Many-Body Anti-Zeno Thermalization and Zeno Determinism in Monitored Hamiltonian Dynamics

Random quantum states are essential for quantum information science, with applications ranging from quantum computing to cryptography. Prior approaches for generating these states often rely on using a large bath to thermalize a smaller system, with a subsequent measurement on the bath used to postselect a random state. To reduce the required size of the bath, we propose a resource-efficient scheme using holographic deep thermalization driven by Hamiltonian evolution, combined with midcircuit measurements. This scheme relies on dynamical circuits, enabling a trade-off between spatial and temporal resources and allowing the generation of genuinely random states with only a constant-size bath. We quantify the randomness using the frame potential and derive its asymptotic behavior, which shows good agreement with our numerical simulations and IBM Quantum Platform results. For a fixed total evolution time, increasing the number of midcircuit measurements initially produces an exponential decrease in the frame potential-a quantum anti-Zeno behavior arising from holographic deep thermalization. Past a critical number of midcircuit measurements, the frame potential rises again, signaling the onset of the quantum Zeno effect.