Hexagonal matching codes with 2-body measurements
Matching codes are stabilizer codes based on Kitaev's honeycomb lattice
model. The hexagonal form of these codes are particularly well-suited to the
heavy-hexagon device layouts currently pursued in the hardware of IBM Quantum.
Here we show how the stabilizers of the code can be measured solely through the
2-body measurements that are native to the architecture. The process is then
run on 27 and 65 qubit devices, to compare results with simulations for a
standard error model. It is found that the results correspond well to
simulations where the noise strength is similar to that found in the
benchmarking of the devices. The best devices show results consistent with a
noise model with an error probability of around $1.5\%-2\%$.
James R. Wootton