“…In this work, we investigate Hilbert space delocalization under the dynamics of quantum circuits comprising 2-qudit Haar random gates arranged in a brick wall pattern [ 23 ]. The locality and unitarity of this setup constitute the minimal requirements for chaotic evolution in many-body systems [ 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 ], hence allowing us to gain a phenomenological understanding of the Hilbert space delocalization under generic quantum dynamics. Our analysis combines rigorous analytical methods, based on the mapping between the average of the IPR over the random circuits and a statistical mechanics model, with exact numerical simulations, including tensor network techniques [ 71 , 72 , 73 , 74 ] (here, our implementation is based on the open-source library ITensor [ 75 , 76 ] and available at [ 77 ]).…”