Cutting stabiliser decompositions of magic state cultivation with ZX-calculus

Abstract: We apply the cutting stabiliser decomposition techniques [arXiv:2403.10964] to the quantum states generated from magic state cultivation [arXiv:2409.17595], post-selected upon all $+1$ measured values for simplicity. The resultant states to the $d=3$ and $d=5$ variant magic state cultivation circuits can be expressed as a sum of $4$ and $8$ Clifford ZX-digrams respectively. Modifications to existing ZX-calculus stabiliser decomposition methods may enable better simulation of non-Clifford circuits containing a moderate number of $T$ gates in the context of quantum error correction.