  Scalable quantum computers hold the promise to solve hard computational
problems, such as prime factorization, combinatorial optimization, simulation
of many-body physics, and quantum chemistry. While being key to understanding
many real-world phenomena, simulation of non-conservative quantum dynamics
presents a challenge for unitary quantum computation. In this work, we focus on
simulating non-unitary parity-time symmetric systems, which exhibit a
distinctive symmetry-breaking phase transition as well as other unique features
that have no counterpart in closed systems. We show that a qutrit, a
three-level quantum system, is capable of realizing this non-equilibrium phase
transition. By using two physical platforms -- an array of trapped ions and a
superconducting transmon -- and by controlling their three energy levels in a
digital manner, we experimentally simulate the parity-time symmetry-breaking
phase transition. Our results indicate the potential advantage of multi-level
(qudit) processors in simulating physical effects, where additional accessible
levels can play the role of a controlled environment.
