论文标题
通过嘈杂的非强制观测值的联合测量来估算量子哈密顿量
Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables
论文作者
论文摘要
估计不兼容可观察到的期望值是量子计算中的重要实用任务，尤其是对于近似化学和其他多体量子系统的能量。在这项工作中，我们为此目的介绍了一种方法，基于执行可以在本地实施的单个关节测量，其边缘的噪声（UNSHARP）版本的非宣传Pauli可观察物的目标集。我们根据估计能量达到一定精度所需的实验重复的数量来得出界限。我们将这种策略与经典的影子形式主义进行了比较，并表明我们的方法与本地有偏见的经典影子协议产生的性能相同。我们还通过表明可以使用经典阴影来构建关节测量，反之亦然，反之，我们还突出了两种方法之间的一些一般连接。最后，当假定测量值嘈杂时，我们适应了关节测量策略，以最大程度地减少样品复杂性。与已知的经典阴影概括到噪音方案相比，这可以提供显着提高的效率。
Estimation of expectation values of incompatible observables is an essential practical task in quantum computing, especially for approximating energies of chemical and other many-body quantum systems. In this work we introduce a method for this purpose based on performing a single joint measurement that can be implemented locally and whose marginals yield noisy (unsharp) versions of the target set of non-commuting Pauli observables. We derive bounds on the number of experimental repetitions required to estimate energies up to a certain precision. We compare this strategy to the classical shadow formalism and show that our method yields the same performance as the locally biased classical shadow protocol. We also highlight some general connections between the two approaches by showing that classical shadows can be used to construct joint measurements and vice versa. Finally, we adapt the joint measurement strategy to minimise the sample complexity when the implementation of measurements is assumed noisy. This can provide significant efficiency improvements compared to known generalisations of classical shadows to noisy scenarios.
