Does quantum logic have anything to do with qubits or quantum computing?
The brief answer is “no,” and if that’s what you are interested in you have probably come to the wrong place. However, there is a connection – our quantum logic, with some additional axioms, determines an infinite dimensional Hilbert space over the field of complex numbers (proved by Maria Solèr in 1995 and refined by René Mayet in 1998 [MegPav2000]). Hilbert space, in turn, provides the theoretical foundation for quantum mechanics and thus quantum computing. But a theory that allows our quantum logic results to be exploited in a practical sense for quantum computing has so far remained an elusive unsolved problem. Quantum logic together with the additional axioms needed for Solèr’s theorem is called the theory of Hilbert lattices. Hilbert lattices and Hilbert space provide dual and equivalent foundations for quantum mechanics, just as the frequency domain and the time domain provide dual descriptions of electrical signals. Just as Fourier transforms have led to greater insight into th
