  At transitions between phases of matter, physical systems can exhibit
universal behavior independent of their microscopic details. Probing such
behavior in quantum many-body systems is a challenging and practically
important problem that can be solved by quantum computers, potentially
exponentially faster than by classical computers. In this work, we use the
Quantinuum H1-1 quantum computer to realize a quantum extension of a simple
classical disease spreading process that is known to exhibit a non-equilibrium
phase transition between an active and absorbing state. Using techniques such
as qubit-reuse and error avoidance based on real-time conditional logic
(utilized extensively in quantum error correction), we are able to implement
large instances of the model with $73$ sites and up to $72$ circuit layers, and
quantitatively determine the model's critical properties. This work
demonstrates how quantum computers capable of mid-circuit resets, measurements,
and conditional logic enable the study of difficult problems in quantum
many-body physics: the simulation of open quantum system dynamics and
non-equilibrium phase transitions.
