论文标题
原子和分子共振的量子计算
Quantum Computing for Atomic and Molecular Resonances
论文作者
论文摘要
假设电子坐标是独立于核坐标的，可以使用复杂尺度方法来计算出生 - 铅内海元近似内的分子共振。通过这种方法，人们将计算非铁官汉密尔顿的复杂能量，其实际部分与共振位置相关，而假想部分是寿命的倒数。在这项研究中，我们提出了模拟量子计算机上共振的技术。首先，我们将缩放的分子哈密顿量转化为第二量化，然后使用Jordan-Wigner Transformation将缩放的Hamiltonian转换为Qubit空间。为了获得复杂的特征值，我们介绍了直接测量方法，该方法用于获得简单的一维模型电位的共振，该模型具有与硅藻分子中发现的相似的预分解共振。最后，我们应用了模拟H $ _2^ - $分子的共振的方法。 IBM Qiskit模拟器和IBM量子计算机的数值结果验证了我们的技术。
The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will calculate the complex energy of a non-Hermitian Hamiltonian, whose real part is associated with the resonance position and the imaginary part is the inverse of the lifetime. In this study, we propose techniques to simulate resonances on a quantum computer. First, we transformed the scaled molecular Hamiltonian to second-quantization and then used the Jordan-Wigner transformation to transform the scaled Hamiltonian to the qubit space. To obtain the complex eigenvalues, we introduce the Direct Measurement method, which is applied to obtain the resonances of a simple one-dimensional model potential that exhibits pre-dissociating resonances analogous to those found in diatomic molecules. Finally, we applied the method to simulate the resonances of the H$_2^-$ molecule. Numerical results from the IBM Qiskit simulators and IBM quantum computers verify our techniques.
