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

Scalable simulation of surface-code quantum error correction with coherent noise

Valentine Nyirahafashimana, Nurisya Mohd Shah, Joseph Ntahompagaze

Published Mar 5, 2026• 0 citations
Publisher

Abstract

Abstract Quantum error correction (QEC) is essential for scalable quantum computing, but its realistic evaluation is hindered by the difficulty of simulating coherent noise in large codes. We propose a unified framework for the rotated surface code that integrates a qubit-reduction strategy preserving error dynamics, a coherent noise model with spatial and temporal correlations, and an effective error model validated through simulations up to d=7. GPU-accelerated simulations using QULACS show that coherent errors in the d=5 code predominantly interfere destructively, reducing their effective impact by about 13%. Based on these results, we establish conditions for break-even QEC, requiring a gate-time-to-coherence-time ratio below 0.005–0.007. Our findings indicate that current superconducting platforms operate close to this regime, with residual coupling-induced coherent errors as the main limitation, and provide a practical tool for optimizing surface-code QEC.

DOI
10.21203/rs.3.rs-8897316/v1

Related papers

Simulation and performance analysis of quantum error correction with a rotated surface code under a realistic noise model

Mitsuki Katsuda, Kosuke Mitarai, Keisuke Fujii

The demonstration of quantum error correction (QEC) is one of the most important milestones in the realization of fully-fledged quantum computers. Toward this, QEC experiments using the surface codes have recently been actively conducted. However, it has not yet been realized to protect logical quantum information beyond the physical coherence time. In this work, we performed a full simulation of QEC for the rotated surface codes with a code distance 5, which employs 49 qubits and is within reach of the current state-of-the-art quantum computers. In particular, we evaluate the logical error probability in a realistic noise model that incorporates not only stochastic Pauli errors but also coherent errors due to a systematic control error or unintended interactions. While a straightforward simulation of 49 qubits is not tractable within a reasonable computational time, we reduced the number of qubits required to 26 qubits by delaying the syndrome measurement in simulation. This and a fast quantum computer simulator, , implemented on GPU allows us to simulate full QEC with an arbitrary local noise within reasonable simulation time. Based on the numerical results, we also construct and verify an effective model to incorporate the effect of the coherent error into a stochastic noise model. This allows us to understand what the effect coherent error has on the logical error probability on a large scale without full simulation based on the detailed full simulation of a small scale. The present simulation framework and effective model, which can handle arbitrary local noise, will play a vital role in clarifying the physical parameters that future experimental QEC should target. Published by the American Physical Society 2024

arXiv:2204.11404•Physical Review Research•Jan 8, 2024•17 citations

Surface Code Error Correction with Crosstalk Noise

Zeyuan Zhou, Andrew Ji, Yongshan Ding

The design and performance analysis of quantum error correction (QEC) codes are often based on incoherent and independent noise models since it is easy to simulate. However, these models fail to capture realistic hardware noise sources, such as correlated errors (crosstalk), which can significantly impact QEC code performance, especially when they occur between data and ancillary qubits. In this paper, we systematically study various types of crosstalk noise and quantify their effects on surface codes through memory and stability experiments. Based on our findings, we introduce crosstalk-robust implementations of QEC via flag qubit designs and redundant stabilizer checks. We perform both numerical and analytical studies to demonstrate the efficacy of these strategies. In addition, we analyze logical crosstalk in an$[[n, k>1, d]]$code block and establish analytical conditions under which physical crosstalk does not lead to logical crosstalk. Together, our analytical and numerical results shed light on designing QEC codes that are robust against hardware realistic crosstalk noise, paving the way for reliable experimental realization of fault-tolerant quantum computing.

arXiv:2503.04642•IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•2 citations

Characterizing Quantum Error Correction Performance of Radiation-induced Errors

Paul G. Baity, Anuj K. Nayak, Lav R. Varshney +4 more

Radiation impacts are a current challenge with computing on superconducting-based quantum devices because they can lead to widespread correlated errors across the device. Such errors can be problematic for quantum error correction (QEC) codes, which are generally designed to correct independent errors. To address this, we have developed a computational model to simulate the effects of radiation impacts on QEC performance. This is achieved by building from recently developed models of quasiparticle density, mapping radiation-induced qubit error rates onto a quantum error channel and simulation of a simple surface code. We also provide a performance metric to quantify the resilience of a QEC code to radiation impacts. Additionally, we sweep various parameters of chip design to test mitigation strategies for improved QEC performance. Our model approach is holistic, allowing for modular performance testing of error mitigation strategies and chip and code designs.

quant-pharXiv:2602.06202•Feb 9, 2026•0 citations

Hierarchical Quantum Error Correction with Hypergraph Product Code and Rotated Surface Code

