Fault-tolerant quantum computation without distillation on a 2D device

We show how looped pipeline architectures-which use short-range shuttling of physical qubits to achieve bounded non-local connectivity-can efficiently implement the fault-tolerant non-Clifford gate between 2D surface codes described in (Sci. Adv. 6, eaay4929 (2020)). The shuttling schedule required is only marginally more complex than is required for implementing the standard 2D surface code in this architecture. We compare the resource cost with the cost of magic state distillation and find that, at present, this comparison is heavily in favour of distillation. The high cost of the non-Clifford gate is largely due to the relatively low performance of the just-in-time decoder used in the procedure, which necessitates very large code distances in order to achieve suitably low logical error rates. We argue that, as little attention has been given to the study and optimisation of these decoders, there are potentially significant improvements to be made in this area.