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arXiv 1802.07347quant-phcond-mat.str-elhep-ph
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通用量子计算机上的电子-声子系统

Electron-Phonon Systems on a Universal Quantum Computer

Alexandru Macridin, Panagiotis Spentzouris, James Amundson, Roni Harnik

摘要:

我们提出了一个算法,扩展了现有的量子算法,用于模拟量子化学和凝聚态物理中的费米子系统,包括玻色子一般,特别是声子。我们引入了一个量子比特表示的低能量子空间的声子,它允许一个有效的模拟的电子-声子系统的演化算子。作为奈奎斯特-香农采样定理的结果,声子在离散化希尔伯特空间上以指数精度表示,其大小随着最大声子数的截止而线性增加。声子的存在所需的额外量子位数与系统的大小成线性比例。对于有限程电子-声子和声子-声子相互作用系统,附加电路深度是常数,而对于长程电子-声子相互作用系统,附加电路深度是线性的。我们的算法的Holstein极化子问题的Atos量子学习机(QLM)量子模拟器上实现的量子相位估计方法。极化子态的能量和声子数分布与弱、中、强电子-声子耦合区的精确对角化结果一致。

英文摘要:

We present an algorithm that extends existing quantum algorithms for simulating fermion systems in quantum chemistry and condensed matter physics to include bosons in general and phonons in particular. We introduce a qubit representation for the low-energy subspace of phonons which allows an efficient simulation of the evolution operator of the electron-phonon systems. As a consequence of the Nyquist-Shannon sampling theorem, the phonons are represented with exponential accuracy on a discretized Hilbert space with a size that increases linearly with the cutoff of the maximum phonon number. The additional number of qubits required by the presence of phonons scales linearly with the size of the system. The additional circuit depth is constant for systems with finite-range electron-phonon and phonon-phonon interactions and linear for long-range electron-phonon interactions. Our algorithm for a Holstein polaron problem was implemented on an Atos Quantum Learning Machine (QLM) quantum simulator employing the Quantum Phase Estimation method. The energy and the phonon number distribution of the polaron state agree with exact diagonalization results for weak, intermediate and strong electron-phonon coupling regimes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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