Fold-transversal surface code cultivation (Part 2)

Magic state cultivation is a state-of-the-art approach for preparing high-fidelity non-Clifford resource states for universal quantum computation with low spacetime overhead. We present an efficient cultivation protocol in the surface code that achieves lower spacetime overhead than all existing schemes, reaching a logical error rate of $10^{-9}$ for a physical error rate of $0.1\%$ using an average of 10 cultivation attempts until success. The improvement arises from three main design choices: (1) measuring the fold-transversal Hadamard of unrotated surface codes in a qubit-efficient way, (2) leveraging compact unitary circuits for code conversion within the surface code family, and (3) employing a hybrid escape strategy that expands to a larger final code without substantial qubit overhead. Furthermore, we perform simulations of the full cultivation process using a ``hand-off'' simulation technique, which transfers the output of state-vector simulations on a few qubits to stabilizer simulations on hundreds of qubits. In contrast to previous works that only benchmark Pauli eigenstates as proxies, our approach enables an exact simulation of magic state cultivation. Our proposal is well suited to practical implementation in architectures with nonlocal connectivity.