📝 SummarXiv

Abstract

Magic state cultivation is a newly proposed protocol that represents the state of the art in magic state generation. It uses the transversality of the $H_{XY}$ gate on the 2D triangular color-code, together with a novel grafting mechanism to transform the color-code into a matchable code with minimal overhead. Still, the resulting code has a longer cycle time and some high weight stabilizers. Here, we introduce three new cultivation protocols, each yielding a different magic state. These protocols avoid grafting by exploiting transversal operations on the surface code using non-local connectivity, allowing for a much lower post-selection rates in the expansion process. Through numerical simulations, we demonstrate that our protocol achieves state-of-the-art infidelities and acceptance rates for magic state generation, on par with another recent proposal on the $\mathbb{RP}^2$ code, while still preserving the local geometry of the surface code. Moreover, in platforms such as cold atoms and trapped ions, where idle error rates are lower than two-qubit gate errors, we demonstrate that cultivation exhibits an even greater advantage, yielding an additional order-of-magnitude reduction in resource requirements. Lastly, we analyze the effect of erasure qubits on cultivation and show that \emph{algorithmically-relevant} infidelities can be achieved using only 9 erasure qubits on a distance-2 surface code with a single cultivation round.