Genetic optimization of ansatz expressibility for enhanced variational quantum algorithm performance

Abstract: Variational quantum algorithms have emerged as a leading paradigm that extracts practical computation from near-term intermediate-scale quantum devices, enabling advances in quantum chemistry simulations, combinatorial optimization, and quantum machine learning. However, the performance of Variational Quantum Algorithms is highly sensitive to the design of the ansatze. To be effective, ansatze must be expressive enough to capture target states but shallow enough to be trainable. We propose a genetic algorithm-inspired framework for designing ansatze that achieve high expressibility while maintaining shallow depth and low parameter count. Our approach evolves ansatze through mutation and selection based on an expressibility metric. The circuit generated by our framework consistently demonstrates high expressibility at any target depth and performs comparably to traditional ansatz design approaches while showing minimal to no signs of barren plateau issues. This work presents a general, scalable solution for ansatz design, producing expressive, low-depth circuits that need to be designed only once and can serve a wide range of applications.