Dynamic Variational Quantum Eigensolver: Incorporating Time-evolution for Ansatz Design and Ground State Simulation

Abstract Variational Quantum Eigensolver (VQE) addresses challenges that conventional computation struggles to overcome. However, VQE lacks the ability to autonomously trend towards the direction of quantum advantage, leading to unnecessary consumption of time and resources during parameter optimization. In this work, we present a Simulating Dynamic VQE (D-VQE) that incorporates time evolution for achieving desired simulation accuracy and parameter optimization. Introducing causal cones for Parameterized Quantum Circuits (PQC) and establishing dynamic judgment rules. Consequently, we can reduce the overstacking of components in PQC ansatz. Based on the requirements of precision and circuit scale, a reasonable operator pool is set to deal with the parameters. Through numerical experiments, our method effectively simulates the search for the ground state in the transverse-field Ising model, achieving a relative energy error below 10^ (-3) and improving ground state approximation capability. Moreover, in the context of optimized Boltzmann machine learning, the Kullback-Leibler divergence (KLD) value converges to 0. 03. These results prove that our work provides an effective and feasible consideration for the improvement of variational quantum algorithms.