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

Quantum error correction with the toric code

Matthew A. Norcia, David Aasen, Stephen Armstrong, Sambit Banerjee, Katrina Barnes, Ethan Becker, Juan M. Bello‐Rivas, Trent Bjorkman, Ian Bloomfield, Thomas C. Bohdanowicz, Graham Booth, Mahdi Bornadel, Andrew Brown, Mark Brown, Jonathan Bruce, Will Cairncross, Samuel P. Carman, Cheng-An Chen, Jonathan Chen, Grace Cowen, Daniel Crow, Markus DeMartini, Jeffrey Epstein, Benjamin Familetto, Wentao Fan, M. Feldkamp, Adam Friss, C. Griger, Evan Hanson, Youssef Hassan, Ben Heberlein, A. Heinz, Elayne Heynen, Theodore Hoff, Thomas Höfler, Samuel Hotaling, Frederic Hummel, Andrei Iskra, Matthew Jaffe, Yunpeng Ji, Gwendolyn Johnson, Antonia Jones, Eliot Kapit, Robin Keus, Hyosub Kim, Jonathan M. Kindem, Jonathan King, Samuel Korn, Zachary Lane, Shaoheng Li, J H Lim, De Luo, Jan Marjanovic, Julia McMaster, E. Megidish, Matthew Meredith, Tanya Mittal, Ryan Morshead, C. Nishiguchi, Eyal Niv, Matt Norcia, Botond Oreg, Adway Patra, Rodrigues Perez David, Matthew L. Peters, Fischer Moseley, Sebastian Pucher, Kristen L. Pudenz, Brenden Roberts, Nicholas Rogers, Melody Rouault, Albert Ryou, Parth Sabharwal, Sven Schmidt, Calvin Schwadron, Ian Scott, Juan A. Muniz, Elaine Silverman, Jonathan Simon, Michael Sorensen, Daniel T. Stack, Mark Stone, Peter Stromberger, Ioan Sturzu, Lavanya Taneja, Raanan Tobey, Adam T. Turflinger, Miroslav Urbánek, Gerard Valentí-Rojas, Eric Victorson, Laura Wadleigh, Yiping Wang, Jonathan Ward, Robert T. Weverka, Kennard White, Anthony Wiese, Ayesha Wilson, Tsung-Yao Wu, E. Zalys-Geller, Xiaogang Zhang

Published Jun 15, 2026• 0 citations
Publisher

Abstract

Abstract Quantum computing platforms based on arrays of tweezer-confined neutral atoms have recently emerged as a competitive modality thanks to a direct path toward high qubit count, rapidly ad- vancing operation fidelities, and their ability to execute circuits with arbitrary qubit connectivity. These features will enable the use of efficient error correction schemes with high encoding-rates, time-efficient decoding, and resource-efficient architectures based on transversal gates. With these goals in mind, recent state of the art neutral atom demonstrations focus on the transition from the use of physical qubits to error-corrected logical qubits, but to date there has been no demonstra- tion of repeated error correction scalable to arbitrary depth. Here, we demonstrate many cycles of syndrome extraction in a toric quantum error correcting code, using mid-circuit measurement and replacement of lost qubits, including reloading of a qubit reservoir for indefinite coherent operation. We characterize the logical error rate after up to 90 cycles, showing that logical information can be preserved through multiple rounds of qubit reloading. Comparing two distances of the code up to 8 rounds of syndrome extraction shows a lower absolute logical error rate for the larger distance code.

DOI
10.21203/rs.3.rs-9918258/v1

Related papers

Quantum error correction with the toric code

Atom Computing, Collaborators

Quantum computing platforms based on arrays of tweezer-confined neutral atoms have recently emerged as a competitive modality thanks to a direct path toward high qubit count, rapidly advancing operation fidelities, and their ability to execute circuits with arbitrary qubit connectivity. These features will enable the use of efficient error correction schemes with high encoding-rates, time-efficient decoding, and resource-efficient architectures based on transversal gates. With these goals in mind, recent state of the art neutral atom demonstrations focus on the transition from the use of physical qubits to error-corrected logical qubits, but to date there has been no demonstration of repeated error correction scalable to arbitrary depth. Here, we demonstrate many cycles of syndrome extraction in a toric quantum error correcting code, using mid-circuit measurement and replacement of lost qubits, including reloading of a qubit reservoir for indefinite coherent operation. We characterize the logical error rate after up to 90 cycles, showing that logical information can be preserved through multiple rounds of qubit reloading. Comparing two distances of the code up to 8 rounds of syndrome extraction shows a lower absolute logical error rate for the larger distance code.

