Simulating magic state cultivation with few Clifford terms

Quantum 10, 2134 (2026).

https://doi.org/10.22331/q-2026-06-12-2134

Building upon $textit{Wan, Zhong (2025)}$ [5] we present a few methods on how to simulate the non-Clifford $d=5$ magic state cultivation circuits[4] with a sum of $approx 8$ 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 $7 times 10^{5}$ 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 $approx 8$ 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 $mathtt{tsim}$ along with optimisations using our cutting decompositions. Nearly $4times 10^{6}$ 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 $sim$$1.1$ times slower than its (circuit-unspecific and un-optimised) fully Clifford proxy simulation via $mathtt{stim}$ using $S$ gates.