论文标题
量子可分离性问题的差异方法
A Variational Approach to the Quantum Separability Problem
论文作者
论文摘要
我们介绍了可分离性验证者（VSV），该验证者是一种新型的变分量子算法（VQA），它确定了相对于Hilbert-Schmidt距离（HSD）的任意量子状态的最接近的可分离状态（CSS）。我们首先使用基于状态向量和基于SHOT的模拟来评估Greenberger-Horne-Zeilinger（GHz）状态的优化程序的融合，以评估VSV的性能。我们还数值确定了最大纠缠的多部分$ x $ -STATES（$ x $ -MEMS）的（CSS），然后随后使用该算法的结果来指出上述（CSS）的分析形式。我们的结果表明，由于使用VSV，当前噪声中间尺度量子（NISQ）设备可能有助于解决$ NP $ -HARD的完全可分离性问题，这是因为通过采用破坏性掉期测试来评估（HSD）而施加的浅量子电路。一旦对算法进行了调整并改进以获得多部分纠缠状态的最接近的$ k $ - $可分离状态（$ k $ -css），（VSV）也可能导致多部分量子状态的表征。
We present the variational separability verifier (VSV), which is a novel variational quantum algorithm (VQA) that determines the closest separable state (CSS) of an arbitrary quantum state with respect to the Hilbert-Schmidt distance (HSD). We first assess the performance of the VSV by investigating the convergence of the optimization procedure for Greenberger-Horne-Zeilinger (GHZ) states of up to seven qubits, using both statevector and shot-based simulations. We also numerically determine the (CSS) of maximally entangled multipartite $X$-states ($X$-MEMS), and subsequently use the results of the algorithm to surmise the analytical form of the aforementioned (CSS). Our results indicate that current noisy intermediate-scale quantum (NISQ) devices may be useful in addressing the $NP$-hard full separability problem using the VSV, due to the shallow quantum circuit imposed by employing the destructive SWAP test to evaluate the (HSD). The (VSV) may also possibly lead to the characterization of multipartite quantum states, once the algorithm is adapted and improved to obtain the closest $k$-separable state ($k$-CSS) of a multipartite entangled state.