Junichi Haruna, Keisuke Fujii

Abstract We propose and analyze a hierarchical quantum error correction (QEC) scheme that concatenates hypergraph product (HGP) codes with rotated surface codes and that is compatible with quantum computers with only nearest-neighbor interactions. The outer code employs (3,4)-random HGP codes, known for their constant encoding rate and favorable distance scaling, while the inner code consists of a rotated surface code with distance 5, allowing hardware compatibility through lattice surgery. To address the decoding bottleneck, we utilize a soft-decision decoding strategy that combines belief propagation with ordered statistics decoding, enhanced by a syndrome-conditioned logical error probability computed via a tailored lookup table for the inner code. Numerical simulations under a code capacity noise model demonstrate that our hierarchical codes achieve logical error suppression below the threshold. Furthermore, we derive explicit conditions under which the proposed codes surpass surface codes as a QEC code in both qubit efficiency and error rate. In particular, for the size parameter $s \ge 4$ (which corresponds to 16 logical qubits) and the distance $d\ge 25$, our construction outperforms the rotated surface code in practical regimes with physical error rates around or less than $10^{-2}$. These results suggest that concatenated quantum low-density parity-check surface architectures can offer a scalable and resource-efficient path toward near-term fault-tolerant quantum computation.

arXiv:2505.18592•Progress of Theoretical and Experimental Physics•Sep 23, 2025•0 citations

Quantum Error Correction

Swathi Mummadi, Gnaneshwara Chary Udari

Quantum Error Correction (QEC) is essential for overcoming the fragility of qubits, enabling reliable and scalable quantum computing by mitigating the effects of noise, decoherence, and operational errors. This chapter explores QEC's foundational principles, including error types, noise impact, and syndrome measurement techniques for identifying and correcting errors. It covers key codes such as Shor and Steane, which provide basic error protection, and advanced codes like concatenated codes, surface codes, and quantum Low-Density Parity-Check (LDPC) codes. Concatenated codes employ hierarchical encoding to exponentially reduce logical error rates, while surface codes, including Toric codes, utilize topological properties of qubits arranged on a 2D lattice to detect and correct errors with high fault tolerance and scalability. Quantum LDPC codes leverage sparse parity-check matrices to offer efficient and scalable error correction, closely approaching theoretical performance limits. The chapter concludes by exploring current research efforts to optimize QEC codes.

Advances in computational intelligence and robotics book series•Apr 17, 2025•1 citation

Method for 3D structure of measurement-free fault tolerant surface code

Gunsik Min, Jun Heo

Abstract Quantum error correction (QEC) is essential for mitigating decoherence in quantum computations, but many QEC schemes rely heavily on mid-circuit measurements, which introduce significant noise due to their high error rates in current hardware. To overcome this limitation, we propose a measurement-free QEC scheme based on the surface code, leveraging its topological robustness while eliminating the need for physical measurements during error correction. Our key innovation is a three-dimensional patch-based architecture that interlinks three logical qubit patches, enabling coherent error extraction and feedback without measurements. By transforming syndrome information into geometric correlations across patches, our design inherently suppresses measurement-induced errors while preserving the surface code’s fault-tolerant thresholds. We analyze the scheme’s performance under realistic noise models and demonstrate its advantages over traditional flag-based or Steane-type QEC in regimes where measurements dominate error rate. This work bridges the gap between measurement-free QEC and scalable surface code architectures, offering a path toward fault-tolerant quantum computing in systems where fast, high-fidelity measurements remain impractical.

