A quantum gate is a logically and thermodynamically reversible situation that effects a unitary transformation of qubits of superimposed information, and essentially constitutes a situation for a reversible quantum decision. A quantum decision is a symmetry break, and the effect of the function of a Szilard engine is a symmetry break. A quantum gate is a situation in which a reversible quantum decision can be made, and so if a logically and thermodynamically reversible Szilard engine can be theoretically constructed then it would function as a quantum gate. While the traditionally theorized Szilard engine is not thermodynamically reversible, if one of the bounding walls of a Szilard engine were to be constructed out of the physical information by which it functions in such a manner as to make that information available to both sides of the wall simultaneously, then such a Szilard engine would be both logically and thermodynamically reversible, and thus capable of function as a quantum gate. A theoretical model of the special case of a reversible Szilard engine functioning as a quantum gate is presented and discussed, and since a quantum decision is made when the shutter of a Szilard engine closes, the coherence of linked reversible Szilard engines should be considered as a state during which all of the shutters of linked Szilard engines are open simultaneously.
F. Matthew Mihelic "Szilard engine reversibility as quantum gate function", Proc. SPIE 8400, Quantum Information and Computation X, 84000C (8 May 2012); https://doi.org/10.1117/12.918687