arXiv 2201.098522022-01-24physics.chem-ph

用互关联哈密顿量精确量子模拟分子基态和激发态

Accurate quantum simulation of molecular ground and excited states with a transcorrelated Hamiltonian

Ashutosh Kumar, Ayush Asthana, Conner Masteran, Edward F. Valeev, Yu Zhang, Lukasz Cincio, Sergei Tretiak, Pavel A. Dub

摘要：

NISQ时代的设备面临着许多挑战，如有限的量子位连接，短的相干时间和相当大的门错误率。因此，需要需要浅电路深度和低量子比特计数的量子算法来利用这些器件。我们试图实现这一点的帮助下，经典的量子化学理论的正则变换和明确的相关。在这项工作中，紧凑的从头算哈密顿量产生经典的通过近似相似变换的哈密顿量与a）一个显式相关的两体幺正算子与广义对激发，从哈密顿量中删除库仑电子-电子奇异性和b）幺正单体算子，以有效地捕获所需的精确描述的激发态的轨道弛豫效应。所得到的互相关哈密顿量能够以平衡的方式描述分子系统的基态和激发态。利用基于幺正耦合团簇的Fermionic-ADAPT-VQE方法，我们证明了互关联哈密顿量可以产生与大得多的cc-pVTZ基相当的基态能量.这导致在这项工作中研究的化学物种的数量可能减少所需的CNOT门的数量超过三个数量级。此外，使用qEOM形式主义与互相关的哈密顿量，我们减少了一个数量级的激发能的错误。这里开发的互关联哈密顿是厄米的，只包含一个和两个体相互作用项，因此可以很容易地与任何量子算法相结合，精确的电子结构模拟。

英文摘要：

NISQ era devices suffer from a number of challenges like limited qubit connectivity, short coherence times and sizable gate error rates. Thus, quantum algorithms are desired that require shallow circuit depths and low qubit counts to take advantage of these devices. We attempt to realize this with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically through an approximate similarity transformation of the Hamiltonian with a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorelated Hamiltonians are able to describe both ground and excited states of molecular systems in a balanced manner. Using the fermionic-ADAPT-VQE method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the much larger cc-pVTZ basis. This leads to a potential reduction in the number of required CNOT gates by more than three orders of magnitude for the chemical species studied in this work. Furthermore, using the qEOM formalism in conjunction with the transcorrelated Hamiltonian, we reduce the errors in excitation energies by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

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。

摘要：

英文摘要：

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