Based on analysis on properties of quantum linear superposition, to overcome the complexity of existing quantum associative memory which was proposed by Ventura, a new storage method for multiply patterns is proposed in this paper by constructing the quantum array with the binary decision diagrams. Also, the adoption of the nonlinear search algorithm increases the pattern recalling speed of this model which has multiply patterns to O(log 2 2 n−t ) = O(n − t) time complexity, where n is the number of quantum bit and t is the quantum information of the t quantum bit. Results of case analysis show that the associative neural network model proposed in this paper based on quantum learning is much better and optimized than other researchers' counterparts both in terms of avoiding the additional qubits or extraordinary initial operators, storing pattern and improving the recalling speed.

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The key of optimizing quantum reversible logic lies in automatically constructing quantum reversible logic circuits with the minimal quantum cost. This paper constructs a 4 × 4 reversible gate called ZS gate to build quantum full adder. At the same time, a novel reversible No-Wait-Carry adder (or carry skip adder) by using ZSCGPD based on ZS gate with the least cost is also designed. The adder circuit using the proposed ZSCGPD is much better and optimized than other researchers' counterparts both in terms of garbage outputs, number and kind of reversible gates, and quantum cost. In order to show the efficiency of the proposed designs, lower bounds of the reversible carry skip adder in terms of garbage outputs and quantum cost are proposed as well.