Estimating the randomness of quantum circuit ensembles up to 50 qubits

Abstract Random quantum circuits have been utilized in the contexts of supremacy demonstrations, variational algorithms for chemistry and machine learning, blackhole information. The ability random to approximate any unitaries has consequences on their complexity, expressibility, trainability. To study this property circuits, we develop numerical protocols estimating frame potential, distance between a given ensemble exact randomness. Our tensor-network-based algorithm polynomial complexity shallow is high-performing using CPU GPU parallelism. We 1. local parallel verify linear growth as stated by Brown–Susskind conjecture, and; 2. hardware-efficient ansätze shed light its expressibility barren plateau problem context algorithms. work shows that large-scale tensor network simulations could provide important hints toward open problems information science.