The paper investigates the techniques of quantum computation in metrological predictions, with a particular emphasis on enhancing prediction potential through variational parameter estimation. The applicability of quantum simulations and quantum metrology techniques for modelling complex physical systems and achieving high-resolution measurements are proposed. The impacts of various parameter distributions and learning rates on predictive accuracy are investigated. Modelling the time evolution of physical systems Hamiltonian simulation and the product formula procedure are adopted. The time block method is analyzed in order to reduce simulation errors, while the Schatten-infinite norm is used to evaluate the simulation precision. Methodology requires estimation of optimized parameters by minimizing loss functions and resource needs. For this purpose, the mathematical formulations of Cramer Rao Bound and Fischer Information are indispensable requirements. The impact of learning rates on regulating the loss function for various parameter values. Using parameterized quantum circuits, the article outlines a four-step procedure for extracting information. This method involves the preparation of input states, the evolution of parameterized quantum states, the measurement of outputs, and the estimation of parameters based on multiple measurements. The study analyses variational unitary circuits with optimized parameter estimation for more precise predictions. The findings shed light on the effects of normal parameter distributions and learning rates on attaining the most optimal state and comparison with classical Long Short Term Memory (LSTM) predictions, providing valuable insights for the development of more appropriate approaches in quantum computing.

翻译：本文研究了量子计算在计量学预测中的技术，特别强调通过变分参数估计来增强预测潜力。提出了量子模拟和量子计量学技术在建模复杂物理系统和实现高分辨率测量方面的适用性。研究了不同参数分布和学习率对预测准确性的影响。采用哈密顿模拟和乘积公式程序对物理系统的时间演化进行建模。分析了时间块方法以减少模拟误差，同时使用Schatten-无穷范数评估模拟精度。该方法需要通过最小化损失函数和资源需求来估计优化参数。为此，克拉默-拉奥界和费希尔信息的数学公式是不可或缺的要求。研究了学习率对不同参数值下损失函数调节的影响。利用参数化量子电路，本文概述了信息提取的四步流程。该方法包括输入态制备、参数化量子态演化、输出测量以及基于多次测量的参数估计。本研究分析了具有优化参数估计的变分酉电路以实现更精确的预测。研究结果阐明了正态参数分布和学习率对获取最优态的影响，并与经典长短期记忆网络预测进行了比较，为量子计算中更适用方法的开发提供了宝贵见解。