Engineering quantum phase transitions via spatio-temporal gapped Hamiltonians

We introduce a general framework for controlling quantum critical phenomena. We engineer quantum phase transitions via constructing spatio-temporal inhomogeneous driving Hamiltonians. We show that non-equilibrium evolution of disordered quantum systems can be manipulated leading to new dynamical critical exponent and correlation length scales that are fundamentally different from corresponding parameters when such complex systems are driven homogeneously. In particular, we construct a class of causally-induced non-adiabatic quantum annealing transitions for low-dimensional spin-glass systems leading to substantial suppression of topological defects beyond standard Kibble-Zurek predications. Using DMRG techniques for such quantum Hamiltonian systems, we demonstrate that our approach could outperform standard (homogeneous) adiabatic quantum computing and simulated annealing by several order of magnitudes in residual energy.