A two-stroke engine quantum cycle equivalent to the Otto cycle based on two qubits has been proposed. The first qubit has frequency ω ω h and the second ω ω c . The cycle is composed of a first stroke of partial equilibration of the two qubits with the hot and cold bath in parallel. The second power stroke is composed of a partial or full swap between the qubits. The swap operation is generated by a unitary transformation which preserves the entropy as a result it is a pure power stroke.