Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much research has been devoted to devising adequate gate-sets, typically respecting some symmetries of the problem, very little is known about how their parameters should be structured. In this work, we show that an ideal parameter structure naturally emerges when carefully considering spatial symmetries (i.e. the symmetries that are permutations of parts of the system under study). Namely, we consider the automorphism group of the problem Hamiltonian, leading us to develop a circuit construction that is equivariant under this symmetry group. The benefits of our novel circuitstructure, called ORB, are numerically probed in several ground-state problems. We find a consistent improvement (in terms of circuit depth, number of parameters required, and gradient magnitudes) compared to literature circuit constructions.

中文翻译：

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将空间对称性构建到参数化量子电路中以加快训练速度

量子学习模型的实际成功取决于参数化量子电路的合适结构。这种结构是由所采用的门的类型及其参数的相关性来定义的。虽然许多研究致力于设计足够的门集，通常尊重问题的某些对称性，但对于如何构建其参数却知之甚少。在这项工作中，我们表明，当仔细考虑空间对称性（即所研究的系统各部分的排列的对称性）时，理想的参数结构自然会出现。也就是说，我们考虑问题哈密顿量的自同构群，导致我们开发出在该对称群下等变的电路结构。我们的新型电路结构（称为 ORB）的优点在几个基态问题中进行了数值探讨。与文献电路结构相比，我们发现了一致的改进（在电路深度、所需参数数量和梯度幅度方面）。