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In analogy with GRB 190114C, we here analyze the ultrarelativistic prompt emission (UPE) of GRB 180720B observed in the rest-frame time interval $t_{\rm rf}=4.84$--$10.89$~s by Fermi-GBM. We reveal the UPE hierarchical structure from the time-resolved spectral analysis performed in time sub-intervals: the spectrum in each shorter time interval is always fitted by a composite blackbody plus cutoff power-law model. We explain this structure with the \textit{inner engine} of binary-driven hypernova (BdHN) model operating in a quantum electrodynamics (QED) regime. In this regime, the electric field induced by the gravitomagnetic interaction of the newborn Kerr BH with the surrounding magnetic field is overcritical, i.e., $|{\bf E}|\geq E_c$, where $E_c=m_e^2 c^3/(e\hbar)$. The overcritical field polarizes the vacuum leading to an $e^+~e^-$ pair plasma that loads baryons from the surroundings during its expansion. We calculate the dynamics of the self-acceleration of the pair-electromagnetic-baryon (PEMB) pulses to their point of transparency. We characterize the quantum vacuum polarization process in the sequences of decreasing time bins of the UPE by determining the radiation timescale, Lorentz factors, and transparency radius of the PEMB pulses. We also estimate the strength of the surrounding magnetic field $\sim 10^{14}$ G, and obtain a lower limit to the BH mass, $M=2.4~M_\odot$, and correspondingly an upper limit to the spin, $α= 0.6$, from the conditions that the UPE is powered by the Kerr BH extractable energy and its mass is bound from below by the NS critical mass.