Correlated decoding of logical algorithms with transversal gates
arxiv(2024)
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
physical 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. By considering deep logical
Clifford circuits, we find that correlated decoding can significantly improve
the space-time cost by reducing the number of rounds of noisy syndrome
extraction per gate. These results demonstrate that correlated decoding
provides a major advantage in early fault-tolerant computation, and indicate it
has considerable potential to reduce the space-time cost in large-scale logical
algorithms.
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