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arXiv · 2502.02784

Quantum State Preparation via Nested Entanglement

Geoffrey L. Warner
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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.

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Geoffrey L. Warner. 2025-02-05. Quantum State Preparation via Nested Entanglement. https://arxiv.org/abs/2502.02784

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