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

We show that the quantum dynamics of interacting and noninteracting quantumparticles are fundamentally different in the context of solving a particularcomputational problem. Specifically, we consider the graph isomorphism problem,in which one wishes to determine whether two graphs are isomorphic (related toeach other by a relabeling of the graph vertices), and focus on a class ofgraphs with particularly high symmetry called strongly regular graphs (SRG's).We study the Green's functions that characterize the dynamical evolutionsingle-particle and two-particle quantum walks on pairs of non-isomorphic SRG'sand show that interacting particles can distinguish non-isomorphic graphs thatnoninteracting particles cannot. We obtain the following specific results: (1)We prove that quantum walks of two noninteracting particles, Fermions orBosons, cannot distinguish certain pairs of non-isomorphic SRG's. (2) Wedemonstrate numerically that two interacting Bosons are more powerful thansingle particles and two noninteracting particles, in that quantum walks ofinteracting bosons distinguish all non-isomorphic pairs of SRGs that weexamined. By utilizing high-throughput computing to perform over 500 milliondirect comparisons between evolution operators, we checked all tabulated pairsof non-isomorphic SRGs, including graphs with up to 64 vertices. (3) Byperforming a short-time expansion of the evolution operator, we derivedistinguishing operators that provide analytic insight into the power of theinteracting two-particle quantum walk.

Two-particle quantum walks applied to the graph isomorphism problem