English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we continue and extend the investigations of the ensembles ofrandom physical states introduced in A. Hamma et al. [http://prl.aps.org/abstract/PRL/v109/i4/e040502 Phys. Rev. Lett. 109, 040502(2012)]. These ensembles are constructed by finite-length random quantumcircuits (RQC) acting on the (hyper)edges of an underlying (hyper)graphstructure. The latter encodes for the locality structure associated withfinite-time quantum evolutions generated by physical i.e., local, Hamiltonians.Our goal is to analyze physical properties of typical states in theseensembles, in particular here we focus on proxies of quantum entanglement aspurity and $\alpha$-Renyi entropies. The problem is formulated in terms ofmatrix elements of superoperators which depend on the graph structure, choiceof probability measure over the local unitaries and circuit length. In the$\alpha=2$ case these superoperators act on a restricted multi-qubit spacegenerated by permutation operators associated to the subsets of vertices of thegraph. For permutationally invariant interactions the dynamics can be furtherrestricted to an exponentially smaller subspace. We consider different familiesof RQCs and study their typical entanglement properties for finite-time as wellas their asymptotic behavior. We find that area law holds in average and thatthe volume law is a typical property (that is, it holds in average and thefluctuations around the average are vanishing for the large system) of physicalstates. The area law arises when the evolution time is O(1) with respect to thesize $L$ of the system, while the volume law arises as typical when theevolution time scales like O(L).

Ensembles of physical states and random quantum circuits on graphs