Tran, Chinzei, and Endo (2602.22061) replace the random circuits in quantum diffusion models with chaotic Hamiltonian evolution — and get comparable accuracy with substantially less engineering overhead.
Quantum denoising diffusion probabilistic models (QuDDPMs) learn distributions over quantum states by scrambling them into noise, then learning to reverse the process. The scrambling step — the forward diffusion — conventionally uses random unitary circuits: sequences of gates applied to qubits. This works but requires precise gate-level control, making it expensive on analog quantum hardware where the natural operations are continuous Hamiltonian evolution, not discrete gates.
Chaotic Hamiltonian dynamics provides a natural alternative. A many-body quantum system with chaotic interactions scrambles information just as effectively as random circuits — that's what quantum chaos means. The chaotic quantum diffusion model uses time evolution under a fixed, time-independent chaotic Hamiltonian as the forward diffusion process. No gate synthesis, no circuit compilation, no sequence of precisely timed pulses. Just let the system evolve under its natural interactions.
The technical mechanism: chaotic evolution generates projected ensembles that approximate the Haar-random unitaries needed for diffusion. The approximation quality depends on the degree of chaos in the Hamiltonian, quantified by spectral statistics matching random matrix theory predictions. Strongly chaotic Hamiltonians produce diffusion processes that are effectively equivalent to the circuit-based approach.
The practical advantages compound. Global, time-independent control means fewer control lines and lower calibration overhead. Robustness to control imperfections is inherent — small errors in a chaotic Hamiltonian still produce chaotic evolution. And trainability improves because the denoising network sees smoother scrambled states than those produced by random circuits with discrete jumps.
The principle generalizes: wherever random circuits are used as a computational primitive, chaotic dynamics may substitute with lower overhead and higher hardware compatibility.