  Quantum computation has suggested new forms of quantum logic, called quantum
computational logics. The basic semantic idea is the following: the meaning of
a sentence is identified with a quregister, a system of qubits, representing a
possible pure state of a compound quantum system. The generalization to mixed
states, which might be useful to analyse entanglement-phenomena, is due to
Gudder. Quantum computational logics represent non standard examples of unsharp
quantum logic, where the non-contradiction principle is violated, while
conjunctions and disjunctions are strongly non-idempotent. In this framework,
any sentence of the language gives rise to a quantum tree: a kind of quantum
circuit that transforms the quregister associated to the atomic subformulas of
the sentence into the quregister associated to the sentence.

Quantum Physics