Memory and its data communication play a vital role in deciding the performance of a Processor. In order to obtain a high performance computing machine, memory access has to be equally faster. In this paper, Dual port memory with Set/Reset is designed using Majority Voter in Quantum-dot Cellular Automata (QCA). Dual port memory consists of basic functional blocks such as 2 to 4 decoder, Control Logic Block (CLB), Address Checker Block (ACB), Memory Cell (MC), Data Router block and Input/Output block. These functional units are constructed using the 3-input majority voters. QCA is one of the recent technologies for the design of nanometer level digital components. The functionality of Dual Port Memory has been simulated and verified in QCADesigner 2.0.3. A novel crossover method called Logical Crossing is utilized to improve the area of the proposed design. The logical crossing does the data transmission with the support of proper Clock zone assignment. The logical crossing based QCA layouts are optimized in terms of area and number of cell counts. It is observed that 29.81%, 18.27%, 8.32%, 11.57% and 3.69% are the percentage of improvement in the number of cells in Decoder, ACB, CLB, Data Router and Memory Cell respectively. Also, 25.71%, 16.83%, 8.62%, 4.74% and 3.73% of improvement is achieved in the area for Decoder, ACB, CLB, Data Router and Memory Cell respectively. In addition to that the proposed Dual port memory using logical crossing attains improvement in the area by 8.26%; that is made possible due to the 8.65% reduction in the number of cells required for its construction. Moreover, the quantum circuits of the RAM are obtained using the RCViewer+ tool. The quantum cost, constant inputs, the number of gates, garbage output and total cost are estimated as 285, 67, 57, 50 and 516 respectively.