Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits

Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard to that of the Anderson impurity model. Quantum algorithms have been proposed to speed up solving the impurity model by preparing and evolving the ground state under the impurity Hamiltonian, which is the most expensive part of the calculation for DMFT. To improve existing quantum algorithms for the two-site DMFT problem and obtain quantitatively accurate results on noisy quantum hardware, we propose a highly optimized fast-forwarding quantum circuit. Our Cartan decomposition based algorithm introduces no time-discretization errors and uses a fixed depth quantum circuit to evolve an initial state over any time. By exploiting the structure of the fast-forwarding circuits, we sufficiently reduce the gate cost to simulate the dynamics of, and extract frequencies from, the Anderson impurity model on noisy quantum hardware and demonstrate the Mott transition. Especially near the Mott phase transition when the quasiparticle resonance frequency approaches zero and evolving the system over long-time scales is necessary, our method maintains accuracy where Trotter error would otherwise dominate.