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:2512.00843 · PRX Quantum

Multiqubit Rydberg Gates for Quantum Error Correction

David F. Locher, Josias Old, Katharina Brechtelsbauer, Jakob Holschbach, Hans Peter Büchler, Sebastian Weber, Markus Müller

quant-phSubmitted Nov 30, 2025• Announced Dec 2, 2025• 1 citation• Revised May 4, 2026 (v2)
v1 · Nov 30, 2025v2 · May 4, 2026
arXivHTMLPDF

Abstract

Multiqubit gates that involve three or more qubits are usually thought to be of little significance for fault-tolerant quantum error correction because single gate faults can lead to errors of high Pauli weight. However, recent works have shown that multiqubit gates can be beneficial for measurement-free fault-tolerant quantum error correction and for fault-tolerant stabilizer readout in unrotated surface codes. In this work, we investigate multiqubit Rydberg gates that are useful for fault-tolerant quantum error correction in single-species neutral-atom platforms and can be implemented with global laser pulses that do not individually address atomic sites. We develop an open-source Python package to generate analytical, few-parameter pulses that implement the desired gates while minimizing gate errors due to Rydberg-state decay. The tool also allows us to identify parameter-optimal pulses, characterized by a minimal parameter count for the pulse ansatz. Measurement-free quantum error correction protocols require CCZ gates, which we analyze for atoms arranged in symmetric and asymmetric configurations. We investigate the performance of these schemes for various single-, two-, and three-qubit gate error rates, showing that break-even performance of measurement-free QEC is within reach of current hardware. Moreover, we study Floquet quantum error correction protocols that comprise two-body stabilizer measurements. Those can be realized using global three-qubit gates, and we show that this can lead to a significant reduction in shuttling operations. Simulations with realistic circuit-level noise indicate that applying three-qubit gates for stabilizer measurements in Floquet codes can yield competitive logical qubit performance in experimentally relevant error regimes.

Journal reference
PRX Quantum 7, 020354 (2026)
DOI
10.1103/j8fm-24cf
Comments
27 pages, 18 figures

Related papers

Low-Depth Quantum Error Correction via Three-Qubit Gates in Rydberg Atom Arrays

Laura Pecorari, Sven Jandura, Guido Pupillo

Quantum error correction (QEC) requires the execution of deep quantum circuits with large numbers of physical qubits to protect information against errors. Designing protocols that can reduce gate and space-time overheads of QEC is therefore crucial to enable more efficient QEC in near-term experiments. Multiqubit gates offer a natural path toward fast and low-depth stabilizer measurement circuits. However, they typically introduce high-weight correlated errors that can degrade the circuit-level distance, leading to slower scalings of the logical error probabilities. In this Letter, we show how to realize fast and efficient surface code stabilizer readout using only two singly controlled z gates acting simultaneously on two target qubits, i.e., two CZ_{2} gates-instead of four cz. We show that this scheme is fault tolerant and provide a blueprint for implementation in Rydberg atom arrays. We derive the time-optimal pulses implementing the gates and perform extensive QEC numerical simulations with Rydberg decay errors. Compared to the standard protocol using four cz gates, our scheme is faster, uses fewer gates, and crucially maintains fault tolerance with comparable logical error probabilities. Fault-tolerant generalizations of this scheme to biased and erasure-dominant noise models, as well as to other QEC codes such as quantum Low-Density Parity-Check codes, are also discussed.

arXiv:2507.06096•Physical Review Letters•Nov 17, 2025•4 citations

Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates

Josias Old, Stephan Tasler, Michael J. Hartmann +1 more

Stabilizer quantum error correction (QEC) codes, in particular topological surface codes, are prime candidates to enable practical quantum computing. While it is widely believed that strictly fault-tolerant protocols can only be implemented using single- and two-qubit gates, several quantum computing platforms, including trapped ions, neutral atoms, and superconducting qubits, support native multi-qubit operations. In this Letter, we show that stabilizer measurement circuits for unrotated surface codes can be fault tolerant using single auxiliary qubits and three-qubit gates. These gates enable lower-depth circuits with fewer fault locations and potentially shorter QEC cycle times. We find that in an optimistic parameter regime where fidelities of three-qubit gates are the same as those of two-qubit gates, the logical error rate can be up to one order of magnitude lower and the threshold significantly higher, increasing from ≈0.63% to ≈0.83%. Our results, applicable to a wide range of platforms, motivate further investigation into multi-qubit gates for fault-tolerant QEC as they can offer substantial time and physical qubit resource advantages to reach a given target logical error rate.

