Quantum computation and quantum computational logics are intrinsically connected with some puzzling epistemic problems. In the framework of a quantum computational approach to epistemic logic we investigate the following question: is it possible to interpret the basic epistemic operations (having information, knowing) as special kinds of Hilbert-space operations? We show that non-trivial knowledge operations cannot be represented by unitary operators. We introduce the notions of strong epistemic quantum computational structure and of epistemic quantum computational structures, where knowledge operations are identified with special examples of quantum operations. This represents the basic tool for developing an epistemic quantum computational seAddress for correspondence: Dipartimento di Filosofia e Teoria delle Scienze Umane, Università di Cagliari, via Is Mirrionis 1, I-09123 Cagliari, Italy Giuseppe Sergioli was supported by Regione Autonoma della Sardegna, POR Sardegna FSE-M.S. 2007-2013 L.R. 7/2007 2 E. Beltrametti et al. / Epistemic Structures mantics, where epistemic sentences (like “Alice knows that the spin-value in the x-direction is up”) are interpreted as quantum pieces of information that may be stored by quantum objects.