具變異數感知之分組量測與動態測量配置：應用於變分量子本徵值計算

Abstract

變分量子本徵值計算(VQE)是一種可應用於化學模擬的量子演算法，其中需要計算許多包利字符串(Pauli strings)的期望值，相較於每個量子電路都只計算一個包利字符串的期望值，人們通常會透過分群量測(grouped measurement)來減少量測量子電路的次數。不過每一群的重要性不盡相同，較重要的群理應分配到較多的測量次數，而且各群之間還能允許有重疊的包利字符串，因此本文主要探討該如何進行分群還有每群應該分配多少測量次數才能盡可能的使用固定的測量數目來獲得更精確的結果。 本文主要改良在於提出一個精確公式來計算該如何分配量測次數給所有的完全子圖(clique partition)，並且基於此公式設計一個演算法來利用量測結果來計算共變異數資訊以尋找更好的完全子圖集合，此外重疊的包利字符串並不是選愈多愈好，因此我們也設計一套流程來選擇想要的重疊包利字符串。實驗顯示，相比於最新的先前方法AEQuO，我們的演算法能夠在更短的時間找到更好的結果。此研究有助於減少VQE演算法所需的量測數目，此研究也可以延伸擴展至其他需要求取大量期望值的量子演算法。

The variational quantum eigensolver (VQE) is a quantum algorithm used in chemical simulations, specifically for calculating the expectation values of various Pauli strings. Typically, instead of computing the expectation value of each Pauli string individually for every quantum circuit, researchers reduce the number of quantum circuits by employing grouped measurements. However, the significance of each group can vary; more critical groups necessitate a larger number of measurements, and overlapping Pauli strings are permitted between groups. Consequently, this paper focuses on how to effectively conduct grouping and determine the appropriate number of measurement counts assigned to each group to achieve more accurate results with a fixed number of measurements. The main contribution of this paper lies in proposing a precise formula for allocating measurement counts to the given clique partition, along with the designed algorithm based on this formula. This algorithm uses the measurement results to calculate covariance information, which helps identify improved clique coverings. Additionally, to avoid excessive selection of overlapping Pauli strings, we have developed a process for down-sampling the redundant overlapping information. Experiments demonstrate that our algorithm outperforms the latest method, AEQuO, by delivering better results in a shorter time. This research aids in reducing the number of measurements required by the VQE algorithm and can be extended to other quantum algorithms that have a requirement to obtain the expectation values of numerous Pauli strings.