Generalized Toffoli gates with customizable single-step multiple-qubit control

Motivated by recent advances in the single-step implementation of n -control-qubit Toffoli gates, we propose a broad class of generalized Toffoli gates with multiple control qubits that can be executed in a single step using a feasible and unified framework based on Ising-type interactions. Unlike the standard Toffoli gate condition, which flips the target qubit only when all control qubits are in the |1 | 1 〉 state, our generalized gates allow for diverse, customizable control conditions, including: mixed control, Hamming weight control, weighted Hamming control, multiple-designated configurations, threshold control, multiple-target control, and multiple-option control. Simulation results demonstrate that these gates offer substantial advantages in both feasibility and reliability over decompositions into standard 2-control-qubit Toffoli gates and other primitive gates, significantly reducing circuit depth, execution time, and error rates.