We study sequential cost-efficient design in a situation where each update of covariates involves a fixed time cost typically considerable compared to a single measurement time. The problem arises from parameter estimation in switching measurements on superconducting Josephson junctions which are components needed in quantum computers and other superconducting electronics. In switching measurements, a sequence of current pulses is applied to the junction and a binary voltage response is observed. The measurement requires a very low temperature that can be kept stable only for a relatively short time, and therefore it is essential to use an efficient design. We use the dynamic programming principle from the mathematical theory of optimal control to solve the optimal update times. Our simulations demonstrate the cost-efficiency compared to the previously used methods.

翻译：我们研究了一种在协变量每次更新均涉及固定时间成本（通常远大于单次测量时间）的情境下的成本高效序贯设计。该问题源于对超导约瑟夫森结的切换测量参数估计——约瑟夫森结是量子计算机及其他超导电子器件中的关键组件。在切换测量中，向结施加一系列电流脉冲并观测二元电压响应。此类测量需在极低温度下进行，而该低温仅能维持较短时间，因此采用高效设计至关重要。我们利用最优控制数学理论中的动态规划原理来求解最优更新时刻。数值模拟表明，相较于先前使用的方法，本方法具有显著的成本效率优势。