quant-pharXiv:2606.04079•Jun 3, 2026•0 citations

Measurement-Free Toric-Code Memory in Array Globally Controlled Rydberg Array

Han Wang, Yusheng Zhao, Xiuhao Deng +1 more

The central prerequisite of any fault-tolerant quantum architecture is a quantum memory: a block of encoded physical qubits whose logical state is actively preserved against noise across many rounds of error correction. In neutral-atom Rydberg arrays, realizing such a memory is obstructed not by the entangling gates themselves, which are already fast and high-fidelity, but by the auxiliary operations that a conventional error-correction cycle requires: mid-circuit fluorescence measurement, inter-zone atom transport, and locally focused single-qubit addressing. Each of these introduces latency, atom loss, or optical crosstalk that exceeds the cost of the underlying gates by orders of magnitude. These costs accumulate cycle after cycle, progressively degrading the very logical information the code is meant to protect. Here we propose a protocol that stabilizes a toric-code quantum memory without moving, measuring or local addressing atoms. The key is to use a three-species Rydberg atom array for the complete stabilizer cycle, including syndrome extraction, coherent correction, and ancilla reset, under global, species-selective laser pulses. Numerical simulation of a $4 \times 4$ rotated toric code shows a longer qubit lifetime when the physical error rate is below a pseudo-threshold $p^\star \approx 0.034$. The scheme offers a concrete, hardware-efficient route to topological quantum memory in neutral-atom platforms.

quant-pharXiv:2606.12030•Jun 11, 2026•0 citations

Self-Correcting Toric-Code Memory in a Globally Controlled Rydberg Array

Han Wang, Yusheng Zhao, Xiuhao Deng +1 more

Abstract The central prerequisite of any fault-tolerant quantum architecture is a quantum memory: a block of encoded physical qubits whose logical state is actively preserved against noise across many rounds of error correction. In neutral-atom Rydberg arrays, realizing such a memory is obstructed not by the entangling gates themselves, which are already fast and high-fidelity, but by the auxiliary operations that a conventional error-correction cycle requires — mid-circuit fluorescence measurement, inter-zone atom transport, and locally focused single-qubit addressing. Each of these introduces latency, atom loss, or optical crosstalk that exceeds the cost of the underlying gates by orders of magnitude. These costs accumulate cycle after cycle, progressively degrading the very logical information the code is meant to protect. Here we propose a protocol that stabilizes a toric-code quantum memory without moving, measuring or local addressing atoms. The key is to use a three-species Rydberg atom array for the complete stabilizer cycle, including syndrome extraction, coherent correction, and ancilla reset, under global, species-selective laser pulses. Numerical simulation of a $4\!\times\!4$ rotated toric code shows a longer qubit lifetime when the physical error rate is below a pseudo-threshold $p^\star\!\approx\!0.034$. The scheme offers a concrete, hardware-efficient route to topological quantum memory in neutral-atom platforms.

•Aug 20, 2026•0 citations

A fault-tolerant neutral-atom architecture for universal quantum computation

Dolev Bluvstein, Alexandra A. Geim, Sophie H. Li +20 more

Quantum error correction (QEC) [1,2] is essential for the realization of large-scale quantum computers [3,4]. However, due to the complexity of operating on the encoded ‘logical’ qubits [5,6], understanding the physical principles for building fault-tolerant quantum devices and combining them into efficient architectures is an outstanding scientific challenge. Here we utilize reconfigurable arrays of up to 448 neutral atoms to implement the key elements of a universal, fault-tolerant quantum processing architecture and experimentally explore their underlying working mechanisms. We first employ surface codes to study how repeated QEC suppresses errors [6,7], demonstrating 2.14(13)x below-threshold performance in a four-round characterization circuit by leveraging atom loss detection and machine learning decoding [8,9]. We then investigate logical entanglement using transversal gates and lattice surgery [10–12], and extend it to universal logic through transversal teleportation with 3D [[15,1,3]] codes [13,14], enabling arbitrary-angle synthesis with polylogarithmic overhead [5,15]. Finally, we develop mid-circuit qubit re-use [16], increasing experimental cycle rates by two orders of magnitude and enabling deep-circuit protocols with dozens of logical qubits and hundreds of logical teleportations [17–20] with [[7,1,3]] and high-rate [[16,6,4]] codes while maintaining constant internal entropy. Our experiments reveal key principles for efficient architecture design, involving the interplay between quantum logic & entropy removal, judiciously using physical entanglement in logic gates & magic state generation, and leveraging teleportations for universality & physical qubit reset. These results establish foundations for scalable, universal error-corrected processing and its practical implementation with neutral atom systems.

