The aim and objectives of this chapter is to introduce the principles and
fundamental concepts of elements which are used as building block of new and
emerging neural systems. The first section introduces quantum logic and quantum
algebra. Only those concepts relevant to ANNs’ gates production are introduced, and as
such the mathematics involved has been kept to a minimum. The second section
introduce a new non-volatile memory elements; the memristance. Since these
phenomena are well known prior to their formal discovery (formulation), the
fundamental concepts and the phenomena forms the subject of discussion in this
chapter. The chapter has striven to be self-contained and brief in order to describe and
impart information relevant to understanding of the ANNs’ elements.
Keywords: Adjoint, Bell state, Cauchy-Schwarz inequality, C-NOT, Conjugate,
Eigenvalue, Eigenvector, EPR pair, Flux linkage, Hadamard gate, Hermittian,
Memristance, NAND, Orthonormal, Pauli matrices, Quantum gate, Qubit, Qu-
NOT, Universal gate, XOR.
