Floquet circuits inspired by holographic matrix models

Inspired by the BFSS matrix model, we study a quantum circuit that captures fast scrambling dynamics with non-random interactions. Specifically, in the spirit of a Trotter decomposition, we propose a Floquet Clifford circuit model whose interaction graph simulates terms such as Tr(Φ⁴) appearing in matrix-model Hamiltonians. This cartoon model, which is designed to be more easily implemented in neutral-atom array experiments, allows efficient numerical simulation of the entanglement spreading within a stabilizer framework. We calculate growth in the operator size and entanglement entropy of the system, and analyze a recovery protocol inspired by the Yoshida–Kitaev decoding scheme that recovers scrambled information effectively. Our simulation results show signatures of fast scrambling despite the absence of randomness, highlighting that this deterministic Clifford dynamics can reproduce chaotic-like information spreading.