A central component of variational quantum algorithms (VQAs) is the state-preparation circuit, also known as ansatz or variational form. This circuit is most commonly designed such as to exploit symmetries of the problem Hamiltonian and, in this way, constrain the variational search to a subspace of interest. Here, we show that this approach is not always advantageous by introducing ansatzes that incorporate symmetry-breaking unitaries. This class of ansatzes, that we call quantum-optimal-Control-inspired ansates (QOCA), is inspired by the theory of quantum optimal control and leads to an improved convergence of VQAs for some important problems. Indeed, we benchmark QOCA against popular variational forms applied to the Fermi-Hubbard model at half-filling and show that our variational circuits can approximate the ground state of this model with high accuracy. We also show how QOCA can be used to find the ground state of the water molecule and compare the performance of our ansatz against other common choices used for chemistry problems. This work constitutes a first step towards the development of a more general class of symmetry-breaking ansatzes with applications to physics and chemistry problems.

中文翻译：

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量子最优控制启发式ansatz用于变分量子算法

变分量子算法（VQA）的核心组件是状态准备电路，也称为ansatz或变分形式。该电路最通常被设计为利用问题哈密顿量的对称性，并以此方式将变分搜索约束到感兴趣的子空间。在这里，我们表明通过引入合并了对称破除unit的突触，这种方法并不总是有利的。此类麻醉剂，我们称为量子最优控制激发型麻醉剂（QOCA），受量子最优控制理论的启发，并导致某些重要问题的VQA的收敛性得到改善。确实，我们针对半填充时适用于Fermi-Hubbard模型的流行变分形式对QOCA进行了基准测试，结果表明，我们的变分电路可以高精度地逼近该模型的基态。我们还将展示如何使用QOCA来发现水分子的基态，并将ansatz的性能与用于化学问题的其他常见选择进行比较。这项工作是迈向开发更广泛的一类对称破译器的第一步，并将其应用于物理和化学问题。