  Transistors play a vital role in classical computers, and their quantum
mechanical counterparts could potentially be as important in quantum computers.
Where a classical transistor is operated as a switch that either blocks or
allows an electric current, the quantum transistor should operate on quantum
information. In terms of a spin model the in-going quantum information is an
arbitrary qubit state (spin-1/2 state). In this paper, we derive a model of
four qubits with Heisenberg interactions that works as a quantum spin
transistor, i.e. a system with perfect state transfer or perfect blockade
depending on the state of two gate qubits. When the system is initialized the
dynamics complete the gate operation, hence our protocol requires minimal
external control. We propose a concrete implementation of the model using
state-of-the-art superconducting circuits. Finally, we demonstrate that our
proposal operates with high-fidelity under realistic decoherence.
