Abstract
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 spatiotemporal 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 outperforms adiabatic quantum computing. Using strong-disorder renormalization group (SDRG), we demonstrate the universality of inhomogeneous quantum critical dynamics and exhibit the reconstructions of causal zones 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 behavior for random cluster-Ising Hamiltonians with higher order interactions.
Highlights
Any further distribution of engineering causally-induced gaps for quantum Hamiltonian systems
Using strong-disorder renormalization group (SDRG), we demonstrate the universality of inhomogeneous quantum critical dynamics and exhibit the reconstructions of causal zones during SDRG flow
We always have a finite annealing time-scale that would inherently violate the adiabaticity condition, even for finite-size systems, leading to emergence of domain walls or topological defects that emerge at a relatively wide effective quantum critical region. This is in sharp contrast to a single, well-defined quantum critical point for pure system, where their density of defects can be estimated via Kibble–Zurek mechanism (KZM) in the thermodynamics limit [10,11,12,13,14]
Summary
Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians. The main difficulties arise from the fact that these systems generally contain high degree of disorders and effectively low dimensions such that they are not prone to exact analytical treatment or mean-field approximations In principle their dynamics can be mapped to the dynamics of spin-glass systems that are driven/quenched by external control fields and could experience various first and second-order quantum phase transitions and Griffiths singularities [2, 3]. There is no known way to guarantee the quality of solutions, given finite space–time physical resources, and there is no constructive or algorithmic way to improve performance for such analog quantum information processors within a given accuracy These issues have lead us to the following fundamental questions: Is it possible to engineer quantum phase transition in disordered systems by inhomogeneous control fields to enforce spatially-induced gaps between low energy sector and higher energy states (see figure 1(b)). The generalization to spin-glass systems will be presented in another subsequent work [16, 17]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
