Thermalization and Criticality on an Analog-Digital Quantum Simulator

Understanding howinteracting particles approach thermal equilibrium is a major 

challenge ofquantum simulators . Unlocking the full potential of such systems toward 

thisgoal requires flexible initial state preparation, precise time evolution, andextensive

 probes for final state characterization. We present a quantumsimulator comprising 69 

superconducting qubits which supports both universal quantumgates and high-fidelity

 analog evolution, with performance beyond the reach ofclassical simulation in cross-

entropy benchmarking experiments. Emulating atwo-dimensional (2D) XY quantum 

magnet, we leverage a wide range of measurementtechniques to study quantum 

states after ramps from an antiferromagneticinitial state. We observe signatures of 

the classical Kosterlitz-Thouless phasetransition , as well as strong deviations from 

Kibble-Zurek scaling predictionsattributed to the interplay between quantum and 

classical coarsening of thecorrelated domains . This interpretation is corroborated by 

injecting variableenergy density into the initial state, which enables studying the 

effects of theeigenstate thermalization hypothesis (ETH) in targeted parts of the 

eigenspectrum. Finally, we digitally prepare the system in pairwise-entangleddimer 

states and image the transport of energy and vorticity duringthermalization. These 

results establish the efficacy of superconductinganalog-digital quantum processors 

for preparing states across many-body spectraand unveiling their thermalization 

dynamics.

Quantum and classical critical coarsening in theXY-model

Our results demonstrate a high-fidelity quantum simulator with the capability of 

emulating beyond-classical chaotic dynamics, a wide range of characterization probes, 

and versatile digital-analog control. Leveraging these features has enabled new i

nsights about the rich interplay of quantum and classical critical behavior in the 2D 

XYmodel, including the KT transition, thermalization dynamics, and their combined 

effects on the KZ scaling relations. Looking ahead, this platform is expected to offer 

an invaluable playground for studies of classically intractablemany-body quantum 

physics, including e.g. dynamical response functions and magnetic frustration.

Article: arXiv:2405.17385v1