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Investigations into quantum computations have begun from the pioneering theoretical studies of Feynman, Deutsch, and others, and detailed studies have been done since the discovery of a quantum algorithm which can solve the problem of factorizing a large integer in polynomial time by Shor in 1994. Recently, the existence of nonalgorithmic quantum computations in microtubules inside a neural circuit has been debated, resulting in the proposal of the concept of the quantum neural computation theory, although detailed studies have not as yet been made. In this paper, in order to construct a new framework for describing the cohesiveness of the distribution and synthesis inherent in a neural network, a neural state is described quantum dynamically and a qubitlike neural network corresponding to the quantum circuit of quantum computations is studied. Specifically, a qubitlike neural network is constructed for a 3 …