  Dynamical mean-field theory (DMFT) maps the local Green's function of the
Hubbard model to that of the Anderson impurity model and thus gives an
approximate solution of the Hubbard model from the solution of simpler quantum
impurity model. Quantum and hybrid quantum-classical algorithms have been
proposed to efficiently solve impurity models by preparing and evolving the
ground state under the impurity Hamiltonian on a quantum computer that is
assumed to have the scalability and accuracy far beyond the current
state-of-the-art quantum hardware. As a proof of principle demonstration
targeting the Anderson impurity model we close the DMFT loop with current noisy
hardware. With a highly optimized fast-forwarding quantum circuit and a noise
resilient spectral analysis we observe a Mott phase transition. Based on a
Cartan decomposition, our algorithm gives a fixed depth, fast-forwarding,
quantum circuit that can evolve the initial state over arbitrarily long times
without time-discretization errors typical of other product decomposition
formulas such as Trotter decomposition. By exploiting the structure of the
fast-forwarding circuits we reduce the gate count (to 77 CNOTs after
optimization), simulate the dynamics, and extract frequencies from the Anderson
impurity model on noisy quantum hardware. We then demonstrate the Mott
transition by mapping the full metal-insulator phase-diagram. Near the Mott
phase transition, our method maintains accuracy where Trotter error would
otherwise dominate due to the long-time evolution required to resolve
quasiparticle resonance frequency extremely close to zero. This work presents
the first computation of the Mott phase transition using noisy digital quantum
hardware, made viable by a highly optimized computation in terms of gate depth,
simulation error, and runtime on quantum hardware.
