Name
Abstract | ||
|---|---|---|
Evolutions of local Hamiltonians in short times are expected to remain local and thus limited. In this paper, we validate this intuition by proving some limitations on short-time evolutions of local time-dependent Hamiltonians. We show that the distribution of the measurement output of short-time (at most logarithmic) evolutions of local Hamiltonians are \emph{concentrated} and satisfy an \emph{isoperimetric inequality}. To showcase explicit applications of our results, we study the \textsc{MaxCut} problem and conclude that quantum annealing needs at least a run-time that scales logarithmically in the problem size to beat classical algorithms on \textsc{MaxCut}. To establish our results, we also prove a Lieb-Robinson bound that works for time-dependent Hamiltonians which might be of independent interest. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.22331/q-2022-06-27-744 | Quantum |
DocType | Volume | Citations |
Journal | 6 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ali Hamed Moosavian | 1 | 0 | 0.34 |
| Seyed Sajad Kahani | 2 | 0 | 0.34 |
| Salman Beigi | 3 | 56 | 11.43 |