Tucker iterative quantum state preparation

TL;DR

The paper introduces Q-Tucker, a new quantum state preparation method that efficiently constructs shallow, deterministic circuits by leveraging Tucker decomposition to exploit the global entanglement structure of quantum states.

Contribution

Q-Tucker is a novel approach that adaptively constructs shallow quantum circuits for state preparation using Tucker decomposition, improving over recursive bipartitions.

Findings

Enables direct decomposition of target states into core tensor and operators.

Constructs shallow, deterministic quantum circuits.

Exploits global entanglement structure for efficient state preparation.

Abstract

Quantum state preparation is a fundamental component of quantum algorithms, particularly in quantum machine learning and data processing, where classical data must be encoded efficiently into quantum states. Existing amplitude encoding techniques often rely on recursive bipartitions or tensor decompositions, which either lead to deep circuits or lack practical guidance for circuit construction. In this work, we introduce Tucker Iterative Quantum State Preparation (Q-Tucker), a novel method that adaptively constructs shallow, deterministic quantum circuits by exploiting the global entanglement structure of target states. Building upon the Tucker decomposition, our method factors the target quantum state into a core tensor and mode-specific operators, enabling direct decompositions across multiple subsystems.