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We introduce a phenomenological theory for many-body control of criticalphenomena by engineering causally-induced gaps for quantum Hamiltonian systems.The core mechanisms are controlling information flow within and/or betweenclusters that are created near a quantum critical point. To this end, weconstruct inhomogeneous quantum phase transitions via designing spatio-temporalquantum fluctuations. We show how non-equilibrium evolution of disorderedquantum systems can create new effective correlation length scales andeffective dynamical critical exponents. In particular, we construct a class ofcausally-induced non-adiabatic quantum annealing transitions for stronglydisordered quantum Ising chains leading to exponential suppression oftopological defects beyond standard Kibble-Zurek predictions. Using exactnumerical techniques for 1D quantum Hamiltonian systems, we demonstrate thatour approach exponentially outperform adiabatic quantum computing. UsingStrong-Disorder Renormalization Group (SDRG), we demonstrate the universalityof inhomogeneous quantum critical dynamics and exhibit the causal zonesreconstructions during SDRG flow. We derive a scaling relation for minimalcausal gaps showing they narrow more slowly than any polynomial with increasingsize of system, in contrast to stretched exponential scaling in standardadiabatic evolution. Furthermore, we demonstrate similar scaling behaviour forrandom cluster-Ising Hamiltonians with higher order interactions.

Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians