Multi-target quantum compilation algorithm

Quantum compilation is the process of converting a target unitary operation into a trainable unitary represented by a quantum circuit. It has a wide range of applications, including gate optimization, quantum-assisted compiling, quantum state preparation, and quantum dynamic simulation. Traditional quantum compilation usually optimizes circuits for a single target. However, many quantum systems require simultaneous optimization of multiple targets, such as thermal state preparation, time-dependent dynamic simulation, and others. To address this, we develop a multi-target quantum compilation algorithm to improve the performance and flexibility of simulating multiple quantum systems. Our benchmarks and case studies demonstrate the effectiveness of the algorithm, highlighting the importance of multi-target optimization in advancing quantum computing. This work lays the groundwork for further development and evaluation of multi-target quantum compilation algorithms.