1,555 research outputs found
Classical-Quantum Mixing in the Random 2-Satisfiability Problem
Classical satisfiability (SAT) and quantum satisfiability (QSAT) are complete
problems for the complexity classes NP and QMA which are believed to be
intractable for classical and quantum computers, respectively. Statistical
ensembles of instances of these problems have been studied previously in an
attempt to elucidate their typical, as opposed to worst case, behavior. In this
paper we introduce a new statistical ensemble that interpolates between
classical and quantum. For the simplest 2-SAT/2-QSAT ensemble we find the exact
boundary that separates SAT and UNSAT instances. We do so by establishing
coincident lower and upper bounds, in the limit of large instances, on the
extent of the UNSAT and SAT regions, respectively.Comment: Updated reference
Many-body localization beyond eigenstates in all dimensions
Isolated quantum systems with quenched randomness exhibit many-body
localization (MBL), wherein they do not reach local thermal equilibrium even
when highly excited above their ground states. It is widely believed that
individual eigenstates capture this breakdown of thermalization at finite size.
We show that this belief is false in general and that a MBL system can exhibit
the eigenstate properties of a thermalizing system. We propose that localized
approximately conserved operators (l-bits) underlie localization in such
systems. In dimensions , we further argue that the existing MBL
phenomenology is unstable to boundary effects and gives way to l-bits.
Physical consequences of l-bits include the possibility of an eigenstate
phase transition within the MBL phase unrelated to the dynamical transition in
and thermal eigenstates at all parameters in . Near-term experiments
in ultra-cold atomic systems and numerics can probe the dynamics generated by
boundary layers and emergence of l-bits.Comment: 12 pages, 5 figure
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