Advancing Quantum State Preparation using LimTDD

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.