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A Statistical Framework for Dynamically Adaptive Logical Qubit Architectures for Scalable Fault-Tolerant Quantum Computing

M. Chandra Naik, M. Srikanth

Published Oct 29, 2026• 0 citations
Publisher

Abstract

The theoretical impediments of quantum computing to the large-scale implementation are inherently noise, decoherence, and inefficiency of the current fault-tolerant schemes. Although quantum hardware and error detection methods have made great advancements, existing methods largely use fixed logic qubit simulations and fixed noise models, which are inefficient at responding to dynamically changing noise models and do not scale. To curb this shortcoming, there is a need to have a framework that incorporates flexibility, statistical intelligence, and system optimization. In this paper, a dynamically adaptive logic qubit architecture is proposed based on a statistical model that can be used to achieve fault-tolerant quantum computing on a scale. The framework makes use of probabilistic noise modeling, real-time feedback-based reconfiguration in the continuous optimization of logical qubit structures and error correction schemes. The proposed architecture reduces the error propagation and reduces resource overhead by adding statistical inference using adaptive control mechanisms. Large-scale simulation experiments show that the given approach can suppress logical errors up to 28 percent better and reduce qubit overhead by 35 percent in comparison to the traditional fault-tolerant models that are based on static models and fault-tolerance in different noise levels. Moreover, the framework has a stable performance when the size of the system is growing, which indicates its stability and scalability. These results put dynamically adaptive logical qubit architectures as a potentially fruitful direction towards real-world and scalable quantum computing, and can be used in optimization, secure communication, and modeling of complex systems.

DOI
10.20944/preprints202610.3004.v1

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The theoretical impediments of quantum computing to the large-scale implementation are inherently noise, decoherence, and inefficiency of the current fault-tolerant schemes. Although quantum hardware and error detection methods have made great advancements, existing methods largely use fixed logic qubit simulations and fixed noise models, which are inefficient at responding to dynamically changing noise models and do not scale. To curb this shortcoming, there is a need to have a framework that incorporates flexibility, statistical intelligence, and system optimization. In this paper, a dynamically adaptive logic qubit architecture is proposed based on a statistical model that can be used to achieve fault-tolerant quantum computing on a scale. The framework makes use of probabilistic noise modeling, real-time feedback-based reconfiguration in the continuous optimization of logical qubit structures and error correction schemes. The proposed architecture reduces the error propagation and reduces resource overhead by adding statistical inference using adaptive control mechanisms. Large-scale simulation experiments show that the given approach can suppress logical errors up to 28 percent better and reduce qubit overhead by 35 percent in comparison to the traditional fault-tolerant models that are based on static models and fault-tolerance in different noise levels. Moreover, the framework has a stable performance when the size of the system is growing, which indicates its stability and scalability. These results put dynamically adaptive logical qubit architectures as a potentially fruitful direction towards real-world and scalable quantum computing, and can be used in optimization, secure communication, and modeling of complex systems.
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Effective error correction is required to mitigate the effects of physical noise and safeguard logical qubits for fault-tolerant computation in order to realize large-scale quantum computers. Because physical gate defects, measurement mistakes, leakage errors, and correlated noise can propagate across processing levels, single-level quantum error correction is typically not appropriate for large-scale quantum structures. This research proposes a multi-level quantum error correction framework for scalable quantum computing architectures. Physical-layer syndrome extraction, logical-layer stabilizer decoding, and architecture-level error propagation control are the methods used. To minimize the buildup of logical errors in the deep circuit and under qubit connection limits, a multi-level decoding technique is employed. According to the simulation results, the suggested framework increases the fault-tolerant circuit success rate by 12.6% over single-level correction and has a logical error rate of 1.7×10⁻5 under a physical error rate of 10⁻³. According to the research, a large-scale quantum computing system can be made more reliable by utilizing many tiers of quantum error correction.
In realistic hardware for quantum computation that possesses fault-tolerance, non-stationary noise and stochastic drift lead to logical failure from the temporal accumulation of errors, not from independent events. Static decoding and fixed calibration techniques are structurally incompatible with this situation because they do not take into account temporal correlations between errors or control-induced back-action of errors. These effects motivate control policies that must track noise evolution across correction cycles, rather than respond to individual syndromes in isolation. We treat fault-tolerant quantum computation as a stochastic control problem, modelled using reduced quantum dynamics in which Pauli error processes are governed by latent noise parameters that vary temporally. From this perspective, logical failure arises through the accumulation of a hazard variable, and the corresponding control objective depends on the full history of observations. Operating under these conditions, a Chronological Deep Q-Network (Ch-DQN) maintains an internal belief state that tracks both noise evolution and accumulated hazard. During training, backward refinement of trajectories is used to sample slowly drifting modes of operation, while runtime inference remains strictly causal. A fractional meta-update stabilizes learning in the presence of non-stationary, control-coupled dynamics. Through multi-distance simulations that incorporate stochastic drift and feedback from decision-making, Ch-DQN suppresses hazard accumulation and extends logical survival time relative to static and recurrent baselines. Error correction in this regime is therefore no longer a static decoding task, but a control process whose success is determined over time by the underlying noise dynamics.
Fault-tolerant quantum computation traditionally incurs substantial resource overhead, with both qubit and time overheads scaling polylogarithmically with the size of the computation. While prior work by Gottesman showed that constant qubit overhead is achievable under stochastic noise using quantum low-density parity-check (QLDPC) codes, it has remained an open question whether similar guarantees hold under more general, non-stochastic noise models. In this work, we address this question by considering a general circuit-level noise model defined via the diamond norm, which captures both stochastic and non-stochastic noise, including coherent and amplitude damping noise. We prove that constant qubit overhead fault-tolerant quantum computation is achievable in this general setting, using QLDPC codes with constant rate and linear minimum distance. To establish our result, we develop a fault-tolerant error correction scheme and a method for implementing logic gates under general circuit noise. These results extend the theoretical foundations of fault-tolerant quantum computation and offer new directions for fault-tolerant architectures under realistic noise models.