Iteratively decoded magic state distillation

We present numerical simulation results for the 7-to-1 and 15-to-1 state distillation circuits, constructed using transversal CNOTs acting on multiple surface code patches. The distillation circuits are decoded iteratively using the method outlined in [arXiv:2407.20976]. We show that, with a re-configurable qubit architecture, we can perform fast magic state distillation in about O(1) code cycles. We confirm that both circuits suppress an injected input logical error rate p to O(p 3) in the presence of additional circuit-level noise. This is done with two types of stabiliser proxies, distilling logical - and Y states, the latter is the intended state of the 7-to-1 circuit while a stabiliser-proxy for the 15-to-1 circuit. We then also provide numerical evidences for actual T state distillation using the 15-to-1 circuit with a faulty- T measurement, leveraging recent near-Clifford simulation tools. Finally, we outline how ZX-calculus and Pauli webs can be used to benchmark stabiliser proxies for these distillation circuits.