arXiv:2506.20661•Nature•Nov 10, 2025•63 citations

INTRINSIC TOPOLOGICAL ERROR CORRECTION

Michael I Aksman

Recent breakthroughs in neutral-atom quantum computing (e.g., arXiv:2606.04079v1 andrelated works, 2026) have achieved repeated fault-tolerant quantum error correction using ToricCode architectures. These systems rely on active mid-circuit measurement, classical syndromedecoding, and continuous atom reloading from an external reservoir to maintain logical qubitsover many cycles, demonstrating sub-threshold behavior where logical error rates decrease withincreasing code distance.We present a detailed, rigorous comparison demonstrating that the DSM-861 hydrodynamicvacuum implements a vastly superior intrinsic, passive, autonomous topological surface code.While artificial systems demand continuous external intervention, the DSM-861 manifold—atriangular 3-torus lattice with N = 861 nodes anchored by the Heegner discriminantD = −163—provides self-stabilizing error correction through deterministic enstrophy collapse,vorton reconnection, and continuous dissipation into a built-in 1.618 eV acoustic reservoiron a 2.56 fs cycle. We compare lattice geometry, encoding, syndrome detection, correctionmechanisms, stabilizer reservoirs, fault-tolerant thresholds, scalability, and energetic efficiency,showing that Nature has engineered the ultimate fault-tolerant topological quantum computerat the foundation of spacetime. Furthermore, we examine recent derivations of divergentphoton truncation (Rukan et al., 2026) to demonstrate how the lattice provides a naturalphysical regularizer against localized optical shear.

