Characterizing a non-equilibrium phase transition on a quantum computer

Quantum systems subject to driving and dissipation display distinctive non-equilibrium phenomena relevant to condensed matter, quantum optics, metrology and quantum error correction. An example is the emergence of phase transitions with uniquely quantum properties, which opposes the intuition that dissipation generally leads to classical behaviour. The quantum and non-equilibrium nature of such systems makes them hard to study with existing tools, such as those from equilibrium statistical mechanics, and represents a challenge for numerical simulations. Quantum computers, however, are well suited to simulating such systems, especially as hardware developments enable the controlled application of dissipative operations in a pristine quantum environment. Here we demonstrate a large-scale accurate quantum simulation of a non-equilibrium phase transition using a trapped-ion quantum computer. We simulate a quantum extension of the classical contact process that has been proposed as a description for driven gases of Rydberg atoms and has stimulated numerous attempts to determine the impact of quantum effects on the classical directed-percolation universality class. We use techniques such as qubit reuse and error avoidance based on real-time conditional logic to implement large instances of the model with 73 sites and up to 72 circuit layers and quantitatively determine the model’s critical properties. Our work demonstrates that today’s quantum computers are able to perform useful simulations of open quantum system dynamics and non-equilibrium phase transitions.