Demonstration of a parity-time-symmetry-breaking phase transition using superconducting and trapped-ion qutrits

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 nonconservative quantum dynamics presents a challenge for unitary quantum computation. In this work, we focus on simulating nonunitary 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 nonequilibrium 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 multilevel (qudit) processors in simulating physical effects, where additional accessible levels can play the role of a controlled environment.