Fock Space Prethermalization and Time-Crystalline Order on a Quantum Processor.

Periodically driven quantum many-body systems exhibit a wide variety of exotic nonequilibrium phenomena and provide a promising pathway for quantum applications. A fundamental challenge for stabilizing and harnessing these highly entangled states of matter is system heating by energy absorption from the drive. Here, we propose and demonstrate a disorder-free mechanism, dubbed Fock space prethermalization (FSP), to suppress heating. This mechanism divides the Fock space network into linearly many sparse subnetworks, thereby prolonging the thermalization timescale even for initial states at high energy densities. Using 72 superconducting qubits, we observe an FSP-based time-crystalline order that persists over 120 cycles for generic initial Fock states. Further, we perform finite-size scaling analysis for domain wall (DW) and Fock space dynamics by varying system sizes, which reveals size-independent regimes for FSP-thermalization crossover and links the dynamical behaviors to the eigenstructure of the Floquet unitary. Our Letter establishes FSP as a robust mechanism for breaking ergodicity and paves the way for exploring novel nonequilibrium quantum matter and its applications.