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:2101.04648 · Quantum Science and Technology

Quantum process tomography of a Mølmer-Sørensen gate via a global beam

Holly N. Tinkey, Adam M Meier, Craig R Clark, Christopher M. Seck, Kenton R. Brown

Published May 26, 2021• 8 citations
arXivHTMLPDF

Abstract

Abstract We present a framework for quantum process tomography of two-ion interactions that leverages modulations of the trapping potential and composite pulses from a global laser beam to achieve individual-ion addressing. Tomographic analysis of identity and delay processes reveals dominant error contributions from laser decoherence and slow qubit frequency drift during the tomography experiment. We use this framework on two co-trapped 40 Ca + ions to analyze both an optimized and an overpowered Mølmer–Sørensen gate and to compare the results of this analysis to a less informative Bell-state tomography measurement and to predictions based on a simplified noise model. These results show that the technique is effective for the characterization of two-ion quantum processes and for the extraction of meaningful information about the errors present in the system. The experimental convenience of this method will allow for more widespread use of process tomography for characterizing entangling gates in trapped-ion systems.

DOI
10.1088/2058-9565/ac0543

Related papers

Mitigation of Preparation, Transformation, and Measurement Errors of a Two-Qubit State in Mølmer–Sørensen Gate Tomography

I. A. Dmitriev, Yu. I. Bogdanov, B. I. Bantysh +2 more

Abstract A method for quantum-process reconstruction using fuzzy measurement operators has been developed, where readout errors and decoherence of an ion-trap quantum register are incorporated into the effective measurement operators. The proposed approach outperforms standard methods that neglect measurement errors and decoherence in accurately reconstructing the Mølmer–Sørensen gate. Numerical experiments with entangled two-qubit states confirm that the proposed model significantly improves the fidelity of quantum process reconstruction. The obtained results demonstrate the potential of the proposed approach for creating more reliable and precise control methods in quantum computing on an ion platform, which is important for the development of quantum computing technologies.

Russian Microelectronics•Feb 1, 2026•0 citations

Quantum process tomography of a Mølmer-Sørensen interaction

Nir Navon, Nitzan Akerman, Shlomi Kotler +2 more

We present a simple tomographic protocol, for two-qubit systems, that relies on a single discriminatory transition and no direct spatially selective imaging. This scheme exploits excess micromotion in the trap to realize all operations required to prepare all input states and analyze all output states. We demonstrate a two-qubit entangling gate with a Bell state production fidelity of 0.981(6), and apply the above protocol to perform the first quantum process tomography of a M\o{}lmer-S\o{}rensen entangling gate. We characterize its $\ensuremath{\chi}$-process matrix, the simplest for an entanglement gate on a separable-states basis, and observe that our dominant source of error is accurately modeled by a quantum depolarization channel.

arXiv:1309.4502•Physical Review A•Jul 28, 2014•23 citations

A hardware-efficient Mølmer–Sørensen gate for superconducting quantum computers

M. AbuGhanem

Abstract The Mølmer–Sørensen gate, a cornerstone entangling operation in trapped-ion systems, represents a promising alternative to standard entangling gates in superconducting quantum architectures. However, its performance on superconducting hardware has remained unverified. In this work, we present a hardware-efficient implementation of the Mølmer–Sørensen gate and characterize its performance using quantum process tomography (QPT) on IBM Quantum’s superconducting processors. Our implementation achieves a process fidelity of 92.47% on the real quantum hardware, a performance competitive with the 93.02% fidelity of the device’s native controlled-NOT (CX) gate. Furthermore, for the $$\vert {00} \rangle $$ | 00 ⟩ input state, the gate prepares the target Bell state with $$94.2\%$$ 94.2 % success probability, confirming its correct logical operation. These results demonstrate that non-native entangling gates can be optimized to perform on par with hardware-native operations. This work expands the effective gate set for algorithm design on fixed-architecture processors and provides a critical benchmark for cross-platform gate evaluation, underscoring the role of hardware-aware compilation in advancing noisy intermediate-scale quantum (NISQ) computing.

arXiv:2510.07352•Quantum Information Processing•Apr 21, 2026•1 citation

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

Entanglement of trapped-ion clock states

P. C. Haljan, P. J. Lee, Kathy-Anne Brickman +3 more

A M\o{}lmer-S\o{}rensen entangling gate is realized for pairs of trapped $^{111}\mathrm{Cd}^{+}$ ions using magnetic-field insensitive ``clock'' states and an implementation offering reduced sensitivity to optical phase drifts. The gate is used to generate the complete set of four entangled states, which are reconstructed and evaluated with quantum-state tomography. An average target-state fidelity of 0.79 is achieved, limited by available laser power and technical noise. The tomographic reconstruction of entangled states demonstrates universal quantum control of two ion qubits, which through multiplexing can provide a route to scalable architectures for trapped-ion quantum computing.

arXiv:quant-ph/0508123•Physical Review A•Dec 9, 2005•124 citations

Experimental characterization of coherent and non-Markovian errors using tangent space decomposition

Elia Perego, Andrea Rodriguez-Blanco, K. Birgitta Whaley +1 more

Accurate characterization of coherent and non-Markovian errors remains a central challenge in quantum information processing, as conventional benchmarking techniques typically rely on Markovian and time-independent noise assumptions. In practice, however, quantum devices exhibit both systematic coherent miscalibrations and temporally correlated fluctuations, which complicate error diagnosis and mitigation. Here, we apply a technique based on tangent-space decomposition to characterize such error in single-qubit quantum gates implemented on a trapped ion platform. Small imperfections in a quantum operation are treated as perturbations of the target quantum map, represented as tangent vectors in the space of quantum channels. This formulations enables a natural decomposition of the deviation into three components corresponding to coherent, Markovian and non-Markovian processes.The relative weights of these components provide a quantitative measure of the contribution from each type of error mechanism, directly from a single tomographic snapshot. We experimentally validate this method on a single-qubit gates implemented on a trapped $^{40}$Ca$^+$ ion, where control is achieved through laser-driven optical transitions. By analyzing experimentally reconstructed process matrices, expressed in the Pauli Transfer Matrix and Choi representations, we identify and quantify non-Markovian effects arising from controlled injection of slow fluctuations in the experimental environment. We also characterize deterministic coherent miscalibrations using the same technique. This approach provides a physically transparent and experimentally accessible tool for diagnosing complex error sources in quantum control systems.

quant-pharXiv:2602.20128•Feb 24, 2026•0 citations
Abstract We present a framework for quantum process tomography of two-ion interactions that leverages modulations of the trapping potential and composite pulses from a global laser beam to achieve individual-ion addressing. Tomographic analysis of identity and delay processes reveals dominant error contributions from laser decoherence and slow qubit frequency drift during the tomography experiment. We use this framework on two co-trapped 40 Ca + ions to analyze both an optimized and an overpowered Mølmer–Sørensen gate and to compare the results of this analysis to a less informative Bell-state tomography measurement and to predictions based on a simplified noise model. These results show that the technique is effective for the characterization of two-ion quantum processes and for the extraction of meaningful information about the errors present in the system. The experimental convenience of this method will allow for more widespread use of process tomography for characterizing entangling gates in trapped-ion systems.
Abstract A method for quantum-process reconstruction using fuzzy measurement operators has been developed, where readout errors and decoherence of an ion-trap quantum register are incorporated into the effective measurement operators. The proposed approach outperforms standard methods that neglect measurement errors and decoherence in accurately reconstructing the Mølmer–Sørensen gate. Numerical experiments with entangled two-qubit states confirm that the proposed model significantly improves the fidelity of quantum process reconstruction. The obtained results demonstrate the potential of the proposed approach for creating more reliable and precise control methods in quantum computing on an ion platform, which is important for the development of quantum computing technologies.
We present a simple tomographic protocol, for two-qubit systems, that relies on a single discriminatory transition and no direct spatially selective imaging. This scheme exploits excess micromotion in the trap to realize all operations required to prepare all input states and analyze all output states. We demonstrate a two-qubit entangling gate with a Bell state production fidelity of 0.981(6), and apply the above protocol to perform the first quantum process tomography of a M\o{}lmer-S\o{}rensen entangling gate. We characterize its $\ensuremath{\chi}$-process matrix, the simplest for an entanglement gate on a separable-states basis, and observe that our dominant source of error is accurately modeled by a quantum depolarization channel.
Abstract The Mølmer–Sørensen gate, a cornerstone entangling operation in trapped-ion systems, represents a promising alternative to standard entangling gates in superconducting quantum architectures. However, its performance on superconducting hardware has remained unverified. In this work, we present a hardware-efficient implementation of the Mølmer–Sørensen gate and characterize its performance using quantum process tomography (QPT) on IBM Quantum’s superconducting processors. Our implementation achieves a process fidelity of 92.47% on the real quantum hardware, a performance competitive with the 93.02% fidelity of the device’s native controlled-NOT (CX) gate. Furthermore, for the ∣00⟩\vert {00} \rangle ∣00⟩ | 00 ⟩ input state, the gate prepares the target Bell state with 94.2%94.2\%94.2% 94.2 % success probability, confirming its correct logical operation. These results demonstrate that non-native entangling gates can be optimized to perform on par with hardware-native operations. This work expands the effective gate set for algorithm design on fixed-architecture processors and provides a critical benchmark for cross-platform gate evaluation, underscoring the role of hardware-aware compilation in advancing noisy intermediate-scale quantum (NISQ) computing.
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.
A M\o{}lmer-S\o{}rensen entangling gate is realized for pairs of trapped 111Cd+^{111}\mathrm{Cd}^{+}111Cd+ ions using magnetic-field insensitive ``clock'' states and an implementation offering reduced sensitivity to optical phase drifts. The gate is used to generate the complete set of four entangled states, which are reconstructed and evaluated with quantum-state tomography. An average target-state fidelity of 0.79 is achieved, limited by available laser power and technical noise. The tomographic reconstruction of entangled states demonstrates universal quantum control of two ion qubits, which through multiplexing can provide a route to scalable architectures for trapped-ion quantum computing.
Accurate characterization of coherent and non-Markovian errors remains a central challenge in quantum information processing, as conventional benchmarking techniques typically rely on Markovian and time-independent noise assumptions. In practice, however, quantum devices exhibit both systematic coherent miscalibrations and temporally correlated fluctuations, which complicate error diagnosis and mitigation. Here, we apply a technique based on tangent-space decomposition to characterize such error in single-qubit quantum gates implemented on a trapped ion platform. Small imperfections in a quantum operation are treated as perturbations of the target quantum map, represented as tangent vectors in the space of quantum channels. This formulations enables a natural decomposition of the deviation into three components corresponding to coherent, Markovian and non-Markovian processes.The relative weights of these components provide a quantitative measure of the contribution from each type of error mechanism, directly from a single tomographic snapshot. We experimentally validate this method on a single-qubit gates implemented on a trapped 40^{40}40Ca+^++ ion, where control is achieved through laser-driven optical transitions. By analyzing experimentally reconstructed process matrices, expressed in the Pauli Transfer Matrix and Choi representations, we identify and quantify non-Markovian effects arising from controlled injection of slow fluctuations in the experimental environment. We also characterize deterministic coherent miscalibrations using the same technique. This approach provides a physically transparent and experimentally accessible tool for diagnosing complex error sources in quantum control systems.