Advancing Quantum State Preparation using LimTDD

2025-07-22

AI Summary

Quantum state preparation (QSP) is a fundamental subroutine in quantum algorithms, yet existing approaches suffer from substantially increased circuit depth and complexity under auxiliary qubit constraints. This paper introduces Local reversible mapping Tensor Decision Diagrams (LimTDDs) to QSP for the first time, proposing a unified algorithmic framework applicable to zero-, single-, and multi-auxiliary-qubit scenarios. Leveraging the compact representation of quantum states afforded by LimTDDs, our method constructs low-depth circuits via local reversible transformations—achieving exponential reduction in gate count in the zero-auxiliary-qubit setting. Experimental evaluation demonstrates that our approach significantly outperforms state-of-the-art methods in both gate complexity and runtime, while exhibiting superior scalability and numerical stability for large-scale state preparation tasks.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Local Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Quantum state preparation (QSP) is a fundamental task in quantum computing and quantum information processing. It is critical to the execution of many quantum algorithms, including those in quantum machine learning. In this paper, we propose a family of efficient QSP algorithms tailored to different numbers of available ancilla qubits - ranging from no ancilla qubits, to a single ancilla qubit, to a sufficiently large number of ancilla qubits. Our algorithms are based on a novel decision diagram that is fundamentally different from the approaches used in previous QSP algorithms. Specifically, our approach exploits the power of Local Invertible Map Tensor Decision Diagrams (LimTDDs) - a highly compact representation of quantum states that combines tensor networks and decision diagrams to reduce quantum circuit complexity. Extensive experiments demonstrate that our methods significantly outperform existing approaches and exhibit better scalability for large-scale quantum states, both in terms of runtime and gate complexity. Furthermore, our method shows exponential improvement in best-case scenarios. This paper is an extended version of [1], with three more algorithms proposed.

Problem

• Efficient quantum state preparation using LimTDDs
• Scalable algorithms for varying ancilla qubit counts
• Reducing quantum circuit complexity with compact representations

Innovation

• Utilizes LimTDDs for quantum state representation
• Tailors QSP algorithms to ancilla qubit availability
• Reduces quantum circuit complexity significantly