Quantum State Preparation via Nested Entanglement

TL;DR

This paper introduces a nested entanglement representation for n-qubit states that simplifies quantum state preparation, circuit construction, and analysis of state separability, potentially reducing circuit complexity.

Contribution

It presents a novel recursive framework for representing quantum states, enabling automated circuit design and insights into state compressibility and complexity.

Findings

Provides a recursive state representation framework

Derives uniform controlled rotations and Fourier transform within this framework

Links state compressibility to circuit complexity

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.