•Sep 25, 2025•0 citations
Abstract Quantum error correction (QEC) is essential for scalable quantum computing, but its realistic evaluation is hindered by the difficulty of simulating coherent noise in large codes. We propose a unified framework for the rotated surface code that integrates a qubit-reduction strategy preserving error dynamics, a coherent noise model with spatial and temporal correlations, and an effective error model validated through simulations up to d=7. GPU-accelerated simulations using QULACS show that coherent errors in the d=5 code predominantly interfere destructively, reducing their effective impact by about 13%. Based on these results, we establish conditions for break-even QEC, requiring a gate-time-to-coherence-time ratio below 0.005–0.007. Our findings indicate that current superconducting platforms operate close to this regime, with residual coupling-induced coherent errors as the main limitation, and provide a practical tool for optimizing surface-code QEC.
The demonstration of quantum error correction (QEC) is one of the most important milestones in the realization of fully-fledged quantum computers. Toward this, QEC experiments using the surface codes have recently been actively conducted. However, it has not yet been realized to protect logical quantum information beyond the physical coherence time. In this work, we performed a full simulation of QEC for the rotated surface codes with a code distance 5, which employs 49 qubits and is within reach of the current state-of-the-art quantum computers. In particular, we evaluate the logical error probability in a realistic noise model that incorporates not only stochastic Pauli errors but also coherent errors due to a systematic control error or unintended interactions. While a straightforward simulation of 49 qubits is not tractable within a reasonable computational time, we reduced the number of qubits required to 26 qubits by delaying the syndrome measurement in simulation. This and a fast quantum computer simulator, , implemented on GPU allows us to simulate full QEC with an arbitrary local noise within reasonable simulation time. Based on the numerical results, we also construct and verify an effective model to incorporate the effect of the coherent error into a stochastic noise model. This allows us to understand what the effect coherent error has on the logical error probability on a large scale without full simulation based on the detailed full simulation of a small scale. The present simulation framework and effective model, which can handle arbitrary local noise, will play a vital role in clarifying the physical parameters that future experimental QEC should target. Published by the American Physical Society 2024
The design and performance analysis of quantum error correction (QEC) codes are often based on incoherent and independent noise models since it is easy to simulate. However, these models fail to capture realistic hardware noise sources, such as correlated errors (crosstalk), which can significantly impact QEC code performance, especially when they occur between data and ancillary qubits. In this paper, we systematically study various types of crosstalk noise and quantify their effects on surface codes through memory and stability experiments. Based on our findings, we introduce crosstalk-robust implementations of QEC via flag qubit designs and redundant stabilizer checks. We perform both numerical and analytical studies to demonstrate the efficacy of these strategies. In addition, we analyze logical crosstalk in an[[n,k>1,d]][[n, k>1, d]][[n,k>1,d]]code block and establish analytical conditions under which physical crosstalk does not lead to logical crosstalk. Together, our analytical and numerical results shed light on designing QEC codes that are robust against hardware realistic crosstalk noise, paving the way for reliable experimental realization of fault-tolerant quantum computing.
Radiation impacts are a current challenge with computing on superconducting-based quantum devices because they can lead to widespread correlated errors across the device. Such errors can be problematic for quantum error correction (QEC) codes, which are generally designed to correct independent errors. To address this, we have developed a computational model to simulate the effects of radiation impacts on QEC performance. This is achieved by building from recently developed models of quasiparticle density, mapping radiation-induced qubit error rates onto a quantum error channel and simulation of a simple surface code. We also provide a performance metric to quantify the resilience of a QEC code to radiation impacts. Additionally, we sweep various parameters of chip design to test mitigation strategies for improved QEC performance. Our model approach is holistic, allowing for modular performance testing of error mitigation strategies and chip and code designs.
Abstract We propose and analyze a hierarchical quantum error correction (QEC) scheme that concatenates hypergraph product (HGP) codes with rotated surface codes and that is compatible with quantum computers with only nearest-neighbor interactions. The outer code employs (3,4)-random HGP codes, known for their constant encoding rate and favorable distance scaling, while the inner code consists of a rotated surface code with distance 5, allowing hardware compatibility through lattice surgery. To address the decoding bottleneck, we utilize a soft-decision decoding strategy that combines belief propagation with ordered statistics decoding, enhanced by a syndrome-conditioned logical error probability computed via a tailored lookup table for the inner code. Numerical simulations under a code capacity noise model demonstrate that our hierarchical codes achieve logical error suppression below the threshold. Furthermore, we derive explicit conditions under which the proposed codes surpass surface codes as a QEC code in both qubit efficiency and error rate. In particular, for the size parameter s≥4s \ge 4s≥4 (which corresponds to 16 logical qubits) and the distance d≥25d\ge 25d≥25, our construction outperforms the rotated surface code in practical regimes with physical error rates around or less than 10−210^{-2}10−2. These results suggest that concatenated quantum low-density parity-check surface architectures can offer a scalable and resource-efficient path toward near-term fault-tolerant quantum computation.
Quantum Error Correction (QEC) is essential for overcoming the fragility of qubits, enabling reliable and scalable quantum computing by mitigating the effects of noise, decoherence, and operational errors. This chapter explores QEC's foundational principles, including error types, noise impact, and syndrome measurement techniques for identifying and correcting errors. It covers key codes such as Shor and Steane, which provide basic error protection, and advanced codes like concatenated codes, surface codes, and quantum Low-Density Parity-Check (LDPC) codes. Concatenated codes employ hierarchical encoding to exponentially reduce logical error rates, while surface codes, including Toric codes, utilize topological properties of qubits arranged on a 2D lattice to detect and correct errors with high fault tolerance and scalability. Quantum LDPC codes leverage sparse parity-check matrices to offer efficient and scalable error correction, closely approaching theoretical performance limits. The chapter concludes by exploring current research efforts to optimize QEC codes.
Abstract Quantum error correction (QEC) is essential for mitigating decoherence in quantum computations, but many QEC schemes rely heavily on mid-circuit measurements, which introduce significant noise due to their high error rates in current hardware. To overcome this limitation, we propose a measurement-free QEC scheme based on the surface code, leveraging its topological robustness while eliminating the need for physical measurements during error correction. Our key innovation is a three-dimensional patch-based architecture that interlinks three logical qubit patches, enabling coherent error extraction and feedback without measurements. By transforming syndrome information into geometric correlations across patches, our design inherently suppresses measurement-induced errors while preserving the surface code’s fault-tolerant thresholds. We analyze the scheme’s performance under realistic noise models and demonstrate its advantages over traditional flag-based or Steane-type QEC in regimes where measurements dominate error rate. This work bridges the gap between measurement-free QEC and scalable surface code architectures, offering a path toward fault-tolerant quantum computing in systems where fast, high-fidelity measurements remain impractical.