Abstract: Aiming at the underconsideration of line structure characteristics and hierarchical demands of the traditional quantum scheduling strategy,and the execution will be occurred to reduce parallelism and increase the circuit depth during optimization execution process,this paper proposes the Quantum Firefly Algorithm(QFA) to apply it to 2QAN quantum circuit scheduling optimization.Quantum information is introduced to explore multiple locations simultaneously,and it increases the coverage of the search space.A balance between the exploration of the new solutions and the development of known solutions through the wave function evolution and collapse mechanism,meanwhile,the random perturbations is imported to enhance the search diversity,and the solutions will be jump out of the local optimum with quantum tunneling effect.The algorithm optimizes the order of quantum gate operations by evaluating the fitness values of different scheduling schemes to reduce the circuit depth and move operations,which in turn improves the circuit parallelism.Tests are conducted on four benchmark functions.The test results show that,compared with the firefly algorithm,the convergence speed of the quantum firefly algorithm is improved by approximately 40%,the quality of the solutions is enhanced by about 67%,and the search efficiency is increased by 45%.In the optimization of quantum circuit scheduling,compared with the traditional algorithm,the 2QAN circuit,the 2HQAA algorithm,and the combined algorithm of LCRA and LTSA,the number of SWAP gates of the quantum firefly algorithm is on average reduced by 42%,6.7%,10.4%,and 3% respectively,and the number of CNOT gates is on average decreased by 15.6%,10.8%,11%,and 2.2% respectively.

Key words: Quantum circuits, Quantum gate scheduling, Quantum firefly algorithm, Wave function evolution, Quantum tunneling