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In contrast to ordered states such as ferromagnets or Bose Einstein condensates,
quantum systems can realize an entirely an entirely new form of emergence termed
intrinsic topological order (ITO). Examples include the fractional quantum Hall states
and spin liquids whose unique properties hold promise for fault-tolerant quantum
computing. However, ITOs are notoriously hard to realize experimentally. For example,
quantum spin liquids were proposed by Anderson in 1973 but remain to be identified.
Besides the tendency for systems to order, the lack of clear experimental signatures
makes detection challenging. In this talk, I will describe our theoretical proposal to
create ITO in synthetic matter platforms such as Rydberg atom arrays, by leveraging
their tunability. Further, I will outline ideas for measuring non-local `string' correlations
which characterize ITOs, and briefly summarize the experimental progress towards
these goals. Finally, I will describe our ongoing exploration of new approaches to
efficiently realize many kinds of ITOs, including fractons and non-Abelian anyons in
synthetic matter.