A discriminator variety of Gödel 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.