Evaluating quantum circuits is currently very noisy. Therefore, developing classical bootstraps that help minimize the number of times quantum circuits have to be executed on noisy quantum devices is a powerful technique for improving the practicality of Variational Quantum Algorithms. CAFQA is a previously proposed classical bootstrap for VQAs that uses an initial ansatz that reduces to Clifford operators. CAFQA has been shown to produce fairly accurate initialization for VQA applied to molecular chemistry Hamiltonians. Motivated by this result, in this paper we seek to analyze the Clifford states that optimize the cost function for a new type of Hamiltonian, namely Transverse Field Ising Hamiltonians. Our primary result connects the problem of finding the optimal CAFQA initialization to a submodular minimization problem which in turn can be solved in polynomial time.

翻译：当前评估量子电路的噪声水平很高。因此，开发经典引导方法以最小化量子电路在噪声量子设备上的执行次数，是提升变分量子算法实用性的有效技术。CAFQA是一种先前提出的VQA经典引导方法，其初始拟设可简化为Clifford算子。研究表明，CAFQA能为应用于分子化学哈密顿量的VQA提供相当精确的初始化。受此结果启发，本文旨在分析针对新型哈密顿量——即横向场Ising哈密顿量——优化代价函数的Clifford态。我们的核心结果将寻找最优CAFQA初始化的问题与一个子模最小化问题联系起来，而该问题可在多项式时间内求解。