  Quantum simulation enables study of many-body systems in non-equilibrium by
mapping to a controllable quantum system, providing a new tool for
computational intractable problems. Here, using a programmable quantum
processor with a chain of 10 superconducting qubits interacted through tunable
couplers, we simulate the one-dimensional generalized Aubry-Andr\'e-Harper
model for three different phases, i.e., extended, localized and critical
phases. The properties of phase transitions and many-body dynamics are studied
in the presence of quasi-periodic modulations for both off-diagonal hopping
coefficients and on-site potentials of the model controlled respectively by
adjusting strength of couplings and qubit frequencies. We observe the spin
transport for initial single- and multi-excitation states in different phases,
and characterize phase transitions by experimentally measuring dynamics of
participation entropies. Our experimental results demonstrate that the newly
developed tunable coupling architecture of superconducting processor extends
greatly the simulation realms for a wide variety of Hamiltonians, and may
trigger further investigations on various quantum and topological phenomena.
