Quantum annealing (QA) is one of the ways of finding ground states of problem Hamiltonians. We initially apply transverse fields corresponding to a driver Hamiltonian and adiabatically change the Hamiltonian to the problem Hamiltonian to obtain the target ground state. However, for some purposes such as quantum chemistry, both ground and excited states are needed to understand the properties of the molecules. Here, we describe a scheme based on QA to search arbitrary excited states of problem Hamiltonians. By splitting the degeneracy of the driver Hamiltonian with inhomogeneous transverse fields, we can prepare a nondegenerate excited state as the initial state, and an adiabatic change of the Hamiltonian provides a target excited state as long as the adiabatic condition holds. We also show that our scheme enables us to find a desired excited state by designing the driver Hamiltonian suitably even in the presence of weak decoherence. These results are important for quantum chemistry and post-quantum cryptography.

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使用量子退火的激发态搜索

量子退火（QA）是发现问题哈密顿量基态的方法之一。我们首先应用对应于驾驶员哈密顿量的横向场，然后将哈密顿量绝热地更改为问题哈密顿量，以获得目标基态。但是，出于某些目的（例如量子化学），既需要基态也需要激发态，以了解分子的特性。在这里，我们描述了一种基于质量保证方案来搜索任意问题哈密顿主义者的兴奋状态。通过用不均匀的横向场分裂驾驶员汉密尔顿的简并性，我们可以准备一个非简并的激发态作为初始状态，并且只要绝热条件成立，汉密尔顿的绝热变化就可以提供目标激发态。我们还表明，即使在存在弱退相干的情况下，通过适当地设计驱动器哈密顿量，我们的方案也使我们能够找到所需的激发态。这些结果对于量子化学和量子后密码学非常重要。