Abstract
As a many-body quantum system evolves in time, it explores an immense Hilbert space whose volume grows exponentially with the number of particles. In this study, we are interested in generating random quantum states that explore this gigantic space as efficiently as possible. Such random states have applications in modern quantum information processing, statistical sampling, and randomised benchmarking. One way to efficiently explore Hilbert space is to utilise scrambling dynamics, which randomises an initial state due to the buildup of global entanglement that delocalizes quantum information. Here we study this phenomenon in large SU(2) angular momentum spin models, where we scramble the information using different unitary models of quantum chaos including Brownian spin dynamics. To study how rapidly information spreads in these models, we calculate the Frame Potential to characterise the evolution of simple operators into complicated ones that span the entire Hilbert Space. This investigation has two possible applications: a. the Frame Potential can tell us how deep our circuit must be or the minimum number of gates required to generate a sufficiently random state, with direct applications to testing and benchmarking state of the art quantum simulators. b. As information gets delocalised over the Hilbert space, it becomes increasingly impervious to the destructive effects of local measurements. When non-unitary elements like measurements are added to the dynamics, we expect to encounter potential Quantum Error Correction Codes due to this competition between measurement and scrambling.