Bierman Joel, Li Yingzhou, Lu Jianfeng
Department of Physics, Duke University, Durham, North Carolina 27708-0187, United States.
School of Mathematical Sciences, Fudan University, Shanghai 200433, China.
J Chem Theory Comput. 2022 Aug 9;18(8):4674-4689. doi: 10.1021/acs.jctc.2c00218. Epub 2022 Jul 25.
We propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parametrized ansatz circuits representing eigenstates, qOMM implements quantum circuits to represent the objective function in the orbital minimization method and adopts a classical optimizer to minimize the objective function with respect to the parameters in ansatz circuits. The objective function has an orthogonality constraint implicitly embedded, which allows qOMM to apply a different ansatz circuit to each input reference state. We carry out numerical simulations that seek to find excited states of H, LiH, and a toy model consisting of four hydrogen atoms arranged in a square lattice in the STO-3G basis with UCCSD ansatz circuits. Comparing the numerical results with existing excited states methods, qOMM is less prone to getting stuck in local minima and can achieve convergence with more shallow ansatz circuits.
我们提出了一种量子 - 经典混合变分算法，即量子轨道最小化方法（qOMM），用于获取厄米算符的基态和低激发态。给定表示本征态的参数化近似电路，qOMM实现量子电路以在轨道最小化方法中表示目标函数，并采用经典优化器相对于近似电路中的参数最小化目标函数。目标函数隐含地嵌入了正交性约束，这使得qOMM能够对每个输入参考态应用不同的近似电路。我们进行了数值模拟，试图在STO - 3G基组下使用UCCSD近似电路找到H、LiH以及由四个氢原子排列成正方形晶格的玩具模型的激发态。将数值结果与现有的激发态方法进行比较，qOMM不太容易陷入局部最小值，并且可以使用更浅的近似电路实现收敛。
