Prepare Ansatz for VQE with Diffusion Model

The Variational Quantum Eigensolver (VQE) is a quantum algorithm used to find the ground state energy of a given Hamiltonian. The key component of VQE is the ansatz, which is a trial wavefunction that the algorithm uses to approximate the ground state. Designing a good ansatz can significantly improve the performance of the VQE algorithm. Typical ansatz structures include the Unitary Coupled Cluster (UCC) ansatz and the Hardware-Efficient Ansatz (HEA). The primary distinction between these two structures lies in their dependence on the problem and hardware. The UCC ansatz is tailored to the target Hamiltonian, whereas the HEA is determined by the hardware topology. We believe that an intermediate approach could combine the benefits of the UCC ansatz while introducing additional parameters to increase its expressiveness and capability. In this paper, we propose utilizing a diffusion model to facilitate the generation of ansatz. We create a sequence of UCC ansatzes as training data and input this data into the diffusion model. The model then generates quantum circuits that have a similar structure to the input data. These quantum circuits are subsequently tested using a VQE task to evaluate their performance. This approach provides a systematic method for generating ansatzes that maintain a similar structure while incorporating additional parameters, enhancing their expressiveness and capability. We validate on small molecules that the diffusion model can help prepare ansatz circuits for VQE.