Heuristic-Guided Genetic Preparation Of Ansatz for Variational Quantum Eigensolvers

Variational Quantum Eigensolvers (VQEs) are an ernerging application of near-term quantum computers due to their low computational requirements and high resistance to errors. The success of VQEs depends on the chosen ansatz, or pararneterized circuit, to approximate the ground state of a problem Hamiltonian. Ansatz selection presents a challenge, as it involves a trade-off between representation accuracy (which typically requires a high circuit depth) and hardware efficiency (which limits expressibility). This project presents a new method that utilizes a reinforcement-leaming-based heuristic to estimate the fitness of genetically generated ansatz, considering measures of expressibility, entanglement, and hardware costs. The protocol trains a genetic algorithm to generate candidate ansatz that can model a class of problems similar to a training Hamiltonian, optimizing both efficiency and accuracy. This project tests the method on various rnolecules (LiH and H2) and finds a significant reduction in the number of two-qubit gates and parameters compared to traditional hardware-efficient methods while maintaining accuracy. Future work will focus on applying particle swarm optimization to optimize the hyperparameters and further using learning to refine the fitness function, enhancing the efficiency and accuracy of ansatz generation.