Catalyzes the oxidation of hydrogen sulfide, with the help of a quinone. Consecutive reaction cycles lead to the accumulation of a polysulfide product on the active site Cys residues; these products are released when they exceed a critical length, typically as cyclooctasulfur. n a quinone + n H(+) + n hydrogen sulfide = n a quinol + n sulfur Binds 1 FAD per subunit. Homotrimer. Belongs to the SQRD family.