High-throughput assessment of defect-nuclear spin register controllability for quantum memory applications

Despite progress in characterizing large spin registers, selecting memory qubits is hindered by the complexity of hyperfine interactions and the computational difficulty of simulating large qubit registers. We present an analytically tractable method for efficient spin register assessment and memory qubit assignment, applicable to any type of defect. We demonstrate its use on defects in silicon carbide, analyzing gates for up to 20 qubits and assessing the impact of isotopic purification on gate fidelities. This approach enables systematic evaluation of dynamical decoupling sequences and qubit assignments, offering experimentally relevant guidance and solutions to many-body challenges.