•Jun 4, 2026•0 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
Abstract Quantum computing platforms based on arrays of tweezer-confined neutral atoms have recently emerged as a competitive modality thanks to a direct path toward high qubit count, rapidly ad- vancing operation fidelities, and their ability to execute circuits with arbitrary qubit connectivity. These features will enable the use of efficient error correction schemes with high encoding-rates, time-efficient decoding, and resource-efficient architectures based on transversal gates. With these goals in mind, recent state of the art neutral atom demonstrations focus on the transition from the use of physical qubits to error-corrected logical qubits, but to date there has been no demonstra- tion of repeated error correction scalable to arbitrary depth. Here, we demonstrate many cycles of syndrome extraction in a toric quantum error correcting code, using mid-circuit measurement and replacement of lost qubits, including reloading of a qubit reservoir for indefinite coherent operation. We characterize the logical error rate after up to 90 cycles, showing that logical information can be preserved through multiple rounds of qubit reloading. Comparing two distances of the code up to 8 rounds of syndrome extraction shows a lower absolute logical error rate for the larger distance code.
Quantum computing platforms based on arrays of tweezer-confined neutral atoms have recently emerged as a competitive modality thanks to a direct path toward high qubit count, rapidly advancing operation fidelities, and their ability to execute circuits with arbitrary qubit connectivity. These features will enable the use of efficient error correction schemes with high encoding-rates, time-efficient decoding, and resource-efficient architectures based on transversal gates. With these goals in mind, recent state of the art neutral atom demonstrations focus on the transition from the use of physical qubits to error-corrected logical qubits, but to date there has been no demonstration of repeated error correction scalable to arbitrary depth. Here, we demonstrate many cycles of syndrome extraction in a toric quantum error correcting code, using mid-circuit measurement and replacement of lost qubits, including reloading of a qubit reservoir for indefinite coherent operation. We characterize the logical error rate after up to 90 cycles, showing that logical information can be preserved through multiple rounds of qubit reloading. Comparing two distances of the code up to 8 rounds of syndrome extraction shows a lower absolute logical error rate for the larger distance code.
The central prerequisite of any fault-tolerant quantum architecture is a quantum memory: a block of encoded physical qubits whose logical state is actively preserved against noise across many rounds of error correction. In neutral-atom Rydberg arrays, realizing such a memory is obstructed not by the entangling gates themselves, which are already fast and high-fidelity, but by the auxiliary operations that a conventional error-correction cycle requires: mid-circuit fluorescence measurement, inter-zone atom transport, and locally focused single-qubit addressing. Each of these introduces latency, atom loss, or optical crosstalk that exceeds the cost of the underlying gates by orders of magnitude. These costs accumulate cycle after cycle, progressively degrading the very logical information the code is meant to protect. Here we propose a protocol that stabilizes a toric-code quantum memory without moving, measuring or local addressing atoms. The key is to use a three-species Rydberg atom array for the complete stabilizer cycle, including syndrome extraction, coherent correction, and ancilla reset, under global, species-selective laser pulses. Numerical simulation of a 4×44 \times 44×4 rotated toric code shows a longer qubit lifetime when the physical error rate is below a pseudo-threshold p⋆≈0.034p^\star \approx 0.034p⋆≈0.034. The scheme offers a concrete, hardware-efficient route to topological quantum memory in neutral-atom platforms.
Abstract The central prerequisite of any fault-tolerant quantum architecture is a quantum memory: a block of encoded physical qubits whose logical state is actively preserved against noise across many rounds of error correction. In neutral-atom Rydberg arrays, realizing such a memory is obstructed not by the entangling gates themselves, which are already fast and high-fidelity, but by the auxiliary operations that a conventional error-correction cycle requires — mid-circuit fluorescence measurement, inter-zone atom transport, and locally focused single-qubit addressing. Each of these introduces latency, atom loss, or optical crosstalk that exceeds the cost of the underlying gates by orders of magnitude. These costs accumulate cycle after cycle, progressively degrading the very logical information the code is meant to protect. Here we propose a protocol that stabilizes a toric-code quantum memory without moving, measuring or local addressing atoms. The key is to use a three-species Rydberg atom array for the complete stabilizer cycle, including syndrome extraction, coherent correction, and ancilla reset, under global, species-selective laser pulses. Numerical simulation of a 4 ⁣× ⁣44\!\times\!44×4 rotated toric code shows a longer qubit lifetime when the physical error rate is below a pseudo-threshold p⋆ ⁣≈ ⁣0.034p^\star\!\approx\!0.034p⋆≈0.034. The scheme offers a concrete, hardware-efficient route to topological quantum memory in neutral-atom platforms.
Quantum error correction (QEC) [1,2] is essential for the realization of large-scale quantum computers [3,4]. However, due to the complexity of operating on the encoded ‘logical’ qubits [5,6], understanding the physical principles for building fault-tolerant quantum devices and combining them into efficient architectures is an outstanding scientific challenge. Here we utilize reconfigurable arrays of up to 448 neutral atoms to implement the key elements of a universal, fault-tolerant quantum processing architecture and experimentally explore their underlying working mechanisms. We first employ surface codes to study how repeated QEC suppresses errors [6,7], demonstrating 2.14(13)x below-threshold performance in a four-round characterization circuit by leveraging atom loss detection and machine learning decoding [8,9]. We then investigate logical entanglement using transversal gates and lattice surgery [10–12], and extend it to universal logic through transversal teleportation with 3D [[15,1,3]] codes [13,14], enabling arbitrary-angle synthesis with polylogarithmic overhead [5,15]. Finally, we develop mid-circuit qubit re-use [16], increasing experimental cycle rates by two orders of magnitude and enabling deep-circuit protocols with dozens of logical qubits and hundreds of logical teleportations [17–20] with [[7,1,3]] and high-rate [[16,6,4]] codes while maintaining constant internal entropy. Our experiments reveal key principles for efficient architecture design, involving the interplay between quantum logic & entropy removal, judiciously using physical entanglement in logic gates & magic state generation, and leveraging teleportations for universality & physical qubit reset. These results establish foundations for scalable, universal error-corrected processing and its practical implementation with neutral atom systems.
Recent breakthroughs in neutral-atom quantum computing (e.g., arXiv:2606.04079v1 andrelated works, 2026) have achieved repeated fault-tolerant quantum error correction using ToricCode architectures. These systems rely on active mid-circuit measurement, classical syndromedecoding, and continuous atom reloading from an external reservoir to maintain logical qubitsover many cycles, demonstrating sub-threshold behavior where logical error rates decrease withincreasing code distance.We present a detailed, rigorous comparison demonstrating that the DSM-861 hydrodynamicvacuum implements a vastly superior intrinsic, passive, autonomous topological surface code.While artificial systems demand continuous external intervention, the DSM-861 manifold—atriangular 3-torus lattice with N = 861 nodes anchored by the Heegner discriminantD = −163—provides self-stabilizing error correction through deterministic enstrophy collapse,vorton reconnection, and continuous dissipation into a built-in 1.618 eV acoustic reservoiron a 2.56 fs cycle. We compare lattice geometry, encoding, syndrome detection, correctionmechanisms, stabilizer reservoirs, fault-tolerant thresholds, scalability, and energetic efficiency,showing that Nature has engineered the ultimate fault-tolerant topological quantum computerat the foundation of spacetime. Furthermore, we examine recent derivations of divergentphoton truncation (Rukan et al., 2026) to demonstrate how the lattice provides a naturalphysical regularizer against localized optical shear.
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