Quantum error correction technology is an important method to eliminate errors during the operation of quantum computers. In order to solve the problem of influence of errors on physical qubits, we propose an approximate error correction scheme that performs dimension mapping operations on surface codes. This error correction scheme utilizes the topological properties of error correction codes to map the surface code dimension to three dimensions. Compared to previous error correction schemes, the present three-dimensional surface code exhibits good scalability due to its higher redundancy and more efficient error correction capabilities. By reducing the number of ancilla qubits required for error correction, this approach achieves savings in measurement space and reduces resource consumption costs. In order to improve the decoding efficiency and solve the problem of the correlation between the surface code stabilizer and the 3D space after dimension mapping, we employ a reinforcement learning (RL) decoder based on deep Q-learning, which enables faster identification of the optimal syndrome and achieves better thresholds through conditional optimization. Compared to the minimum weight perfect matching decoding, the threshold of the RL trained model reaches 0.78%, which is 56% higher and enables large-scale fault-tolerant quantum computation.
Quantum error correction technology is an important method to eliminate errors during the operation of quantum computers. In order to solve the problem of influence of errors on physical qubits, we propose an approximate error correction scheme that performs dimension mapping operations on surface codes. This error correction scheme utilizes the topological properties of error correction codes to map the surface code dimension to three dimensions. Compared to previous error correction schemes, the present three-dimensional surface code exhibits good scalability due to its higher redundancy and more efficient error correction capabilities. By reducing the number of ancilla qubits required for error correction, this approach achieves savings in measurement space and reduces resource consumption costs. In order to improve the decoding efficiency and solve the problem of the correlation between the surface code stabilizer and the 3D space after dimension mapping, we employ a reinforcement learning (RL) decoder based on deep Q-learning, which enables faster identification of the optimal syndrome and achieves better thresholds through conditional optimization. Compared to the minimum weight perfect matching decoding, the threshold of the RL trained model reaches 0.78%, which is 56% higher and enables large-scale fault-tolerant quantum computation.
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.
Abstract To address qubits' high environmental sensitivity and reduce the significant error rates in current quantum devices, quantum error correction stands as one of the most dependable approaches. The topological surface code, renowned for its unique qubit lattice structure, is widely considered a pivotal tool for enabling fault-tolerant quantum computation. Through redundancy introduced across multiple qubits, the surface code safeguards quantum information and identifies errors via state changes captured by syndrome qubits. However, simultaneous errors in data and syndrome qubits substantially escalate decoding complexity. Quantum Generative Adversarial Networks (QGANs) have emerged as promising deep learning frameworks, effectively harnessing quantum advantages for practical tasks such as image processing and data optimization. Consequently, a topological code trainer for quantum-classical hybrid GANs is proposed as an auxiliary model to enhance error correction in machine learning-based decoders, demonstrating significantly improved training accuracy compared to the traditional Minimum Weight Perfect Matching (MWPM) algorithm, which achieves an accuracy of 65 . Numerical experiments reveal that the decoder achieves a fidelity threshold of P=0.1978, substantially surpassing the traditional algorithm's threshold of P=0.1024. To enhance decoding efficiency, a Transformer decoder is integrated, incorporating syndrome error outputs trained via QGANs into its framework. By leveraging its self-attention mechanism, the Transformer effectively captures long-range qubit dependencies at a global scale, enabling high-fidelity error correction over larger dimensions. Numerical validation of the surface code error threshold demonstrates an 8.5 threshold with a correction success rate exceeding 94, whereas the local MWPM decoder achieves only 55 and fails to support large-scale computation at a 4 threshold.
In quantum fault-tolerant computing, fast decoding of encoded bits is related to the running speed of quantum computers. In this paper, we propose a decoding agent based on reinforcement learning for correcting rotated surface codes in quantum error correction. The intelligent agent is trained using Deep Q-Network (DQN) and uses Convolutional Neural Network (CNN) to extract features of error syndrome and calculate the corresponding Q values for X, Y, and Z error correction operations. In the environment of depolarizing noise, the trained model achieves a fault-tolerant threshold that is superior to the Minimum Weight Perfect Matching (MWPM) and CNN decoder, providing a feasible framework for surface code error correction in practical applications.
