Low-rank approximation to entangled multipartite quantum systems
Low-rank approximation to entangled multipartite quantum systems
复制标题
纠缠多部分量子系统的低阶近似
DOI：
10.1007/s11128-022-03467-z
复制
发表时间：
2022
影响因子：
2.5
通讯作者：
Chu, Moody T.
中科院分区：
文献类型：
--
作者：
Lin, Matthew M.;Chu, Moody T.
在量子技术中，通过测量混合多体态到固定秩的最近可分态的距离来限定混合多体态的纠缠是一个具有挑战性但至关重要的任务。这样的任务是计算要求，部分原因是为了正确地表征潜在的量子特性，部分原因是由于多体相互作用的高非线性，在复杂的领域的优化的必要性。将量子态表示为关于一些适当选择的基的复密度矩阵，这项工作提供了两种途径来数值解决这个问题。对于秩-1逼近，研究了一个求解非线性奇异值问题的迭代格式。对于一般的概率组合系数低秩近似，提出了投影梯度动力学。这两种技术被证明是全球收敛到一个当地的解决方案。数值实验证明了这些方法的有效性和效率。
Qualifying the entanglement of a mixed multipartite state by gauging its distance to the nearest separable state of a fixed rank is a challenging but critically important task in quantum technologies. Such a task is computationally demanding partly because of the necessity of optimization over the complex field in order to characterize the underlying quantum properties correctly and partly because of the high nonlinearity due to the multipartite interactions. Representing the quantum states as complex density matrices with respect to some suitably selected bases, this work offers two avenues to tackle this problem numerically. For the rank-1 approximation, an iterative scheme solving a nonlinear singular value problem is investigated. For the general low-rank approximation with probabilistic combination coefficients, a projected gradient dynamics is proposed. Both techniques are shown to converge globally to a local solution. Numerical experiments are carried out to demonstrate the effectiveness and the efficiency of these methods.
影响因子：
1.8
作者：
Thirring, W.;Bertlmann, R. A.;Narnhofer, H.
通讯作者：
Narnhofer, H.
DOI：
--
发表时间：
2001
期刊：
影响因子：
--
作者：
M. Horodecki;P. Horodecki;R. Horodecki
通讯作者：
R. Horodecki