Advancing Quantum State Preparation Using Decision Diagram with Local Invertible Maps

TL;DR

This paper introduces a family of efficient quantum state preparation algorithms utilizing Local Invertible Map Tensor Decision Diagrams, significantly improving scalability and performance over existing methods in quantum computing.

Contribution

The paper presents a novel approach combining tensor networks and decision diagrams for quantum state preparation, adaptable to various numbers of ancilla qubits.

Findings

Outperforms existing quantum state preparation methods

Exhibits better scalability for large quantum states

Shows exponential improvement in best-case scenarios

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 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.