A discriminator variety of Gِdel algebras with operators arising in quantum computation

In order to appropriately model the strong quantum computational logic of Cattaneo et al., we introduce an expansion of ′ quasi-MV algebras by lattice operations and a Gödel-like implication. We call the resulting algebras Gödel quantum computational algebras, and we show that every such algebra arises as a pair algebra over a Heyting–Wajsberg algebra. After proving a standard completeness theorem, we prove that Gödel quantum computational algebras form a discriminator variety and we point out some consequences thereof.