Entropy constraints for ground energy optimization
Entropy constraints for ground energy optimization
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DOI：
10.1063/5.0159108
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发表时间：
2023-05
影响因子：
1.3
通讯作者：
Hamza Fawzi;Omar Fawzi;Samuel O. Scalet
中科院分区：
文献类型：
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作者：
Hamza Fawzi;Omar Fawzi;Samuel O. Scalet
我们研究了使用冯诺依曼熵约束获得量子多体系统的基态能量的下界。用于获得关于地面能量的证书的已知方法通常使用局部可观测量的一致性，并且被表示为半定规划松弛。由这种松弛定义的局部边缘不一定满足全局状态存在所带来的熵不等式。在这里，我们建议增加这样的熵约束，导致更严格的凸松弛地面能量问题。我们给出的分析和数值结果说明这种熵约束的优点。我们还表明，我们构建的熵约束的限制：他们暗示的网站数量增加一倍的放松，因此，他们可以在最好的情况下导致二次改进的变量的矩阵大小。我们解释的关系，以近似的方法称为马尔可夫熵分解方法的自由能。
We study the use of von Neumann entropy constraints for obtaining lower bounds on the ground energy of quantum many-body systems. Known methods for obtaining certificates on the ground energy typically use consistency of local observables and are expressed as semidefinite programming relaxations. The local marginals defined by such a relaxation do not necessarily satisfy entropy inequalities that follow from the existence of a global state. Here, we propose to add such entropy constraints that lead to tighter convex relaxations for the ground energy problem. We give analytical and numerical results illustrating the advantages of such entropy constraints. We also show limitations of the entropy constraints we construct: they are implied by doubling the number of sites in the relaxation and as a result they can at best lead to a quadratic improvement in terms of the matrix sizes of the variables. We explain the relation to a method for approximating the free energy known as the Markov Entropy Decomposition method.