Quantum Firefly Algorithm: A Novel Approach for Quantum Circuit Scheduling Optimization

In the noisy intermediate-scale quantum (NISQ) era, as the scale of existing quantum hardware continues to expand, the demand for effective methods to schedule quantum gates and minimize the number of operations has become increasingly urgent. To address this demand, the Quantum Firefly Algorithm (QFA) has been designed by incorporating quantum information into the traditional firefly algorithm. This integration enables fireflies to explore multiple positions simultaneously, thereby increasing search space coverage and utilizing quantum tunneling effects to escape local optima. Through wave function evolution and collapse mechanisms described by the Schrödinger equation, a balance between exploring new solutions and exploiting known solutions is achieved by the QFA. Additionally, random perturbation steps are incorporated into the algorithm to enhance search diversity and prevent the algorithm from being trapped in local optima. In quantum circuit scheduling problems, the QFA optimizes quantum gate operation sequences by evaluating the fitness of scheduling schemes, reducing circuit depth and movement operations, while improving parallelism. Experimental results demonstrate that, compared to traditional algorithms, the QFA reduces SWAP gates by an average of 44% and CNOT gates by an average of 16%. When compared to modern algorithms, it reduces SWAP gates by an average of 7% and CNOT gates by an average of 12%.