论文标题
使用决策图有效地确定量子状态
Efficient Deterministic Preparation of Quantum States Using Decision Diagrams
论文作者
论文摘要
将经典数据加载到量子寄存器中是量子计算最重要的原始图之一。虽然准备通用量子状态的复杂性在量子数的数量中是指数级的，但在许多实际任务中，要准备的实际任务具有一定的结构，可以进行更快的准备。在本文中，我们考虑可以通过（降低）决策图有效地表示的量子状态，这是一种用于布尔函数的表示和分析的多功能数据结构。我们设计了一种利用决策图的结构来准备其相关量子状态的算法。我们的算法具有在决策图中的路径数中线性的电路复杂性。数值实验表明，与最先进的算法相比，我们的算法将电路复杂性降低了31.85％，因为在准备具有不同程度的非零振幅的通用$ n $ qubit状态时。此外，对于稀疏决策图的状态（包括量子拜占庭协议协议的初始状态），我们的算法将CNOT的数量减少了86.61％$ \ sim $ 99.9％。
Loading classical data into quantum registers is one of the most important primitives of quantum computing. While the complexity of preparing a generic quantum state is exponential in the number of qubits, in many practical tasks the state to prepare has a certain structure that allows for faster preparation. In this paper, we consider quantum states that can be efficiently represented by (reduced) decision diagrams, a versatile data structure for the representation and analysis of Boolean functions. We design an algorithm that utilises the structure of decision diagrams to prepare their associated quantum states. Our algorithm has a circuit complexity that is linear in the number of paths in the decision diagram. Numerical experiments show that our algorithm reduces the circuit complexity by up to 31.85% compared to the state-of-the-art algorithm, when preparing generic $n$-qubit states with different degrees of non-zero amplitudes. Additionally, for states with sparse decision diagrams, including the initial state of the quantum Byzantine agreement protocol, our algorithm reduces the number of CNOTs by 86.61% $\sim$ 99.9%.
