The Quantum theory for a mesoscopic electric circuit with charge discreteness is investigated. Taking the Caldirola-Kanai Hamiltonian in studding Quantum mechanics of dissipative systems, we obtain the persistent current and the energy spectrum of a damped Quantum LC-design mesoscopic circuit under the influence of a time-dependent external field.

Quantum computing is a new method of information processing that is based on the concepts of Quantum mechanics and leads to strange and powerful events in the Quantum field. The logic synthesis of Quantum Circuits refers to the process of converting a given Quantum gate into a set of gates that can be implemented in Quantum technologies. The most famous logic synthesis methods are CSD and QSD. The main goal of this study is to present a multi-objective logical synthesis method combining the above two methods in the Quantum circuit model with the aim of optimizing the evaluation criteria. In this proposed method, the solution space is created from different combinations of CSD and QSD decomposition methods. The created solution space is a space with a very large exponential size. Then, using a bottom-up approach of multi-objective dynamic programming, a method is presented to search only a part of the entire solution space to find Circuits with the optimal Pareto costs. The obtained results show that this method creates a balance between the evaluation criteria and produces many optimal Pareto solutions that can be selected according to different Quantum technologies.

The Quantum dynamics of a charged particle in an infinite chain of single-state Quantum wells, in tight-binding approximation and under the action of an arbitrary time-dependent external field is investigated. The connection between the Hamiltonian description of this model and the Hamiltonian of a discrete-charge mesoscopic Quantum circuit is elucidated. Based on this connection, the persistent current on a L-design nondissipative circuit is obtained.