Estimating the frame potential of large-scale quantum circuit sampling using tensor networks up to 50 qubits. (arXiv:2205.09900v1 [quant-ph])

We develop numerical protocols for estimating the frame potential, the 2-norm
distance between a given ensemble and the exact Haar randomness, using the
\texttt{QTensor} platform. Our tensor-network-based algorithm has polynomial
complexity for shallow circuits and is high performing using CPU and GPU
parallelism. We apply the above methods to two problems: the Brown-Susskind
conjecture, with local and parallel random circuits in terms of the Haar
distance and the approximate $k$-design properties of the hardware efficient
ans{\"a}tze in quantum machine learning, …

arxiv networks quantum qubits sampling scale tensor