近日，美国加州大学的Scott E. Smart与Prineha Narang合作并取得一项新进展。经过不懈努力，他们揭示了源于量子流形优化中的多体特征态。相关研究成果已于2024年11月21日在国际知名学术期刊《物理评论A》上发表。

在这项工作中，研究人员运用流形优化技术，通过直接在斯蒂费尔流形和格拉斯曼流形上进行最小化，来求解多体本征态问题。这种方法避免了状态参数化，能够同时计算多个本征态。

这些黎曼流形自然地编码了正交性约束，并且具有状态和切向量的高效量子表示。研究人员为量子多体分子系统提供了计算示例，并讨论了解决多本征态问题的不同途径。

据悉，量子计算为寻找多体本征态提供了多条新途径，其中变分方法是最具灵活性和近期可行性的方法之一。这些方法需要对状态进行特定的参数化，并且在求解多个本征态时，必须考虑正交性。

附：英文原文

Title: Many-body eigenstates from quantum manifold optimization

Author: Scott E. Smart, Prineha Narang

Issue&Volume: 2024/11/21

Abstract: Quantum computing offers several new pathways toward finding many-body eigenstates, with variational approaches being some of the most flexible and near-term oriented. These require particular parametrizations of the state and, for solving multiple eigenstates, must incorporate orthogonality. In this work, we use techniques from manifold optimization to arrive at solutions of the many-body eigenstate problem via direct minimization over the Stiefel and Grassmannian manifolds, avoiding parametrizations of the states and allowing for multiple eigenstates to be simultaneously calculated. These Riemannian manifolds naturally encode orthogonality constraints and have efficient quantum representations of the states and tangent vectors. We provide example calculations for quantum many-body molecular systems and discuss different pathways for solving the multiple eigenstate problem.

DOI: 10.1103/PhysRevA.110.052430

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.052430