Near-term Quantum Error Correction for IBM Quantum Processors

We review some of the most important quantum error correcting code (QEC) families, focusing on codes that impose milder requirements on current devices, both in terms of required error rates and small local connectivities. We describe different techniques to adapt these codes to the even sparser connectivity of IBM Quantum systems, specifically targeting a heavy-hexagonal lattice qubit layout. We design an embedding of the surface code based on SWAP gates, which provides good performance for near-term QEC experiments on IBM computers. Finally, we present benchmarking data from noisy simulations under different noise models, examining the code threshold and physical qubit footprint.