arXiv 2011.139992020-11quant-ph

原子分子共振的量子计算

Quantum Computing for Atomic and Molecular Resonances

Teng Bian, Sabre Kais

备注：: To be published in J. Chem. Phys. 2021
DOI：: 10.1063/5.0040477

摘要：

复数标度法可用于在玻恩-奥本海默近似下计算分子共振，假设电子坐标独立于核坐标膨胀。用这种方法，人们将计算一个非厄米哈密顿量的复能量，其实部与共振位置相关，虚部是寿命的倒数。在这项研究中，我们提出了在量子计算机上模拟共振的技术。首先，我们将标度化的分子哈密顿量转化为二次量子化，然后利用Jordan-Wigner变换将标度化的分子哈密顿量转化为量子比特空间。为了获得复杂的本征值，我们介绍了直接测量方法，这是适用于获得一个简单的一维模型的潜力，表现出类似于在双原子分子中发现的预解离共振的共振。最后，我们应用该方法模拟了H $_2^-$分子的共振态。IBM Qiskit模拟器和IBM量子计算机的数值结果验证了我们的技术。

英文摘要：

The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will calculate the complex energy of a non-Hermitian Hamiltonian, whose real part is associated with the resonance position and the imaginary part is the inverse of the lifetime. In this study, we propose techniques to simulate resonances on a quantum computer. First, we transformed the scaled molecular Hamiltonian to second-quantization and then used the Jordan-Wigner transformation to transform the scaled Hamiltonian to the qubit space. To obtain the complex eigenvalues, we introduce the Direct Measurement method, which is applied to obtain the resonances of a simple one-dimensional model potential that exhibits pre-dissociating resonances analogous to those found in diatomic molecules. Finally, we applied the method to simulate the resonances of the H$_2^-$ molecule. Numerical results from the IBM Qiskit simulators and IBM quantum computers verify our techniques.

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