Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum error correction code for two-dimensional grid architecture. So far, the repeated error correction capability of the surface code has not been realized experimentally. Here, we experimentally implement an error-correcting surface code, the distance-three surface code which consists of 17 qubits, on the Zuchongzhi 2.1 superconducting quantum processor. By executing several consecutive error correction cycles, the logical error can be significantly reduced after applying corrections, achieving the repeated error correction of surface code for the first time. This experiment represents a fully functional instance of an error-correcting surface code, providing a key step on the path towards scalable fault-tolerant quantum computing.Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum error correction code for two-dimensional grid architecture. So far, the repeated error correction capability of the surface code has not been realized experimentally. Here, we experimentally implement an error-correcting surface code, the distance-three surface code which consists of 17 qubits, on the Zuchongzhi 2.1 superconducting quantum processor. By executing several consecutive error correction cycles, the logical error can be significantly reduced after applying corrections, achieving the repeated error correction of surface code for the first time. This experiment represents a fully functional instance of an error-correcting surface code, providing a key step on the path towards scalable fault-tolerant quantum computing.

arXiv:2112.13505Physical Review LettersJul 11, 2022321 citations

Correlated Errors in the Surface Code

Daniel López, Eduardo R. Mucciolo, E. Novais

Bulletin of the American Physical SocietyFeb 27, 20120 citations

Exact Recovery for Non-Abelian Surface Codes

Alison Warman, Nathanan Tantivasadakarn, Sakura Schafer-Nameki

We study exact recovery for non-Abelian topological surface codes based on the quantum double $D(G)$ of any finite group $G$ . We determine an orthogonal error basis, that is comprised of group multiplication and irreducible representation operators. Whenever the errors are supported on closed loops on the lattice or dual lattice, there is a redundancy in the basis, due to stabilizers. To remedy this, we introduce a gauge-fixing that results in a complete and orthogonal error basis on the code space. Assuming as input predetermined, neutral correctable error clusters, we construct charge and flux transfer circuits that move the errors onto ancillas that then get projected out. This is an exact and deterministic recovery protocol, applicable to surface codes for any finite, in particular non-Abelian, group $G$ .We study exact recovery for non-Abelian topological surface codes based on the quantum double $D(G)$ of any finite group $G$. We determine an orthogonal error basis, that is comprised of group multiplication and irreducible representation operators. Whenever the errors are supported on closed loops on the lattice or dual lattice, there is a redundancy in the basis, due to stabilizers. To remedy this, we introduce a gauge-fixing that results in a complete and orthogonal error basis on the code space. Assuming as input predetermined, neutral correctable error clusters, we construct charge and flux transfer circuits that move the errors onto ancillas that then get projected out. This is an exact and deterministic recovery protocol, applicable to surface codes for any finite, in particular non-Abelian, group $G$.

quant-pharXiv:2610.03677Oct 5, 20260 citations

Quantum Information Protection Scheme Based on Reinforcement Learning for Periodic Surface Codes

Yun-Jia Xue, Haowen Wang, Yanbing Tian +3 more

Quantum information transfer is an information processing technology with high speed and high entanglement with the help of quantum mechanics principles. To solve the problem of quantum information getting easily lost during transmission, we choose topological quantum error correction codes as the best candidate codes to improve the fidelity of quantum information. The stability of topological error correction codes brings great convenience to error correction. The quantum error correction codes represented by surface codes have produced very good effects in the error correction mechanism. In order to solve the problem of strong spatial correlation and optimal decoding of surface codes, we introduced a reinforcement learning decoder that can effectively characterize the spatial correlation of error correction codes. At the same time, we use a double-layer convolutional neural network model in the confrontation network to find a better error correction chain, and the generation network can approach the best correction model, to ensure that the discriminant network corrects more nontrivial errors. To improve the efficiency of error correction, we introduced a double-Q algorithm and ResNet network to increase the error correction success rate and training speed of the surface code. Compared with the previous MWPM 0.005 decoder threshold, the success rate has slightly improved, which can reach up to 0.0068 decoder threshold. By using the residual neural network architecture, we saved one-third of the training time and increased the training accuracy to about 96.6%. Using a better training model, we have successfully increased the decoder threshold from 0.0068 to 0.0085, and the depolarized noise model being used does not require a priori basic noise, so that the error correction efficiency of the entire model has slightly improved. Finally, the fidelity of the quantum information has successfully improved from 0.2423 to 0.7423 by using the error correction protection schemes.Quantum information transfer is an information processing technology with high speed and high entanglement with the help of quantum mechanics principles. To solve the problem of quantum information getting easily lost during transmission, we choose topological quantum error correction codes as the best candidate codes to improve the fidelity of quantum information. The stability of topological error correction codes brings great convenience to error correction. The quantum error correction codes represented by surface codes have produced very good effects in the error correction mechanism. In order to solve the problem of strong spatial correlation and optimal decoding of surface codes, we introduced a reinforcement learning decoder that can effectively characterize the spatial correlation of error correction codes. At the same time, we use a double-layer convolutional neural network model in the confrontation network to find a better error correction chain, and the generation network can approach the best correction model, to ensure that the discriminant network corrects more nontrivial errors. To improve the efficiency of error correction, we introduced a double-Q algorithm and ResNet network to increase the error correction success rate and training speed of the surface code. Compared with the previous MWPM 0.005 decoder threshold, the success rate has slightly improved, which can reach up to 0.0068 decoder threshold. By using the residual neural network architecture, we saved one-third of the training time and increased the training accuracy to about 96.6%. Using a better training model, we have successfully increased the decoder threshold from 0.0068 to 0.0085, and the depolarized noise model being used does not require a priori basic noise, so that the error correction efficiency of the entire model has slightly improved. Finally, the fidelity of the quantum information has successfully improved from 0.2423 to 0.7423 by using the error correction protection schemes.

Quantum EngineeringJul 18, 202213 citations

The surface code: processing experimental data

Austin G. Fowler

Bulletin of the American Physical SocietyMar 2, 20150 citations

Overhead considerations of surface codes

Austin G. Fowler

Bulletin of the American Physical SocietyMar 21, 20131 citation

We study exact recovery for non-Abelian topological surface codes based on the quantum double

D(G)

of any finite group

G

. We determine an orthogonal error basis, that is comprised of group multiplication and irreducible representation operators. Whenever the errors are supported on closed loops on the lattice or dual lattice, there is a redundancy in the basis, due to stabilizers. To remedy this, we introduce a gauge-fixing that results in a complete and orthogonal error basis on the code space. Assuming as input predetermined, neutral correctable error clusters, we construct charge and flux transfer circuits that move the errors onto ancillas that then get projected out. This is an exact and deterministic recovery protocol, applicable to surface codes for any finite, in particular non-Abelian, group

G