Researchers at Paris-Saclay University have developed a novel methodology for propagating the density matrix through simulated quantum memory experiments, enabling the determination of optimal decoding decisions for a range of syndrome histories. Anthony Benois and colleagues analysed the repetition code and a cellular automaton code, revealing crucial performance differences between decoders, particularly concerning belief propagation, when subjected to realistic circuit-level noise. The analysis quantifies the limitations inherent in commonly employed heuristic decoders and demonstrates that a limited number of syndrome histories dominate the logical error rate at low physical error rates. This provides a robust benchmark for evaluating quantum error correction decoders, addressing a vital challenge in the construction of fault-tolerant quantum computers. Density matrix propagation unlocks high-accuracy quantum error correction decoding Scientists at Paris-Saclay University have achieved a five-fold reduction in the discrepancy between theoretical and practical quantum error correction performance. Attaining a maximum-likelihood decoding accuracy of 99.9% for small codes, this level of precision was previously unattainable due to significant computational constraints. Their innovative method propagates the density matrix, a comprehensive mathematical description of a quantum system’s state, through simulated quantum memory. This allows for the precise determination of the optimal decoding decision for every possible error sequence, formerly known as a syndrome history. The density matrix, represented as a matrix describing the probabilities of all possible quantum states, is particularly suited to modelling the effects of noise and decoherence, which are inherent challenges in quantum computation. Propagating this matrix allows the researchers to track the evolution of the quantum state under the influence of errors, providing a complete picture of the error landscape. This detailed analysis revealed that, at low physical error rates, typically below 1%, representing increasingly stable quantum systems, less than 10% of all possible syndrome histories contribute significantly to the overall logical error rate.