Analog quantum simulation of the Lipkin-Meshkov-Glick model in a transmon qudit

The simulation of large-scale quantum systems is one of the most sought-after applications of quantum computers in the near term. Of particular interest for near-term demonstrations of quantum computational advantage are analog quantum simulations, in which analog controls are applied to quantum processors in order to emulate other quantum systems. Most analog quantum simulations to date have been performed using qubit-based processors, despite the fact that many physical systems are more naturally represented in terms of qudits (i.e., d-level systems). Motivated by this, in this talk I will present an experimental realization of the Lipkin-Meshkov-Glick (LMG) model using an analog simulator based on a single superconducting transmon qudit with up to d = 9 levels. I will discuss experiments that investigate several aspects of quantum criticality in the LMG model, including protocols for extracting the relevant properties of the system which do not require any prior knowledge of the system eigenstates. I will furthermore interpret our results in terms of a semiclassical approximation, which serves to provide intuition and guide the experiments. Our results cement high-dimensional transmon qudits as an exciting path towards scalable quantum simulation.