  At continuous phase transitions, quantum many-body systems exhibit
scale-invariance and complex, emergent universal behavior. Most strikingly, at
a quantum critical point, correlations decay as a power law, with exponents
determined by a set of universal scaling dimensions. Experimentally probing
such power-law correlations is extremely challenging, owing to the complex
interplay between decoherence, the vanishing energy gap, and boundary effects.
Here, we employ a Rydberg quantum simulator to adiabatically prepare critical
ground states of both a one-dimensional ring and a two-dimensional square
lattice. By accounting for and tuning the openness of our quantum system, which
is well-captured by the introduction of a single phenomenological length scale,
we are able to directly observe power-law correlations and extract the
corresponding scaling dimensions. Moreover, in two dimensions, we observe a
decoupling between phase transitions in the bulk and on the boundary, allowing
us to identify two distinct boundary universality classes. Our work
demonstrates that direct adiabatic preparation of critical states in quantum
simulators can complement recent approaches to studying quantum criticality
using the Kibble-Zurek mechanism or digital quantum circuits.
