Hilbert-space signatures of non-ergodic glassy dynamics

The dynamics of interacting quantum particles in disordered landscapes is a central problem in non-equilibrium physics. Theoretical and numerical approaches are severely limited by exponential Hilbert space scaling and the absence of translational symmetry. Here, we leverage the high data rates of a superconducting qubit quantum processor to efficiently sample Hilbert space configurations. Using a 2D grid of up to 70 qubits, we measure the return probability $R(t)$ across a broad range of disorder strengths.

At long times, $R(t)$ develops a heavy-tailed distribution, while its typical value follows a power-law scaling—both suggestive of glass-like dynamics. Furthermore, the probability distribution of z-configurations evolves from a Porter–Thomas form at low disorder to a power-law—spanning eight orders of magnitude—at higher disorder strengths. We cluster the wavefunctions on the basis of Hamming distance in Hilbert space, identifying three distinct regimes as a function of disorder strength. By directly probing Hilbert space dynamics, we provide a complementary perspective to the existing real-space picture of two-dimensional quantum systems, demonstrating the potential of current quantum processors to yield deeper insights into non-equilibrium physics. A semi-quantitative theory of the observed phenomena will be presented as well.

References: https://arxiv.org/abs/2601.01309