Fermilab, P.O. Box 500, Batavia, Illinois 60510, USA.
Phys Rev Lett. 2018 Sep 14;121(11):110504. doi: 10.1103/PhysRevLett.121.110504.
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 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.
我们提出了一种算法，将现有的用于模拟量子化学和凝聚态物理中费米子系统的量子算法扩展到包括一般的玻色子和特别的声子。我们引入了一种声子低能子空间的量子位表示，允许有效地模拟电子-声子系统的演化算符。由于奈奎斯特-香农采样定理，声子在离散希尔伯特空间上以指数精度表示，其大小随最大声子数截止值的线性增加而增加。由于声子的存在而需要的附加量子位数与系统的大小呈线性关系。对于具有有限范围电子-声子和声子-声子相互作用的系统，附加的电路深度是常数，对于长程电子-声子相互作用则是线性的。我们的 Holstein 极化子问题算法是在使用量子相位估计方法的 Atos 量子学习机量子模拟器上实现的。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。
