Recent breakthroughs in quantum processing software and hardware have shown substantial development toward operational results. We anticipate quantum computing to have significant applications in some domains ranging from machine learning and optimization to drug development in the future. Quantum computing and designing have gotten a lot of interest from investigators. Physical design is one of the two main stages in designing nano-scale circuits that receive a list of circuit nodes as input and produce the final arrangement in a particular technology. However, it has encountered several design issues and execution limits in the long term. Moreover, designing nano-scale circuits is an NP-hard problem in terms of cost, delay, and energy consumption. This paper has provided a new method for solving the optimal design of nano-scale circuits using a fuzzy-based Fish Swarm Algorithm (FSA). The FSA represents fish, hunting, and fish behavior to get the best results. It has a quick integration speed, a powerful global search capacity, and a significant shortcoming. In our proposed method, the fuzzy observer is responsible for detecting the system's state within the defined area and maintaining the state within it. The proposed method has been evaluated against some benchmarks, and cost, delay, energy, and area characteristics have been reduced. Simulation outcomes demonstrated the suggested method's correct performance in terms of "energy," "cost", "area", and "delay" where the suggested technique outperforms others (GA, PSO, FSA and ACO).