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arXiv:2212.11890

Decoding surface codes with deep reinforcement learning and probabilistic policy reuse

Elisha S. Matekole, Esther Ye, Iyer, Ramya, Samuel Yen-Chi Chen

Published Dec 22, 2022• 1 citation
arXivHTMLPDF

Abstract

Quantum computing (QC) promises significant advantages on certain hard computational tasks over classical computers. However, current quantum hardware, also known as noisy intermediate-scale quantum computers (NISQ), are still unable to carry out computations faithfully mainly because of the lack of quantum error correction (QEC) capability. A significant amount of theoretical studies have provided various types of QEC codes; one of the notable topological codes is the surface code, and its features, such as the requirement of only nearest-neighboring two-qubit control gates and a large error threshold, make it a leading candidate for scalable quantum computation. Recent developments of machine learning (ML)-based techniques especially the reinforcement learning (RL) methods have been applied to the decoding problem and have already made certain progress. Nevertheless, the device noise pattern may change over time, making trained decoder models ineffective. In this paper, we propose a continual reinforcement learning method to address these decoding challenges. Specifically, we implement double deep Q-learning with probabilistic policy reuse (DDQN-PPR) model to learn surface code decoding strategies for quantum environments with varying noise patterns. Through numerical simulations, we show that the proposed DDQN-PPR model can significantly reduce the computational complexity. Moreover, increasing the number of trained policies can further improve the agent's performance. Our results open a way to build more capable RL agents which can leverage previously gained knowledge to tackle QEC challenges.

DOI
10.48550/arxiv.2212.11890

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Quantum computers promise significant computational advantages over classical computers for specific tasks. However, one of the challenges in the noisy intermediate-scale quantum (NISQ) era is the efficient compilation of quantum states and gates, which is crucial for the implementation of quantum algorithms. Given the high dimensionality of quantum systems, this compilation task is non-trivial. Reinforcement learning (RL) is a machine learning subfield focused on developing algorithms for decision-making in dynamic environments. An agent learns by interacting with its environment, how to act to optimize its performance on a certain task. Recently, the integration of deep learning has given rise to deep reinforcement learning (DRL), where deep neural networks approximate functions like value or policy, allowing agents to tackle high-dimensional and complex tasks with greater efficiency and success. Recently, deep reinforcement learning (DRL) has been proposed as a method to automate quantum compiling. In this thesis, we explore the application of RL for quantum state and unitary matrix synthesis, focusing on the use of two reinforcement learning algorithms Deep Q-Networks (DQN) and Proximal Policy Optimization (PPO). Our results indicate that DRL shows promise in generalizing the task of quantum unitary synthesis and quantum state preparation. However, the current state-of-the-art is still limited to working in the no-volume law entangled part of the Hilbert space.
The practical realization of fault-tolerant quantum computing depends critically on the efficiency and adaptability of quantum error correction (QEC) decoders. Recent advancements have highlighted deep reinforcement learning (DRL) as a promising approach for decoding topological codes. However, training these agents typically assumes simplified, uniform noise models, which fail to capture the complex, compounding errors characteristic of near-term quantum hardware. In this paper, we rigorously formulate the synthesis of compound error models—encompassing thermal relaxation, spatial cross-talk, and non-Markovian memory effects—within the framework of deep reinforcement learning for surface code decoding. We propose a methodological framework for simulating these mismatch environments during training to foster robust policy generalization. Extensive simulations demonstrate that DRL agents trained on our synthesized compound error models achieve up to a 24%24\%24% reduction in logical error rates under realistic noise conditions compared to agents trained on standard depolarizing noise. This work provides a rigorous foundation for synthesizing accurate quantum noise environments for reinforcement learning applications.
Quantum error correction (QEC) is the primary strategy for protecting a quantum computer from the environment. Its prerequisite is that errors must remain sufficiently rare, which requires perpetually adapting the computer's control parameters to the drifting environment conditions. The current solution to this problem is to terminate the entire quantum computation for recalibration, but it is incompatible with the long runtimes of future quantum algorithms. We address this challenge by unifying calibration with computation. We grant the QEC process a dual role: its error detection events are not only used to correct the logical quantum state, but are also repurposed as a learning signal, teaching a reinforcement learning (RL) agent to continuously steer the control parameters and stabilize the quantum system during computation. We experimentally demonstrate this framework on a Willow superconducting processor, improving the logical stability of the surface code 3.5-fold against injected drift. By synthesizing our full suite of technological advances, we achieve record performance of the surface and color codes, with average logical error per cycle of 7.72(9)×10−47.72(9)\times10^{-4}7.72(9)×10−4 and 8.19(14)×10−38.19(14)\times10^{-3}8.19(14)×10−3 respectively. Numerical simulations of large codes with tens of thousands of control parameters confirm the scalability of our RL framework, revealing an optimization speed that is independent of system size. This work thus enables a new paradigm: a quantum computer that learns from its errors and never stops computing.