement from the gate • Most quantum computers have not previously offered arbitrary 𝜃 for the two-qubit gate (IonQ only offers 𝑀𝑆( 𝜋 2 ), Quantinuum recently announced 𝑀𝑆(𝜃)) Enables: • Reduction in quantum circuit depth • Less error / more coherence per gate for smaller 𝜽 Key Elements of 𝑀𝑆(𝜃) 3• How do we realize an arbitrary-angle 𝑴𝑺(𝜽) gate?• Global tone and two individual tones to form the needed red-and blue-detuned Raman transition• All tones have a Gaussian pulse envelope to limit displacement errors [see B. Ruzic B67.00012 (this session)]• To set the angular enclosure, we adjust the global beam power Distortion correctionSources of Error:• 𝜹𝜽 (coherent rotation errors) → distortion/saturation in global beam control electronics• 𝜹𝝓 (coherent phase errors) → resulting AC Stark shifts
Qudits, or multi-level quantum information carriers, present a promising path for scaling quantum computers. However, their use introduces increased complexity in quantum logic, necessitating careful control of relative phases between different qudit levels. In trapped-ion systems, entangling operations accumulate phases on specific levels that are no longer global, unlike in qubit architectures. Furthermore, the structure of multi-level gates becomes increasingly intricate with higher-dimensional Hilbert spaces. This work explores the theory of these additional local and nonlocal phases, accumulated in Mølmer--Sørensen and Light-shift gates. We propose methods to actively compensate for these phases, enhance gate robustness against parameter fluctuations, and simplify native gates for more efficient circuit decomposition. Our results pave the way toward the practical and scalable implementation of qudit-based quantum processors.
A major challenge for the realization of useful universal quantum computers is achieving high fidelity two-qubit entangling gate operations. However, calibration errors can affect the quantum gate operations and limit their fidelity. To reduce such errors it is desirable to have an analytical understanding and quantitative predictions of the effects that miscalibrations of gate parameters have on the gate performance. In this work, we study a systematic perturbative expansion in miscalibrated parameters of the M\o{}lmer-S\o{}rensen entangling gate, which is widely used in trapped-ion quantum processors. Our analytical treatment particularly focuses on systematic center-line detuning miscalibrations. Via a unitary Magnus expansion, we compute the gate evolution operator, which allows us to obtain relevant key properties such as relative phases, electronic populations, quantum state purity and fidelities. These quantities, subsequently, are used to assess the performance of the gate using the fidelity of entangled states as performance metric. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor. The method and the results presented here can help design and calibrate high-fidelity gate operations of large-scale quantum computers.
State-of-the-art two-qubit gates with trapped ions employ open-loop control that rely on simplified models to precompute control sequences. Our aim is to introduce closed-loop control for two-qubit gates to correct disturbances as they occur during the gate implementation. We introduce a spectator ion into the ion chain used for quantum logic processing, where it couples with the other ions through collective motional modes. The spectator ion's position is continuously monitored by driving dipole transitions and detecting the resultant fluorescence. We show that incorporating a spectator ion is feasible for linear Paul trap implementations and is expected to reduce the two-qubit gate Bell-state preparation infidelity by an order of magnitude with the deleterious effects of position monitoring being negligible compared to the thermal effects that exist in the system, even in the absence of the spectator ions. Mathematically, we describe driven ion-trap dynamics, including the spectator ion, by a stochastic quantum master equation involving the amplitude-modulation multimode-motional coupling gate, motional drift, thermal effects, recoil from photon scattering, spontaneous decay, and light shift. Our on-the-fly control method employs reinforcement learning with the reward function based on the actual geometric phase of the spectator ion. A key advantage of our approach is that we introduce a control method that involves `learning' and correcting disturbances happening in the trap on-the-fly, thus achieving high-fidelity gates. Our approach will lead to a significantly higher two-qubit gate fidelity at a reduced calibration overhead owing to the small parameter drift in the control system.
The performance of quantum gate operations is experimentally determined by how correctly operational parameters can be determined and set, and how stable these parameters can be maintained.In addition, gates acting on different sets of qubits require unique sets of control parameters.Thus, an efficient multidimensional parameter estimation procedure is crucial to calibrate even medium-sized quantum processors.Here, we develop and characterize an efficient calibration protocol to automatically estimate and adjust experimental parameters of the widely used two-qubit Mølmer-Sørensen entangling gate operation in a trapped-ion quantum information processor.The protocol exploits Bayesian parameter estimation methods that include a stopping criterion based on a desired gate infidelity.We experimentally demonstrate a tune-up procedure that leads to a residual median gate infidelity due to miscalibration of 1.3(1) × 10 -3 , requiring 1200 ± 500 experimental cycles, while completing the entire gate calibration procedure in less than one minute, which provides a significant speedup over commonly used manual tune-up routines.This approach is applicable to other quantum information processor architectures with known or sufficiently characterized theoretical models.