  Quantum phase transitions (QPTs) involve transformations between different
states of matter that are driven by quantum fluctuations. These fluctuations
play a dominant role in the quantum critical region surrounding the transition
point, where the dynamics are governed by the universal properties associated
with the QPT. While time-dependent phenomena associated with classical,
thermally driven phase transitions have been extensively studied in systems
ranging from the early universe to Bose Einstein Condensates, understanding
critical real-time dynamics in isolated, non-equilibrium quantum systems is an
outstanding challenge. Here, we use a Rydberg atom quantum simulator with
programmable interactions to study the quantum critical dynamics associated
with several distinct QPTs. By studying the growth of spatial correlations
while crossing the QPT, we experimentally verify the quantum Kibble-Zurek
mechanism (QKZM) for an Ising-type QPT, explore scaling universality, and
observe corrections beyond QKZM predictions. This approach is subsequently used
to measure the critical exponents associated with chiral clock models,
providing new insights into exotic systems that have not been understood
previously, and opening the door for precision studies of critical phenomena,
simulations of lattice gauge theories and applications to quantum optimization.
