**9. Conclusions**

We have proposed a new scheme for describing quantum computation bringing vagueness into consideration, in which each state is characterized by a "measure of truth" A membership amplitude is introduced in addition to the probability ampli- \_ tude in order to achieve this, and we are led thereby to the concept of an obscure qubit. Two kinds of these are considered: the "product" obscure qubit, in which the total amplitude is the product of the quantum and membership amplitudes, and the "Kronecker" obscure qubit, where the amplitudes are manipulated separately. In latter case, the quantum part of the computation is based, as usual, in Hilbert space, while the "truth" part requires a vague/fuzzy set formalism, and this can be performed in the framework of a corresponding fuzzy space. Obscure-quantum computation may be considered as a set of rules (defining obscure-quantum gates) for managing quantum and membership amplitudes independently in different spaces. In this framework we obtain not only the probabilities of final states, but also their membership functions, i.e. how much "trust" we should assign to these probabilities. Our approach considerably extends the theory of quantum computing by adding the logic part directly to the computation process. Future challenges could lie in the direction of development of the corresponding logic hardware in parallel with the quantum devices.

### **Acknowledgements**

The first author (S.D.) is deeply thankful to Geoffrey Hare and Mike Hewitt for thorough language checking.

*Obscure Qubits and Membership Amplitudes DOI: http://dx.doi.org/10.5772/intechopen.98685*
