Adaptive estimation of quantum observables
Adaptive estimation of quantum observables
复制标题
DOI：
10.22331/q-2023-01-26-906
复制
发表时间：
2021-10
期刊：
影响因子：
6.4
通讯作者：
Ariel Shlosberg;Andrew Jena;Priyanka Mukhopadhyay;J. Haase;Felix Leditzky;Luca Dellantonio
中科院分区：
文献类型：
--
作者：
Ariel Shlosberg;Andrew Jena;Priyanka Mukhopadhyay;J. Haase;Felix Leditzky;Luca Dellantonio
量子观测的精确估计是科学中的一项关键任务。随着硬件的进步，测量量子系统将变得越来越苛刻，特别是对于需要大量采样的变分协议。在这里，我们引入了一种基于先前获得的数据自适应修改估计量的测量方案。我们的算法，我们称之为AEQuO，持续监测所考虑的可观察到的估计平均值和相关误差，并根据这些信息确定下一个测量步骤。我们允许在同时探测的泡利算子的子集中存在重叠和非位交换关系，从而最大化收集的信息量。AEQuO有两种变体：一种贪婪的桶填充算法，对于小问题实例具有良好的性能；另一种基于机器学习的算法，对于较大的实例具有更有利的可扩展性。由这些子例程确定的测量配置被进一步后处理，以降低估计器上的误差。我们在化学哈密顿量上测试了我们的协议，为此AEQuO提供了误差估计，改进了基于各种分组技术或随机测量的所有最先进的方法，从而大大降低了当前和未来量子应用中测量的代价。
The accurate estimation of quantum observables is a critical task in science. With progress on the hardware, measuring a quantum system will become increasingly demanding, particularly for variational protocols that require extensive sampling. Here, we introduce a measurement scheme that adaptively modifies the estimator based on previously obtained data. Our algorithm, which we call AEQuO, continuously monitors both the estimated average and the associated error of the considered observable, and determines the next measurement step based on this information. We allow both for overlap and non-bitwise commutation relations in the subsets of Pauli operators that are simultaneously probed, thereby maximizing the amount of gathered information. AEQuO comes in two variants: a greedy bucket-filling algorithm with good performance for small problem instances, and a machine learning-based algorithm with more favorable scaling for larger instances. The measurement configuration determined by these subroutines is further post-processed in order to lower the error on the estimator. We test our protocol on chemistry Hamiltonians, for which AEQuO provides error estimates that improve on all state-of-the-art methods based on various grouping techniques or randomized measurements, thus greatly lowering the toll of measurements in current and future quantum applications.