In the same spirit, we can construct spin transistors with longer spin chains (see Supplementary Note 3 for N=5), the above case of N=4 being the shortest and simplest one. The general idea illustrated in Fig. 1a–c is as follows: The gate region consists of N−2 strongly coupled spins, for all j∈{2,…, N−2}. Therefore, the single excitation space of the gate has N−2 eigenstates split by . With the magnetic field hj, we tune one of these eigenstates, say , in resonance with the single excitation input and output states. Assuming , all the other eigenstates will remain decoupled during the transfer, and we will have a simple three-level dynamics for a single target spin. Note that if the resonant eigenstate is antisymmetric, the output state will be the same as the input state, independent on the sign of Jj (see also Supplementary Note 2), while if we chose symmetric resonant state , we would obtain the output state which would be identical to the input state upon the application of the Pauli-Z quantum gate ( operation) to the output port. To close the transistor gate, we place a single spin excitation in one of the gate eigenstates from where the control spin cannot leak out since this eigenstate is non-resonant. Simultaneously, the target spin cannot enter the gate region since the double-excitation subspace, to which it is coupled, is shifted in energy due to the spin–spin interaction, resulting in the transfer blockade.