Variational Time Evolution Compression for Solving Impurity Models on Quantum Hardware

Dynamical mean-field theory (DMFT) is a useful tool to analyze models of strongly correlated fermions like the Hubbard model. In DMFT, the lattice of the model is replaced by a single impurity site embedded in an effective bath. The resulting single impurity Anderson model (SIAM) can then be solved self-consistently with a quantum-classical hybrid algorithm. This procedure involves repeatedly preparing the ground state on a quantum computer and evolving it in time to measure the Greens function. We here develop an approximation of the time evolution operator for this setting by training a Hamiltonian variational ansatz. The parameters of the ansatz are obtained via a variational quantum algorithm that utilizes a small number of time steps, given by the Suzuki-Trotter expansion of the time evolution operator, to guide the evolution of the parameters. The resulting circuit has a fixed depth for the time evolution depending on the size of the bath and is significantly shallower than a comparable Suzuki-Trotter expansion.