  We introduce a phenomenological theory for many-body control of critical
phenomena by engineering causally-induced gaps for quantum Hamiltonian systems.
The core mechanisms are controlling information flow within and/or between
clusters that are created near a quantum critical point. To this end, we
construct inhomogeneous quantum phase transitions via designing spatio-temporal
quantum fluctuations. We show how non-equilibrium evolution of disordered
quantum systems can create new effective correlation length scales and
effective dynamical critical exponents. In particular, we construct a class of
causally-induced non-adiabatic quantum annealing transitions for strongly
disordered quantum Ising chains leading to exponential suppression of
topological defects beyond standard Kibble-Zurek predictions. Using exact
numerical techniques for 1D quantum Hamiltonian systems, we demonstrate that
our approach exponentially outperform adiabatic quantum computing. Using
Strong-Disorder Renormalization Group (SDRG), we demonstrate the universality
of inhomogeneous quantum critical dynamics and exhibit the causal zones
reconstructions during SDRG flow. We derive a scaling relation for minimal
causal gaps showing they narrow more slowly than any polynomial with increasing
size of system, in contrast to stretched exponential scaling in standard
adiabatic evolution. Furthermore, we demonstrate similar scaling behaviour for
random cluster-Ising Hamiltonians with higher order interactions.
