PRX Quantum (Jul 2025)

Adaptive Syndrome Extraction

  • Noah Berthusen,
  • Shi Jie Samuel Tan,
  • Eric Huang,
  • Daniel Gottesman

DOI
https://doi.org/10.1103/ps3r-wf84
Journal volume & issue
Vol. 6, no. 3
p. 030307

Abstract

Read online Read online

Device error rates on current quantum computers have improved enough to where demonstrations of error correction below break even are now possible. Still, the circuits required for quantum error correction introduce significant overhead and sometimes inject more errors than they correct. In this work, we introduce adaptive syndrome extraction as a scheme to improve code performance and reduce the quantum error-correction cycle time by measuring only the stabilizer generators that are likely to provide useful syndrome information. We provide a concrete example of the scheme through the [[4,2,2]] code concatenated with a hypergraph product code and a syndrome-extraction cycle that uses quantum error detection to modify the syndrome-extraction circuits in real time. Compared to nonconcatenated codes and nonadaptive syndrome extraction, we find that the adaptive scheme achieves over an order of magnitude lower logical error rates while requiring fewer cnot gates and physical qubits. Furthermore, we show how to achieve fault-tolerant universal logical computation with [[4,2,2]]-concatenated hypergraph product codes.