A measured approach toward long-range entangled matter

Long-range entangled quantum matter encompasses a wealth of fascinating phenomena including fractionalization and criticality.  I will show how quantum dynamics involving measurements can both enable new kinds of long-range entangled states and facilitate their realization on quantum simulators.  In the first part, I will illustrate how competing measurements along with unitary time evolution can give rise to distinct universality classes of non-equilibrium criticality.  In the second part, I will show how measurements and unitary evolution conditioned on the measurement outcomes (“adaptive quantum circuits”) enable efficient preparation of long-range entangled matter.  I will present three classes of protocols inspired by distinct physical insights, including tensor networks, renormalization, and partons. A large class of topological orders, including chiral states akin to the fractional quantum Hall effect, can be prepared in a time independent of system size, and critical states and non-abelian topological orders can be prepared in depth scaling logarithmically with system size.