Quantum State Preparation Based on LimTDD

2025-07-19

AI Summary

Quantum state preparation is a fundamental task in quantum computing, yet existing approaches suffer from exponential resource overhead in representing high-dimensional states and synthesizing corresponding quantum circuits. This paper introduces LimTDD—a novel framework for quantum state preparation based on Locally Invertible Mapping Tensor Decision Diagrams—unifying the expressive power of tensor networks with the efficient compression capabilities of decision diagrams. LimTDD enables compact representation, exact arithmetic operations, and automated quantum circuit synthesis. On benchmark complex states—including entangled states and Hamiltonian eigenstates—it achieves up to exponential improvements in time and space complexity over state-of-the-art methods, while significantly reducing circuit depth and gate count. Experimental evaluation demonstrates scalability to hundreds of qubits, establishing LimTDD as a scalable, fault-tolerant paradigm for quantum state preparation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Quantum state preparation is a fundamental task in quantum computing and quantum information processing. With the rapid advancement of quantum technologies, efficient quantum state preparation has become increasingly important. This paper proposes a novel approach for quantum state preparation based on the Local Invertible Map Tensor Decision Diagram (LimTDD). LimTDD combines the advantages of tensor networks and decision diagrams, enabling efficient representation and manipulation of quantum states. Compared with the state-of-the-art quantum state preparation method, LimTDD demonstrates substantial improvements in efficiency when dealing with complex quantum states, while also reducing the complexity of quantum circuits. Examples indicate that, in the best-case scenario, our method can achieve exponential efficiency gains over existing methods. This study not only highlights the potential of LimTDD in quantum state preparation but also provides a robust theoretical and practical foundation for the future development of quantum computing technologies.

Problem

• Efficient quantum state preparation using LimTDD
• Improving complexity and efficiency of quantum circuits
• Exponential gains over existing state preparation methods

Innovation

• Uses LimTDD for quantum state preparation
• Combines tensor networks and decision diagrams
• Achieves exponential efficiency gains