论文标题
有效的状态准备量子估计
Efficient State Preparation for Quantum Amplitude Estimation
论文作者
论文摘要
量子振幅估计（QAE）可以实现通过Monte Carlo Simulation经典解决的应用的二次加速。实现这一优势的关键要求是有效的状态准备。如果状态准备太昂贵，则可以降低量子优势。准备任意的量子状态相对于量子数的数量具有指数的复杂性，因此不适用。当前已知的有效技术需要基于对数符号概率分布的问题，涉及从经验数据中学习未知分布或完全依赖量子算术。在本文中，我们介绍了一种简化状态准备的方法，以及电路优化技术，这两种技术都可以大大减少QAE状态制备的电路复杂性。我们演示了有关实际量子硬件的数值集成示例的引入技术，以及使用仿真的赫斯顿模型（即基于随机波动率过程）下的选项定价。
Quantum Amplitude Estimation (QAE) can achieve a quadratic speed-up for applications classically solved by Monte Carlo simulation. A key requirement to realize this advantage is efficient state preparation. If state preparation is too expensive, it can diminish the quantum advantage. Preparing arbitrary quantum states has exponential complexity with respect to the number of qubits, thus, is not applicable. Currently known efficient techniques require problems based on log-concave probability distributions, involve learning an unknown distribution from empirical data, or fully rely on quantum arithmetic. In this paper, we introduce an approach to simplify state preparation, together with a circuit optimization technique, both of which can help reduce the circuit complexity for QAE state preparation significantly. We demonstrate the introduced techniques for a numerical integration example on real quantum hardware, as well as for option pricing under the Heston model, i.e., based on a stochastic volatility process, using simulation.
