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arXiv 2404.19554quant-ph
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用于计算动力学响应函数的纠缠辅助相位估计算法

Entanglement-assisted phase estimation algorithm for calculating dynamical response functions

Rei Sakuma, Shu Kanno, Kenji Sugisaki, Takashi Abe, Naoki Yamamoto

发表信息：
Phys. Rev. A 110, 022618 (2024)
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AI总结：

本文提出一种采用最优纠缠输入态的纠缠辅助量子相位估计算法，有效缓解了固有频谱泄漏问题，实现了更精确的跃迁能与跃迁概率估计，并在凝聚态物理、量子化学和核物理的数值模拟中验证了其有效性。

摘要：

动力学响应函数是描述量子多体系统激发态性质的基本物理量。已有研究提出通过量子相位估计（QPE）来评估这些量，其中能谱直接从频域的QPE测量结果中提取。然而，由于QPE算法固有的频谱泄漏（或峰值展宽）问题，使用这些基于QPE的方法准确估计激发能和跃迁概率具有挑战性。为了克服这一问题，本工作考虑采用最优纠缠输入态对基于QPE的方法进行扩展，已知该方法能够实现估计精度的海森堡极限标度。我们证明，使用这种方法计算出的能谱峰值比原始基于QPE的方法计算出的峰值更加局域化，这表明频谱泄漏问题得到了缓解。通过分析纠缠相位估计的概率分布，我们提出了一种简单的方案，以更好地估计目标能谱中峰值的跃迁能和相应的跃迁概率。我们通过多个量子多体问题中的数值模拟验证了该方法的有效性：凝聚态物理中简单电子-等离子体模型的谱函数、量子化学中H$_2$O分子的偶极跃迁，以及核物理中$^6$Li核的电磁跃迁。

英文摘要：

Dynamical response functions are fundamental quantities to describe the excited-state properties in quantum many-body systems. Quantum algorithms have been proposed to evaluate these quantities by means of quantum phase estimation (QPE), where the energy spectra are directly extracted from the QPE measurement outcomes in the frequency domain. Accurate estimation of excitation energies and transition probabilities with these QPE-based approaches is, however, challenging because of the problem of spectral leakage (or peak broadening) which is inherent in the QPE algorithm. To overcome this issue, in this work we consider an extension of the QPE-based approach adopting the optimal entangled input states, which is known to achieve the Heisenberg-limited scaling for the estimation precision. We show that with this method the peaks in the calculated energy spectra are more localized than those calculated by the original QPE-based approaches, suggesting the mitigation of the spectral leakage problem. By analyzing the probability distribution with the entangled phase estimation, we propose a simple scheme to better estimate both the transition energies and the corresponding transition probabilities of the peaks of interest in the spectra. The validity of our prescription is demonstrated by numerical simulations in various quantum many-body problems: the spectral function of a simple electron-plasmon model in condensed-matter physics, the dipole transitions of the H$_2$O molecule in quantum chemistry, and the electromagnetic transitions of the $^6$Li nucleus in nuclear physics.

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