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This breakthrough demonstrates that exact maximum-likelihood decoding for quantum error correction can be achieved at scales of 1,023 qubits by shifting from exponential tensor network methods to polynomial-time rank-decomposition algorithms. By leveraging the rank-width of Tanner graphs instead of treewidth, researchers have overcome previous computational bottlenecks, enabling the practical evaluation of punctured Reed-Muller codes and Steane-concatenated families under realistic noise conditions. This advancement is a critical step toward scaling fault-tolerant quantum computing architectures by making high-fidelity decoding computationally feasible.

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Researchers Decode up to 1,023 Qubits Using Rank Decomposition

Quantum ZeitgeistOctober 3, 20266 min read

Full likelihood evaluation for Reed-Muller codes has now been demonstrated across 1,023 qubits, a scale previously inaccessible due to computational limits. Existing methods relied on exponential scaling linked to tensor network treewidth, demanding superpolynomial processing time. This advance achieves polynomial complexity dependent only on the rank-width of a Tanner graph, representing a substantial shift in decoding efficiency.

The leading exact tensor-network contraction requires time exponential in treewidth. A new decoding algorithm based on rank-decomposition dynamic programming (Rank DP) is introduced. Decoding partition functions with independent local fault factors are expressed as quadratic sums of powers and Rank DP is applied. The resulting exact evaluator has arithmetic complexity polynomial in input size and exponential in the Tanner graph’s rank-width concerning the fault partition, including decomposition construction. Following Gaussian elimination, it gives polynomial-time decoding for punctured quantum Reed-Muller codes and a Steane-concatenated family with growing distance under indepen. ## Decoding Quantum Error Correction Codes via Rank Decomposition Dynamic Programming Scientists at National University of Singapore, alongside collaborators at Singapore University of Technology and Design, have fully evaluated quantum Reed-Muller codes…

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