The Hitchhiker’s Guide to the Surface Code

Error correction is an essential part of the theory of quantum computation. However, new quantum computation students may find the theories of error correction and fault tolerance daunting, or they may be stuck with theoretical/outdated schemes (such as the one in the original proof of the threshold theorem by Aharonov and Ben-or) with unrealistically low thresholds and/or high overhead. In this article, we describe an adequately modern approach to fault-tolerant quantum computation based on the surface code and lattice surgery. The reader is assumed to have a basic understanding of quantum computation (state vectors, unitary gates, and measurements, etc.), but no prior knowledge about quantum codes or quantum error correction is needed.