Correlated decoding of logical algorithms with transversal gates

TL;DR

This paper demonstrates that joint, correlated decoding of logical qubits during transversal gates significantly enhances quantum error correction performance, reducing overhead and error propagation in fault-tolerant quantum computing.

Contribution

It introduces correlated decoding methods that improve logical algorithm performance by accounting for error propagation during transversal gates, reducing resource overhead.

Findings

Correlated decoding improves performance of transversal gates in quantum error correction.

Reduces syndrome extraction rounds from O(d) to O(1) in Clifford circuits.

Substantially decreases space-time cost of deep logical circuits.

Abstract

Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation of logical qubits using transversal gates (Bluvstein et al., Nature 626, 58-65 (2024)), we show that the performance of logical algorithms can be substantially improved by decoding the qubits jointly to account for error propagation during transversal entangling gates. We find that such correlated decoding improves the performance of both Clifford and non-Clifford transversal entangling gates, and explore two decoders offering different computational runtimes and accuracies. In particular, by leveraging the deterministic propagation of stabilizer measurement errors through transversal Clifford gates, we find that correlated decoding enables the number of noisy syndrome extraction rounds between these gates to be reduced from $O(d)$ to $O(1)$ in Clifford circuits, where $d$ is the code distance. We verify numerically that this approach substantially reduces the space-time cost of deep logical Clifford circuits. These results demonstrate that correlated decoding provides a major advantage in early fault-tolerant computation, as realized in recent experiments, and further indicate it has considerable potential to reduce the space-time cost in large-scale logical algorithms.