One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory. We demonstrate a general method for obtaining the exact functional as a machine learned model from a sufficiently powerful quantum computer. Only existing assumptions for the current feasibility of solutions on the quantum computer are used. Several known algorithms including quantum phase estimation, quantum amplitude estimation, and quantum gradient methods are used to train a machine learned model. One advantage of this combination of algorithms is that the quantum wavefunction does not need to be completely re-prepared at each step, lowering a sizable prefactor. Using the assumptions for solutions of the ground-state algorithms on a quantum computer, we demonstrate that finding the Kohn-Sham potential is not necessarily more difficult than the ground-state density. Once constructed, a classical user can use the resulting machine learned functional to solve for the ground state of a system self-consistently, provided the machine learned approximation is accurate enough for the input system. It is also demonstrated how the classical user can access commonly used time- and temperature-dependent approximations from the ground-state model. Minor modifications to the algorithm can learn other types of functional theories including exact time and temperature dependence. Several other algorithms—including quantum machine learning—are demonstrated to be impractical in the general case for this problem.

中文翻译：

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量子计算机上具有最少波函数准备的密度泛函和Kohn-Sham势

量子计算机的潜在应用之一是解决量子化学系统。众所周知，经典地获得某种程度精确解的最快方法之一是使用密度泛函理论的近似值。我们演示了一种从功能强大的量子计算机中获取作为机器学习模型的确切功能的通用方法。仅使用有关量子计算机上解决方案当前可行性的现有假设。几种已知的算法（包括量子相位估计，量子幅度估计和量子梯度方法）用于训练机器学习模型。这种算法组合的一个优点是，不需要在每个步骤中都完全重新准备量子波函数，从而降低了相当大的系数。使用量子计算机上的基态算法解的假设，我们证明了找到Kohn-Sham势并不一定比基态密度困难。一旦构建，经典用户就可以使用所得到的机器学习的功能来自洽地解决系统的基态，只要机器学习的近似对于输入系统足够准确。还演示了经典用户如何从基态模型访问常用的与时间和温度相关的近似值。对算法的微小修改可以学习其他类型的功能理论，包括确切的时间和温度依赖性。对于该问题，在一般情况下，包括量子机器学习在内的其他几种算法也被证明是不切实际的。