Quantum State Preparation via Nested Entanglement
Abstract
We develop a representation of an n-qubit register that parameterizes its statevector as a series of nested entanglements. We show that the recursive substructure of this representation provides a natural framework for automating the construction of quantum circuits for state preparation. It also allows for a straightforward treatment of pure state separability. We discuss a novel derivation of uniformly controlled rotations and the quantum Fourier transform within this representation, and consider the effects of single-qubit basis changes on its overall structure. We end with a discussion of the apparent connection between the compressibility of the state description in this representation, and the circuit complexity required to prepare it.
Cite
@article{arxiv.2502.02784,
title = {Quantum State Preparation via Nested Entanglement},
author = {Geoffrey L. Warner},
journal= {arXiv preprint arXiv:2502.02784},
year = {2025}
}