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. Of particular interest for near-term demonstrations of quantum computational advantage are analog quantum simulations, which employ analog controls instead of digitized gates. Most analog quantum simulations to date, however, 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, we 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. This is accomplished by moving to a rotated frame in which evolution under any time-dependent local field and one-axis twisting can be realized by the application of multiple simultaneous drives. Combining this analog drive scheme with universal control and single-shot readout of the qudit state, we provide a detailed study of five finite-size precursors of quantum criticality in the LMG model: dynamical phase transitions, closing of the energy gap, Kibble-Zurek-like dynamics, statistics of the order parameter, and excited-state phase transitions. For each experiment we devise a protocol for extracting the relevant properties which does not require any prior knowledge of the system eigenstates, and can therefore be readily extended to higher dimensions or more complicated models. Our results cement high-dimensional transmon qudits as an exciting path towards simulating many-body physics.