Speaker
Description
The quantum state preparation of probability distributions is an important subroutine for many quantum algorithms. When embedding $D$-dimensional multivariate probability distributions by discretizing each dimension into $2^n$-point, we need a state preparation circuit comprising a total of $nD$ qubits, which is often difficult to compile. In this study, we propose a method to generate state preparation circuits for $D$-dimensional multivariate normal distributions, utilizing tensor networks. We represent the probability distribution with a tree tensor network and perform the task of quantum circuit compilation through the optimization of tensor networks. Especially, by employing structural optimization, we can search for a network structure that efficiently represents the correlations between variables. The numerical results suggest that our method can dramatically reduce the circuit depth while maintaining fidelity compared to existing approaches. Moreover, for normal distributions with one-dimensional correlations, we can construct state preparation circuits in a scalable manner, regardless of the number of variables, by using tensor cross interpolation.