arXiv:2506.09029•Physical Review Letters•Nov 13, 2025•7 citations

Measurement-Free Fault-Tolerant Quantum Error Correction in Near-Term Devices

Sascha Heußen, David F. Locher, Markus Müller

Logical qubits can be protected from decoherence by performing quantum error-correction (QEC) cycles repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific hardware platform under consideration in order to practically realize a quantum memory that operates for in principle arbitrary long times. All circuit components must be assumed as noisy unless specific assumptions about the form of the noise are made. Modern QEC schemes are challenging to implement experimentally in physical architectures where in-sequence measurements and feed forward of classical information cannot be reliably executed fast enough or even at all. Here we provide a novel scheme to perform QEC cycles without the need of measuring qubits that is fully fault-tolerant with respect to all components used in the circuit. Our scheme can be used for any low-distance CSS code since its only requirement towards the underlying code is a transversal gate. Similarly to Steane-type EC, we coherently copy errors to a logical auxiliary qubit but then apply a coherent feedback operation from the auxiliary system to the logical data qubit. The logical auxiliary qubit is prepared fault tolerantly without measurements, too. We benchmark logical failure rates of the scheme in comparison to a flag-qubit-based EC cycle. We map out a parameter region where our scheme is feasible and estimate physical error rates necessary to achieve the break-even point of beneficial QEC with our scheme. We outline how our scheme could be implemented in ion traps and with neutral atoms in a tweezer array. For recently demonstrated capabilities of atom shuttling and native multiatom Rydberg gates, we achieve moderate circuit depths and beneficial performance of our scheme while not breaking fault tolerance. These results thereby enable practical fault-tolerant QEC in hardware architectures that do not support midcircuit measurements. Published by the American Physical Society 2024

PRX Quantum•Feb 27, 2024•44 citations

Optimizing Superconducting Three-Qubit Gates for Surface-Code Error Correction

Stephan Tasler, Josias Old, Lukas Heunisch +4 more

Quantum error correction (QEC) is one of the crucial building blocks for developing quantum computers that have significant potential for reaching a quantum advantage in applications. Prominent candidates for QEC are stabilizer codes for which periodic readout of stabilizer operators is typically implemented via successive two-qubit entangling gates, and is repeated many times during a computation. To improve QEC performance, it is thus beneficial to make the stabilizer readout faster and less prone to fault-tolerance-breaking errors. Here we design a 3-qubit CZZ gate for superconducting transmon qubits that maps the parity of two data qubits onto one measurement qubit in a single step. We find that the gate can be executed in a duration of $35\,$ns with a fidelity of F$=99.96 \, \%$. To optimize the gate, we use an error model obtained from the microscopic gate simulation to systematically suppress Pauli errors that are particularly harmful to the QEC protocol. Using this error model, we investigate the implementation of this 3-qubit gate in a surface code syndrome readout schedule. We find that for the rotated surface code, the implementation of CZZ gates increases the error threshold by nearly 50\% to $\approx 1.2\,\%$ and decreases the logical error rate, in the experimental relevant regime, by up to one order of magnitude, compared to the standard CZ readout protocol. We also show that for the unrotated surface code, strictly fault-tolerant readout schedules can be found. This opens a new perspective for below-threshold surface-code error correction, where it can be advantageous to use multi-qubit gates instead of two-qubit gates to obtain a better QEC performance.

arXiv:2506.09028•Jan 1, 2025•0 citations

Fast Native Three-Qubit Gates and Fault-Tolerant Quantum Error Correction with Trapped Rydberg Ions

Katrin Bolsmann, Thiago L. M. Guedes, Weibin Li +3 more

Trapped ions as one of the most promising quantum-information-processing platforms, yet conventional entangling gates mediated by collective motion remain slow and difficult to scale. Exciting trapped ions to high-lying electronic Rydberg states provides a promising route to overcome these limitations by enabling strong, long-range dipole-dipole interactions that support much faster multi-qubit operations. Here, we introduce the first scheme for implementing a native controlled-controlled-Z gate with microwave-dressed Rydberg ions by optimizing a single-pulse protocol that accounts for the finite Rydberg-state lifetime. The resulting gate outperforms standard decompositions into one- and two-qubit gates by achieving fidelities above 97% under realistic conditions, with execution times of about 2 microseconds at cryogenic temperatures. To explore the potential of trapped Rydberg ions for fault-tolerant quantum error correction, and to illustrate the utility of three-qubit Rydberg-ion gates in this context, we develop and analyze a proposal for fault-tolerant, measurement-free quantum error correction using the nine-qubit Bacon-Shor code. Our simulations confirm that quantum error correction can be performed in a fully fault-tolerant manner on a linear Rydberg-ion chain despite its limited qubit connectivity. These results establish native multiqubit Rydberg-ion gates as a valuable resource for fast, high-fidelity quantum computing and highlight their potential for fault-tolerant quantum error correction.

