Extracting Bayesian networks from multiple copies of a quantum system

利用有限副本量子态进行有效且高效的纠缠验证

Valid and efficient entanglement verification with finite copies of a quantum state

针对有限样本下的多体纠缠检测，本文提出兼顾有效性与效率的优化方法，基于频率学派和贝叶斯有限统计模型，适用于任意纠缠见证，并用至多20个态副本验证。

多拷贝双态鉴别与个体测量

Multiple copy 2-state discrimination with individual measurements

我们解决的问题，非正交两个国家的歧视时，多个副本的未知状态。当只允许固定的个体测量时，我们给出了最优策略，并证明了其误差概率渐近饱和集体（下限）界。我们还给出了最佳策略时，个人冯诺依曼测量的自适应性是允许的（这需要经典的通信），并表明，相应的错误概率是完全等于集体的任何数量的副本。我们表明，这种策略可以被视为贝叶斯更新。

二维广义Pauli稳定子码拓扑序的提取

Extracting topological orders of generalized Pauli stabilizer codes in two dimensions

本文提出一种适用于$\u2124_d$量子比特（含非素数d）的算法，可提取二维平移不变广义Pauli稳定子码的拓扑数据，识别新拓扑序并为量子纠错码研究提供系统方法。

Adaptive Quantum State Tomography with Neural Networks

Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements -- as well as in terms of the computational time to analyze those measurements. In this paper, we address the problem of analysis speed and flexibility, introducing \textit{Neural Adaptive Quantum State Tomography} (NA-QST), a machine learning based algorithm for quantum state tomography that adapts measurements and provides orders of magnitude faster processin…

利用低深度数字量子电路实现海森堡极限的贝叶斯相位估计

Heisenberg-limited Bayesian phase estimation with low-depth digital quantum circuits

本研究提出了一种利用低深度数字量子电路实现海森堡极限的贝叶斯相位估计方案，通过优化测量策略和初始态选择，提升了相位估计的精度和效率。

可分离测量的纯度估计

Purity estimation with separable measurements

给定一个量子比特状态的大量N个副本，我们希望估计其纯度，我们证明了可分离测量协议可以作为最佳的联合测量，如果使用经典通信的有效性。这表明，两个量子比特态的纠缠的最佳估计也可以渐近地实现与完全可分离的测量。因此，量子存储器在这种情况下没有优势。我们的全球贝叶斯方法和量子克拉美-罗界之间的关系进行了讨论。

Beyond the swap test: optimal estimation of quantum state overlap

We study the estimation of the overlap between two unknown pure quantum states of a finite dimensional system, given $M$ and $N$ copies of each type. This is a fundamental primitive in quantum information processing that is commonly accomplished from the outcomes of $N$ swap-tests, a joint measurement on one copy of each type whose outcome probability is a linear function of the squared overlap. We show that a more precise estimate can be obtained by allowing for general collective measurements on all copies. We derive the statistics of the optimal measurement and compute the optimal mean squa…

Quantum approximate Bayesian computation for NMR model inference

Recent technological advances may lead to the development of small scale quantum computers capable of solving problems that cannot be tackled with classical computers. A limited number of algorithms has been proposed and their relevance to real world problems is a subject of active investigation. Analysis of many-body quantum system is particularly challenging for classical computers due to the exponential scaling of Hilbert space dimension with the number of particles. Hence, solving problems relevant to chemistry and condensed matter physics are expected to be the first successful applicatio…

Quantum Multi-Parameter Adaptive Bayesian Estimation and Application to Super-Resolution Imaging

In Bayesian estimation theory, the estimator ${\hat θ} = E[θ|l]$ attains the minimum mean squared error (MMSE) for estimating a scalar parameter of interest $θ$ from the observation of $l$ through a noisy channel $P_{l|θ}$, given a prior $P_θ$ on $θ$. In quantum sensing tasks, the user gets $ρ_θ$, the quantum state that encodes $θ$. They choose a measurement, a positive-operator valued measure (POVM) $Π_l$, which induces the channel $P_{l|θ} = {\rm Tr}(ρ_θΠ_l)$ to the measurement outcome $l$, on which the aforesaid classical MMSE estimator is employed. Personick found the optimum POVM $Π_l$ th…

用弱测量和投影测量估计量子态

Estimation of quantum states by weak and projective measurements

我们探索了利用“弱”测量进行量子态层析成像的可能性。给定一个量子比特的相同准备状态的一定数量的副本，我们使用弱以及投影测量来模拟状态断层扫描。由于测量后状态的崩溃，我们不能重新使用投影测量后的状态。如果使量子系统和测量装置之间的耦合强度变弱，则可以降低对状态造成的扰动。这使我们能够重新使用集合的同一成员进行进一步的测量，从而从系统中提取更多的信息。然而，这是以从第一次测量中获得不精确的信息为代价的。我们模拟了一个量子比特的方案，并表明在某些情况下，它可以优于基于投影测量的层析成像方案。这开辟了从量子系综中提取信息的新方法的可能性。我们研究了不同耦合强度下该方案的有效性。

Haar-贝叶斯纯态预测在相对熵损失下的研究：任意效应约化与全局最优性

Haar-Bayesian Pure-State Prediction under Relative-Entropy Loss: Arbitrary-Effect Reduction and Global Optimality

本文研究Haar-贝叶斯纯态预测，通过任意效应约化证明最高权重协变POVM在相对熵损失下全局最优，并给出精确风险与纯度最优值。

用于基于偏微分方程（PDE）的贝叶斯反问题的量子辅助框架

A quantum-assisted framework for PDE-based Bayesian inverse problems

针对基于PDE的贝叶斯反问题，提出量子-经典混合框架，用量子处理器处理PDE演化与损失评估、经典计算机调整超参数，经实验验证其在采样噪声下的参数反演可行性，为相关问题提供量子辅助方案。