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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study numerically the population transfer protocol on the Quantum RandomEnergy Model and its relation to quantum computing, for system sizes of $n\leq20$ quantum spins. We focus on the energy matching problem, i.e. findingmultiple approximate solutions to a combinatorial optimization problem when aknown approximate solution is provided as part of the input. We study thedelocalization process induced by the population transfer protocol by observingthe saturation of the Shannon entropy of the time-evolved wavefunction as ameasure of its spread over the system. The scaling of the value of this entropyat saturation with the volume of the system identifies the three knowndynamical phases of the model. In the non-ergodic extended phase, we observethat the time necessary for the population transfer to complete follows along-tailed distribution. We devise two statistics to quantify how effectivelyand uniformly the protocol populates the target energy shell. We find thatpopulation transfer is most effective if the transverse-field parameter$\Gamma$ is chosen close to the critical point of the Anderson transition ofthe model. In order to assess the use of population transfer as a quantumalgorithm we perform a comparison with random search. We detect a "black box"advantage in favour of PT, but when the running times of population transferand random search are taken into consideration we do not see strong indicationsof a speedup at the system sizes that are accessible to our numerical methods.We discuss these results and the impact of population transfer on NISQ devices.

Multifractal Dynamics of the QREM