论文标题
通过差异最小化的变异量子本质量
Variational quantum eigensolvers by variance minimization
论文作者
论文摘要
变异量子本素（VQE）通常通过杂交量子式优化优化最大程度地减少能量，旨在找到基态。在这里，我们通过最小化能量方差提出了一个VQE，该方差称为方差-VQE（VVQE）。通过设计，VVQE可以看作是任意特征态的自我验证的特征，因为哈密顿量的特征态应为零能量方差。我们展示了VVQE解决具有量子化学问题的激发态的特性和优势。值得注意的是，我们表明，与单独减少能量或方差最小化相比，能量和方差组合的优化可能更有效地找到低能激发态。我们进一步揭示了通过哈密顿采样的随机梯度下降可以提高优化，该采样仅使用了哈密顿量的几个术语，因此可以显着降低量子资源来评估方差及其梯度。
Variational quantum eigensolver(VQE) typically minimizes energy with hybrid quantum-classical optimization, which aims to find the ground state. Here, we propose a VQE by minimizing energy variance, which is called as variance-VQE(VVQE). The VVQE can be viewed as an self-verifying eigensolver for arbitrary eigenstate by designing, since an eigenstate for a Hamiltonian should have zero energy variance. We demonstrate properties and advantages of VVQE for solving a set of excited states with quantum chemistry problems. Remarkably, we show that optimization of a combination of energy and variance may be more efficient to find low-energy excited states than those of minimizing energy or variance alone. We further reveal that the optimization can be boosted with stochastic gradient descent by Hamiltonian sampling, which uses only a few terms of the Hamiltonian and thus significantly reduces the quantum resource for evaluating variance and its gradients.
