Quantum entanglement is a key resource in quantum technology, and its quantification is a vital task in the current noisy intermediate-scale quantum (NISQ) era. This paper combines hybrid quantum-classical computation and quasi-probability decomposition to propose two variational quantum algorithms, called variational entanglement detection (VED) and variational logarithmic negativity estimation (VLNE), for detecting and quantifying entanglement on near-term quantum devices, respectively. VED makes use of the positive map criterion and works as follows. Firstly, it decomposes a positive map into a combination of quantum operations implementable on near-term quantum devices. It then variationally estimates the minimal eigenvalue of the final state, obtained by executing these implementable operations on the target state and averaging the output states. Deterministic and probabilistic methods are proposed to compute the average. At last, it asserts that the target state is entangled if the optimized minimal eigenvalue is negative. VLNE builds upon a linear decomposition of the transpose map into Pauli terms and the recently proposed trace distance estimation algorithm. It variationally estimates the well-known logarithmic negativity entanglement measure and could be applied to quantify entanglement on near-term quantum devices. Experimental and numerical results on the Bell state, isotropic states, and Breuer states show the validity of the proposed entanglement detection and quantification methods.

量子纠缠是量子技术的关键资源，其量化是当前嘈杂的中尺度量子（NISQ）时代的一项重要任务。本文结合混合量子经典计算和准概率分解，提出了两种变分量子算法，称为变分纠缠检测（VED）和变分对数负估计（VLNE），分别用于检测和量化近期量子设备上的纠缠。VED 使用正映射标准并按如下方式工作。首先，它将正映射分解为可在近期量子设备上实现的量子操作的组合。然后它变分地估计最终状态的最小特征值，通过对目标状态执行这些可实现的操作并对输出状态进行平均而获得。提出了确定性和概率性方法来计算平均值。最后，如果优化的最小特征值为负，则断言目标状态是纠缠的。VLNE 建立在将转置图线性分解为泡利项和最近提出的轨迹距离估计算法的基础上。它可变地估计众所周知的对数负纠缠度量，并可用于量化近期量子设备上的纠缠。贝尔态、各向同性态和布鲁尔态的实验和数值结果表明了所提出的纠缠检测和量化方法的有效性。如果优化的最小特征值为负，它断言目标状态是纠缠的。VLNE 建立在将转置图线性分解为泡利项和最近提出的轨迹距离估计算法的基础上。它可变地估计众所周知的对数负纠缠度量，并可用于量化近期量子设备上的纠缠。贝尔态、各向同性态和布鲁尔态的实验和数值结果表明了所提出的纠缠检测和量化方法的有效性。如果优化的最小特征值为负，它断言目标状态是纠缠的。VLNE 建立在将转置图线性分解为泡利项和最近提出的轨迹距离估计算法的基础上。它可变地估计众所周知的对数负纠缠度量，并可用于量化近期量子设备上的纠缠。贝尔态、各向同性态和布鲁尔态的实验和数值结果表明了所提出的纠缠检测和量化方法的有效性。它可变地估计众所周知的对数负纠缠度量，并可用于量化近期量子设备上的纠缠。贝尔态、各向同性态和布鲁尔态的实验和数值结果表明了所提出的纠缠检测和量化方法的有效性。它可变地估计众所周知的对数负纠缠度量，并可用于量化近期量子设备上的纠缠。贝尔态、各向同性态和布鲁尔态的实验和数值结果表明了所提出的纠缠检测和量化方法的有效性。