Adaptive Syndrome Extraction

TL;DR

This paper introduces an adaptive syndrome extraction scheme that selectively measures stabilizer generators to improve quantum error correction efficiency, significantly reducing logical error rates and resource requirements.

Contribution

It presents a novel adaptive syndrome extraction method that enhances quantum error correction performance and demonstrates fault-tolerant universal logical computation with concatenated codes.

Findings

Over an order of magnitude lower logical error rates with adaptive extraction

Fewer CNOT gates and physical qubits needed compared to non-adaptive methods

Successful implementation of fault-tolerant universal logical computation

Abstract

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 non-concatenated codes and non-adaptive 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.