论文标题
带有COVAR的训练变量量子电路：与经典阴影的协方差root。
Training variational quantum circuits with CoVaR: covariance root finding with classical shadows
论文作者
论文摘要
利用近期量子计算机并实现实践价值是一个巨大而令人兴奋的挑战。最突出的候选人作为变异算法通常是通过最大程度地减少量子计算机对单个经典（能量）表面来找到哈密顿量的基态。在这里，我们介绍了一种我们称为Covar的方法，这是一种利用变异电路功能的替代方法：我们通过找到量子状态多数态增长的特性的关节根来找到特征态，以作为汉密尔顿和我们选择的操作员库之间的协方差函数。我们Covar方法的最显着特征是，它使我们能够完全利用极其强大的古典影子技术，即，我们同时估计一个非常大的$> 10^4-10^7 $的协方差。我们在每次迭代处随机选择协方差和分析衍生物，并通过我们使用经典计算机求解的大型但可拖延的线性方程式使用随机的Levenberg-Marquardt步骤。我们证明，每个迭代的量子资源的成本与标准梯度估计相当，但是，我们在数值模拟中观察到了许多数量级的收敛速度的显着改善。 Covar直接类似于基于随机梯度对经典机器学习至关重要的优化，同时我们还将重要但可拖延的作品卸载到经典处理器上。
Exploiting near-term quantum computers and achieving practical value is a considerable and exciting challenge. Most prominent candidates as variational algorithms typically aim to find the ground state of a Hamiltonian by minimising a single classical (energy) surface which is sampled from by a quantum computer. Here we introduce a method we call CoVaR, an alternative means to exploit the power of variational circuits: We find eigenstates by finding joint roots of a polynomially growing number of properties of the quantum state as covariance functions between the Hamiltonian and an operator pool of our choice. The most remarkable feature of our CoVaR approach is that it allows us to fully exploit the extremely powerful classical shadow techniques, i.e., we simultaneously estimate a very large number $>10^4-10^7$ of covariances. We randomly select covariances and estimate analytical derivatives at each iteration applying a stochastic Levenberg-Marquardt step via a large but tractable linear system of equations that we solve with a classical computer. We prove that the cost in quantum resources per iteration is comparable to a standard gradient estimation, however, we observe in numerical simulations a very significant improvement by many orders of magnitude in convergence speed. CoVaR is directly analogous to stochastic gradient-based optimisations of paramount importance to classical machine learning while we also offload significant but tractable work onto the classical processor.