The advent of promising quantum error correction (QEC) codes with efficient resource utilization and high-performance fault-tolerant quantum memories signifies a critical step towards realizing practical quantum computation. While surface codes have been a dominant approach, their limitations have spurred the development of more advanced QEC architectures. These advanced codes often present increased complexity, demanding innovative decoding methodologies. This work investigates the application of reinforcement learning (RL) techniques, including hybrid and multi-agent approaches, to enhance the decoding of various advanced QEC architectures. By leveraging the ability of RL to learn optimal strategies from noisy syndrome measurements, we explore the potential for achieving improved logical error rates and scalability compared to traditional decoding methods. Our approach examines the adaptation of reinforcement learning to exploit the structural properties of these modern QEC models. We also explore the benefits of combining different RL algorithms to address the multifaceted nature of the decoding problem, considering factors such as code degeneracy and real-world noise characteristics. With our proposed method, we are able to demonstrate that an autonomously trained agent can derive decoding schemes for the complex decoding requirement of advanced QEC architectures.
Quantum error correction (QEC) is indispensable for the realization of fault-tolerant quantum computers. Surface codes are a leading QEC architecture due to their high error thresholds and planar design. The core challenge lies in the decoding process: inferring latent physical errors from syndrome measurements and applying appropriate corrections. Although there are classical decoders, their performance can degrade with complex noise or be computationally demanding. This paper investigates an advanced Deep Reinforcement Learning (DRL) approach, employing a Dueling Double Deep Q-Network (DQN), to decode X-type Pauli errors on ad=3rotated surface code. The DRL agent leverages syndrome history to discern temporal error correlations and utilizes a multi-round correction strategy, enabling iterative refinement of corrective actions within an environment that simulates both physical qubit errors and syndrome measurement noise. After 30,000 training episodes with a 5 % physical error rate and 1 % measurement noise, the agent achieved a 0.00 % logical error rate in the extended test, an average episode reward of 0.38, and successfully cleared syndromes in 63 % of the test cases, demonstrating robust learning of a safe decoding policy. The persistent challenge of high training loss, despite good policy performance, is discussed, offering insights into value function approximation in complex QEC environments.
Quantum computers are far more error-prone than their classical counterparts. Therefore, to build a quantum computer capable of running large-scale quantum algorithms, we must use the techniques of quantum error correction to ensure that the computer produces the correct output even when its components are unreliable. However, the resource requirements of building such a fault-tolerant quantum computer are currently prohibitive. Here, we examine the utility of using three-dimensional (3D) surface codes in a fault-tolerant quantum computer. This family of topological error-correcting codes is a generalization of the well-known 2D surface code to three spatial dimensions. We show that certain 3D surface codes have a transversal logical non-Clifford gate. In a quantum computing architecture, a non-Clifford gate is required to achieve computational universality. Transversal gates do not entangle qubits in different codes, so they are naturally fault tolerant because they do not spread errors. Next, we consider the problem of decoding 3D surface codes. In a quantum error-correcting code, we cannot observe the qubits directly, so we measure parity-check operators to gain information about the state of the code. Decoding is the problem of estimating what error has occurred given a list of unsatisfied parity checks. We observe that 3D surface codes offer asymmetric protection against bit-flip and phase-flip errors, but in both cases, we find that a threshold error rate exists below which we can suppress logical errors by increasing the size of the code. We use our results about logical gates and decoding to propose two fault-tolerant quantum computing architectures that utilize 3D surface codes. Finally, we compare the resource requirements of our architectures with the requirements of leading quantum computing architectures based on topological codes. We find that one of our architectures may be competitive with the leading architectures, depending on the properties of the physical systems used to build the qubits.