A fault-tolerant non-Clifford gate for the surface code in two dimensions
Abstract: Performing non-Clifford gates with magic state distillation will consume an overwhelming majority of the resources of a two-dimensional fault-tolerant quantum computing architecture. Here we show how to perform a fault-tolerant non-Clifford gate with the surface code; a quantum error-correcting code now under intensive experimental development. This alleviates the need for distillation or higher-dimensional components to complete a universal set of quantum logical gates. The operation uses local transversal gates and code deformations on a two-dimensional architecture over a time that scales with the size of the qubit array. An important component of the gate is a just-in-time decoder. Such decoding algorithms allow us to draw upon the advantages of a three-dimensional model using only a two-dimensional array of live qubits. Remarkably, our gate is completed using parity checks of weight no greater than four. As such, we expect it to be experimentally amenable with technology that is now under development. As this gate circumvents the need for magic-state distillation, it may reduce the resource overhead of surface-code quantum computation dramatically.