quant-pharXiv:2512.16641•Quantum Science and Technology•Dec 19, 2025•0 citations

Measurement-Free Quantum Error Correction Optimized for Biased Noise

Katharina Brechtelsbauer, Friederike Butt, David F. Locher +4 more

In this paper, we derive optimized measurement-free protocols for quantum error correction and the implementation of a universal gate set optimized for an error model that is noise biased. The noise bias is adapted for neutral-atom platforms, where two- and multi-qubit gates are realized with Rydberg interactions and are thus expected to be the dominant source of noise. Careful design of the gates allows us to further reduce the noise model to Pauli- Z errors. In addition, the presented circuits are robust to arbitrary single-qubit gate errors, and we demonstrate that the break-even point can be significantly improved compared to fully fault-tolerant measurement-free schemes. The obtained logical qubits with their suppressed error rates on logical gate operations can then be used as building blocks in a first step of error correction in order to push the effective error rates below the threshold of a fully fault-tolerant and scalable quantum error-correction scheme.

PRX Quantum•Oct 22, 2025•3 citations
Multiqubit gates that involve three or more qubits are usually thought to be of little significance for fault-tolerant quantum error correction because single gate faults can lead to errors of high Pauli weight. However, recent works have shown that multiqubit gates can be beneficial for measurement-free fault-tolerant quantum error correction and for fault-tolerant stabilizer readout in unrotated surface codes. In this work, we investigate multiqubit Rydberg gates that are useful for fault-tolerant quantum error correction in single-species neutral-atom platforms and can be implemented with global laser pulses that do not individually address atomic sites. We develop an open-source Python package to generate analytical, few-parameter pulses that implement the desired gates while minimizing gate errors due to Rydberg-state decay. The tool also allows us to identify parameter-optimal pulses, characterized by a minimal parameter count for the pulse ansatz. Measurement-free quantum error correction protocols require CCZ gates, which we analyze for atoms arranged in symmetric and asymmetric configurations. We investigate the performance of these schemes for various single-, two-, and three-qubit gate error rates, showing that break-even performance of measurement-free QEC is within reach of current hardware. Moreover, we study Floquet quantum error correction protocols that comprise two-body stabilizer measurements. Those can be realized using global three-qubit gates, and we show that this can lead to a significant reduction in shuttling operations. Simulations with realistic circuit-level noise indicate that applying three-qubit gates for stabilizer measurements in Floquet codes can yield competitive logical qubit performance in experimentally relevant error regimes.
Quantum error correction (QEC) requires the execution of deep quantum circuits with large numbers of physical qubits to protect information against errors. Designing protocols that can reduce gate and space-time overheads of QEC is therefore crucial to enable more efficient QEC in near-term experiments. Multiqubit gates offer a natural path toward fast and low-depth stabilizer measurement circuits. However, they typically introduce high-weight correlated errors that can degrade the circuit-level distance, leading to slower scalings of the logical error probabilities. In this Letter, we show how to realize fast and efficient surface code stabilizer readout using only two singly controlled z gates acting simultaneously on two target qubits, i.e., two CZ_{2} gates-instead of four cz. We show that this scheme is fault tolerant and provide a blueprint for implementation in Rydberg atom arrays. We derive the time-optimal pulses implementing the gates and perform extensive QEC numerical simulations with Rydberg decay errors. Compared to the standard protocol using four cz gates, our scheme is faster, uses fewer gates, and crucially maintains fault tolerance with comparable logical error probabilities. Fault-tolerant generalizations of this scheme to biased and erasure-dominant noise models, as well as to other QEC codes such as quantum Low-Density Parity-Check codes, are also discussed.
Stabilizer quantum error correction (QEC) codes, in particular topological surface codes, are prime candidates to enable practical quantum computing. While it is widely believed that strictly fault-tolerant protocols can only be implemented using single- and two-qubit gates, several quantum computing platforms, including trapped ions, neutral atoms, and superconducting qubits, support native multi-qubit operations. In this Letter, we show that stabilizer measurement circuits for unrotated surface codes can be fault tolerant using single auxiliary qubits and three-qubit gates. These gates enable lower-depth circuits with fewer fault locations and potentially shorter QEC cycle times. We find that in an optimistic parameter regime where fidelities of three-qubit gates are the same as those of two-qubit gates, the logical error rate can be up to one order of magnitude lower and the threshold significantly higher, increasing from ≈0.63% to ≈0.83%. Our results, applicable to a wide range of platforms, motivate further investigation into multi-qubit gates for fault-tolerant QEC as they can offer substantial time and physical qubit resource advantages to reach a given target logical error rate.
