From Qubits to Qudits

In spite of their strongly non-classical features, quantum computational logics include a subtheory that behaves classically, both from the logical and from the computational point of view. The holistic quantum computational semantics has a special fragment where pieces of information are represented by classical bits and registers, while the basic Boolean functions are represented as reversible operations. One can generalize this approach, by assuming a many-valued classical basis for quantum computation. In this way, qubits are replaced by qudits: quantum superpositions living in a Hilbert space whose dimension may be greater than two. The question whether the “qudit-semantics” (which gives rise to some interesting physical implementations) and the “qubit-semantics” characterize the same logic is an open problem.