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Decoding under Backlog Constraints as a Sequential Control Problem: A Deep Reinforcement Learning Approach for Quantum Error Correction

Anwar Ali, Hiroshi Tanaka, MUHAMMAD Imran

Published Jul 21, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.23736.10248

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Decoding under Backlog Constraints as a Sequential Control Problem: A Deep Reinforcement Learning Approach for Quantum Error Correction

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The practical realization of fault-tolerant quantum computing relies fundamentally on the rapid and accurate decoding of quantum error-correcting codes. However, existing analyses of decoding algorithms often treat the problem as a sequence of independent, state-less optimization tasks, typically optimizing for a scalar metric such as logical error rate or average latency. In reality, the decoding process in a continuously operating quantum computer is tightly constrained by the physical rate of syndrome extraction and the finite capacity of the classical processing buffer, creating a non-trivial backlog dynamic. In this work, we present a rigorous mathematical framework that formulates the quantum decoding problem under strict backlog constraints as a discrete-time Markov Decision Process (MDP). By augmenting the state space to include both the real-time syndrome weight and the instantaneous buffer backlog, we shift the paradigm from one-dimensional thresholding to a multi-dimensional sequential control problem. We demonstrate mathematically and empirically that when the queue dynamics are explicitly modeled, the optimal policy diverges significantly from simple syndrome-weight thresholds. Furthermore, we employ Deep Q-Networks (DQN) to discover non-linear policies that inherently balance the trade-off between logical error suppression and queue stability. Our control-theoretic analysis reveals that incorporating state-space representations of the backlog allows RL agents to robustly prevent buffer overflow while maintaining near-optimal logical fidelity. Through extensive simulation on surface codes under circuit-level noise, our DQN agent strictly outperforms naive two-dimensional grid-search baselines, achieving a zero overflow rate in critical regimes where traditional thresholding fails catastrophically.

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The practical realization of fault-tolerant quantum computing relies fundamentally on the rapid and accurate decoding of quantum error-correcting codes. However, existing analyses of decoding algorithms often treat the problem as a sequence of independent, state-less optimization tasks, typically optimizing for a scalar metric such as logical error rate or average latency. In reality, the decoding process in a continuously operating quantum computer is tightly constrained by the physical rate of syndrome extraction and the finite capacity of the classical processing buffer, creating a non-trivial backlog dynamic. In this work, we present a rigorous mathematical framework that formulates the quantum decoding problem under strict backlog constraints as a discrete-time Markov Decision Process (MDP). By augmenting the state space to include both the real-time syndrome weight and the instantaneous buffer backlog, we shift the paradigm from one-dimensional thresholding to a multi-dimensional sequential control problem. We demonstrate mathematically and empirically that when the queue dynamics are explicitly modeled, the optimal policy diverges significantly from simple syndrome-weight thresholds. Furthermore, we employ Deep Q-Networks (DQN) to discover non-linear policies that inherently balance the trade-off between logical error suppression and queue stability. Our control-theoretic analysis reveals that incorporating state-space representations of the backlog allows RL agents to robustly prevent buffer overflow while maintaining near-optimal logical fidelity. Through extensive simulation on surface codes under circuit-level noise, our DQN agent strictly outperforms naive two-dimensional grid-search baselines, achieving a zero overflow rate in critical regimes where traditional thresholding fails catastrophically.
The practical realization of fault-tolerant quantum computing relies fundamentally on the rapid and accurate decoding of quantum error-correcting codes. However, existing analyses of decoding algorithms often treat the problem as a sequence of independent, state-less optimization tasks, typically optimizing for a scalar metric such as logical error rate or average latency. In reality, the decoding process in a continuously operating quantum computer is tightly constrained by the physical rate of syndrome extraction and the finite capacity of the classical processing buffer, creating a non-trivial backlog dynamic. In this work, we present a rigorous mathematical framework that formulates the quantum decoding problem under strict backlog constraints as a discrete-time Markov Decision Process (MDP). By augmenting the state space to include both the real-time syndrome weight and the instantaneous buffer backlog, we shift the paradigm from one-dimensional thresholding to a multi-dimensional sequential control problem. We demonstrate mathematically and empirically that when the queue dynamics are explicitly modeled, the optimal policy diverges significantly from simple syndrome-weight thresholds. Furthermore, we employ Deep Q-Networks (DQN) to discover non-linear policies that inherently balance the trade-off between logical error suppression and queue stability. Our control-theoretic analysis reveals that incorporating state-space representations of the backlog allows RL agents to robustly prevent buffer overflow while maintaining near-optimal logical fidelity. Through extensive simulation on surface codes under circuit-level noise, our DQN agent strictly outperforms naive two-dimensional grid-search baselines, achieving a zero overflow rate in critical regimes where traditional thresholding fails catastrophically.