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：评估量子电路目前存在显著的噪声。因此，开发能够最大限度减少在噪声量子设备上执行量子电路次数的经典引导策略，是提升变分量子算法实用性的有力技术。CAFQA是一种此前提出的用于VQA的经典引导方法，它采用初始拟设并简化为克利福德算子。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——即横向场伊辛哈密顿量——最优成本函数的克利福德态。我们的主要发现将寻找最优CAFQA初始化的问题与次模最小化问题联系起来，而后者可在多项式时间内求解。