Iteratively decoded magic state distillation

TL;DR

This paper demonstrates efficient iterative decoding of magic state distillation circuits using surface codes, achieving rapid error suppression and providing benchmarking methods for stabiliser proxies.

Contribution

It introduces a fast, re-configurable architecture for magic state distillation with iterative decoding, confirmed to suppress errors effectively.

Findings

Distillation circuits suppress input error rate to cubic order

Fast distillation achievable in constant code cycles

ZX-calculus and Pauli webs used for benchmarking

Abstract

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 $\sim\mathcal{O}(1)$ code cycles. We confirm that both circuits suppress an injected input error rate $p$ to $\mathcal{O}(p^3)$ in the presence of additional circuit-level noise. We also outline how ZX-calculus and Pauli webs can be used to benchmark stabiliser proxies for these distillation circuits.