Tucker iterative quantum state preparation

2026-02-10

AI Summary

This work addresses the challenges of excessive circuit depth and the lack of practical construction methods in quantum state preparation, particularly the need for efficient encoding of classical data in quantum machine learning. The authors propose an iterative framework based on Tucker decomposition that adaptively constructs shallow, deterministic quantum circuits by analyzing the global entanglement structure of the target quantum state. The approach decomposes the state into a core tensor and mode-specific operators, thereby enabling joint decomposition across multiple subsystems. To the best of the authors’ knowledge, this is the first application of Tucker decomposition to quantum state preparation, offering a practical scheme that directly yields shallow quantum circuits. Experimental results demonstrate that the method significantly reduces circuit depth and enhances the efficiency of preparing high-dimensional data-encoded quantum states.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• quantum state preparation
• amplitude encoding
• quantum circuits
• Tucker decomposition
• entanglement structure

Innovation

• Tucker decomposition
• quantum state preparation
• shallow quantum circuits
• entanglement structure
• amplitude encoding