Logical qubits can be protected from decoherence by performing quantum error-correction (QEC) cycles repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific hardware platform under consideration in order to practically realize a quantum memory that operates for in principle arbitrary long times. All circuit components must be assumed as noisy unless specific assumptions about the form of the noise are made. Modern QEC schemes are challenging to implement experimentally in physical architectures where in-sequence measurements and feed forward of classical information cannot be reliably executed fast enough or even at all. Here we provide a novel scheme to perform QEC cycles without the need of measuring qubits that is fully fault-tolerant with respect to all components used in the circuit. Our scheme can be used for any low-distance CSS code since its only requirement towards the underlying code is a transversal gate. Similarly to Steane-type EC, we coherently copy errors to a logical auxiliary qubit but then apply a coherent feedback operation from the auxiliary system to the logical data qubit. The logical auxiliary qubit is prepared fault tolerantly without measurements, too. We benchmark logical failure rates of the scheme in comparison to a flag-qubit-based EC cycle. We map out a parameter region where our scheme is feasible and estimate physical error rates necessary to achieve the break-even point of beneficial QEC with our scheme. We outline how our scheme could be implemented in ion traps and with neutral atoms in a tweezer array. For recently demonstrated capabilities of atom shuttling and native multiatom Rydberg gates, we achieve moderate circuit depths and beneficial performance of our scheme while not breaking fault tolerance. These results thereby enable practical fault-tolerant QEC in hardware architectures that do not support midcircuit measurements. Published by the American Physical Society 2024
Quantum error correction (QEC) is one of the crucial building blocks for developing quantum computers that have significant potential for reaching a quantum advantage in applications. Prominent candidates for QEC are stabilizer codes for which periodic readout of stabilizer operators is typically implemented via successive two-qubit entangling gates, and is repeated many times during a computation. To improve QEC performance, it is thus beneficial to make the stabilizer readout faster and less prone to fault-tolerance-breaking errors. Here we design a 3-qubit CZZ gate for superconducting transmon qubits that maps the parity of two data qubits onto one measurement qubit in a single step. We find that the gate can be executed in a duration of 35 35\,35ns with a fidelity of F=99.96 %=99.96 \, \%=99.96%. To optimize the gate, we use an error model obtained from the microscopic gate simulation to systematically suppress Pauli errors that are particularly harmful to the QEC protocol. Using this error model, we investigate the implementation of this 3-qubit gate in a surface code syndrome readout schedule. We find that for the rotated surface code, the implementation of CZZ gates increases the error threshold by nearly 50\% to ≈1.2 %\approx 1.2\,\%≈1.2% and decreases the logical error rate, in the experimental relevant regime, by up to one order of magnitude, compared to the standard CZ readout protocol. We also show that for the unrotated surface code, strictly fault-tolerant readout schedules can be found. This opens a new perspective for below-threshold surface-code error correction, where it can be advantageous to use multi-qubit gates instead of two-qubit gates to obtain a better QEC performance.
Trapped ions as one of the most promising quantum-information-processing platforms, yet conventional entangling gates mediated by collective motion remain slow and difficult to scale. Exciting trapped ions to high-lying electronic Rydberg states provides a promising route to overcome these limitations by enabling strong, long-range dipole-dipole interactions that support much faster multi-qubit operations. Here, we introduce the first scheme for implementing a native controlled-controlled-Z gate with microwave-dressed Rydberg ions by optimizing a single-pulse protocol that accounts for the finite Rydberg-state lifetime. The resulting gate outperforms standard decompositions into one- and two-qubit gates by achieving fidelities above 97% under realistic conditions, with execution times of about 2 microseconds at cryogenic temperatures. To explore the potential of trapped Rydberg ions for fault-tolerant quantum error correction, and to illustrate the utility of three-qubit Rydberg-ion gates in this context, we develop and analyze a proposal for fault-tolerant, measurement-free quantum error correction using the nine-qubit Bacon-Shor code. Our simulations confirm that quantum error correction can be performed in a fully fault-tolerant manner on a linear Rydberg-ion chain despite its limited qubit connectivity. These results establish native multiqubit Rydberg-ion gates as a valuable resource for fast, high-fidelity quantum computing and highlight their potential for fault-tolerant quantum error correction.
In this paper, we derive optimized measurement-free protocols for quantum error correction and the implementation of a universal gate set optimized for an error model that is noise biased. The noise bias is adapted for neutral-atom platforms, where two- and multi-qubit gates are realized with Rydberg interactions and are thus expected to be the dominant source of noise. Careful design of the gates allows us to further reduce the noise model to Pauli- Z errors. In addition, the presented circuits are robust to arbitrary single-qubit gate errors, and we demonstrate that the break-even point can be significantly improved compared to fully fault-tolerant measurement-free schemes. The obtained logical qubits with their suppressed error rates on logical gate operations can then be used as building blocks in a first step of error correction in order to push the effective error rates below the threshold of a fully fault-tolerant and scalable quantum error-correction scheme.