Simulating magic state cultivation with few Clifford terms

Building upon Wan, Zhong (2025) \cite{wan2025cuttingstabiliserdecompositionsmagic} we present a few methods on how to simulate the non-Clifford d = 5 magic state cultivation circuits\cite{gidney2024magicstatecultivationgrowing} with a sum of ≈ 8 Clifford ZX-diagrams on average, at 0.1 % noise. Compared to a magic cat state stabiliser decomposition of all 53 non-Clifford spiders ( 6,377,292 terms required), this is more than 7 × 10 5 times reduction in the number of terms. Our stabiliser decomposition has the advantage of representing the final non-Clifford state (in light of circuit errors) as a sum of Clifford ZX-diagrams. This will be useful in simulating the escape stage of magic state cultivation, where one needs to port the resultant state of cultivation into a larger Clifford circuit with many more qubits. Still, it's necessary to only track ≈ 8 Clifford terms. Our result sheds light on the simulability of operationally relevant, high T -count quantum circuits with some internal structure.Finally, we provide numerical results for full non-Clifford stabiliser rank simulation based on t s i m along with optimisations using our cutting decompositions. Nearly 4 × 10 6 shots per second can be obtained on a laptop for the smaller d = 3 circuits at uniform circuit level noise p = 0.0005 , making it only ∼ 1.1 times slower than its (circuit-unspecific and un-optimised) fully Clifford proxy simulation via s t i m using S gates.