  Quantum computing is a new way of data processing based on the concept of
quantum mechanics. Quantum circuit design is a process of converting a quantum
gate to a series of basic gates and is divided into two general categories
based on the decomposition and composition. In the second group, using
evolutionary algorithms and especially genetic algorithms, multiplication of
matrix gates was used to achieve the final characteristic of quantum circuit.
Genetic programming is a subfield of evolutionary computing in which computer
programs evolve to solve studied problems. In past research that has been done
in the field of quantum circuits design, only one cost metrics (usually quantum
cost) has been investigated. In this paper for the first time, a
multi-objective approach has been provided to design quantum circuits using
genetic programming that considers the depth and the cost of nearest neighbor
metrics in addition to quantum cost metric. Another innovation of this article
is the use of two-step fitness function and taking into account the equivalence
of global phase in quantum gates. The results show that the proposed method is
able to find a good answer in a short time.
