Scalable, pipelined stabilizer measurement scheme and high-fidelity logical operations in a distance-2 surface code*

The ability to perform simultaneous multi-round stabilizer measurements and high-fidelity logical operations are necessary to realize quantum error correction. We present the realization and comparison of high-fidelity fault-tolerant and non-fault tolerant logical operations (initialization, gates and measurement) in Surface-7, the distance-2 surface code, implemented in a superconducting quantum processor. We demonstrate superior performance of the pipelined [Versluis et al., Phys. Rev. Applied 8, 034021, (2017)] implementation of multi-round error detection over the parallel alternative, a key step enabling scalability to larger surface codes.