量子版主成分分析法直接计算激发态，无需传统迭代修正。
Quantum EigenGame for excited state calculation
- 用博弈论框架设计量子版本的主成分分析算法
- 在无删减步骤下收敛到哈密顿量的激发态
- 适合研究量子化学或材料模拟的学者参考
计算大系统哈密顿量的激发态在经典计算中极为困难，而量子计算机方法可实现可扩展计算。该问题等价于主成分分析（PCA），即矩阵分解为若干主成分。经典领域中已有集中式与分布式方法，其中近期的分布式方法为基于博弈论的EigenGame，各特征向量通过纳什均衡求解，可串行或并行进行。本文将EigenGame拓展至0阶近似与量子计算机场景，利用量子计算优势实现激发态计算。结果表明，量子EigenGame可在不进行删减步骤的情况下收敛至激发态。同时建立了有限差分与参数化方法下的误差累积理论。
原文摘要 · Abstract (English)
Computing the excited states of a given Hamiltonian is computationally hard for large systems, but methods that do so using quantum computers scale tractably. This problem is equivalent to the PCA problem where we are interested in decomposing a matrix into a collection of principal components. Classically, PCA is a well-studied problem setting, for which both centralized and distributed approaches have been developed. On the distributed side, one recent approach is that of EigenGame, a game-theoretic approach to finding eigenvectors where each eigenvector reaches a Nash equilibrium either sequentially or in parallel. With this work, we extend the EigenGame algorithm for both a $0^\text{th}$-order approach and for quantum computers, and harness the framework that quantum computing provides in computing excited states. Results show that using the Quantum EigenGame allows us to converge to excited states of a given Hamiltonian without the need of a deflation step. We also develop theory on error accumulation for finite-differences and parameterized approaches.
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