The process of carbon burning is vital to understanding late stage stellar evolution of massive stars and the conditions of certain supernovae. Carbon burning is a complex problem, involving quantum tunnelling and nuclear molecular states. Quantum dynamical calculations of carbon burning are presented, combining the time-dependent wave-packet method and the density-constrained time-dependent Hartree-Fock (DC-TDHF) approach. We demonstrate that the state-of-the-art DC-TDHF interaction potential successfully explains the appearance of some resonant structures in the sub-barrier fusion cross-section. We study the dynamic response of the compound nucleus to further explain resonant structure seen in the Gamow energy region. The results show the critical role of nucleon-nucleon interactions and compound nucleus excitations in the 12C + 12C fusion resonances observed at astrophysical energies.