发表机构
Hanyang University; Korea Institute of Science and Technology (KIST)（汉阳大学; 韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一种基于冯·米塞斯-费希尔分布的迭代贝叶斯变分量子本征求解器，将单成功结果方案推广到多成功结果情况，证明其收敛性并在多种量子系统上验证了算法的收敛性。
AI 中文摘要
我们开发了一种迭代贝叶斯变分量子本征求解器，其中未知基态被参数化为实单位向量，通过对单个辅助量子比特进行哈达玛测试测量得到的冯·米塞斯-费希尔分布进行序贯更新来推断。在一篇相关论文中，我们通过精确矩匹配处理了单个成功结果，在此基础上，我们将该方案推广到每次迭代的似然函数以m个成功结果为条件的情况。由于当m>1时精确矩匹配变得不切实际，我们利用高集中度 regime，其中对数似然的一阶展开产生了闭式冯·米塞斯-费希尔后验，m仅通过一个乘性权重进入。我们证明，只要m处于明确表征的范围内，单结果方案的两个收敛性质——非递减重叠和非递减集中度——得以保留。基于该理论，我们提出了一种基于测量的算法，并在随机生成的三量子比特和四量子比特哈密顿矩阵、HeH⁺以及H₂上展示了收敛性。
英文摘要
We develop an iterative Bayesian variational quantum eigensolver in which the unknown ground state, parametrised as a real unit vector, is inferred through a von Mises--Fisher distribution sequentially updated from Hadamard-test measurements on a single ancilla qubit. Building on a companion paper that treated a single success outcome via exact moment matching, we generalise the scheme to condition on $m$ success outcomes for the likelihood function per iteration. Since exact moment matching becomes impractical for $m>1$, we exploit the large-concentration regime, in which a first-order expansion of the log-likelihood yields a closed-form von Mises--Fisher posterior with $m$ entering only through a multiplicative weight. We prove that the two convergence properties of the single-outcome scheme---non-decreasing overlap and non-decreasing concentration---are preserved provided $m$ lies within an explicitly characterised range. Based on the theory, we propose a measurement-based algorithm and illustrate the convergence on randomly generated three- and four-qubit Hamiltonian matrices, on $\mathrm{HeH}^+$, and on $\mathrm{H}_2$.
