论文标题
将空间对称性建立到参数化的量子电路中，以进行更快的训练
Building spatial symmetries into parameterized quantum circuits for faster training
论文作者
论文摘要
量子学习模型的实际成功取决于具有适当的参数化量子电路结构。这种结构既由所采用的门的类型和参数的相关性来定义。尽管许多研究致力于设计足够的栅极组，通常尊重问题的某些对称性，但关于如何构造其参数的知之甚少。在这项工作中，我们表明，当仔细考虑空间对称性时（即，所研究的部分部分的置换），理想的参数结构自然会出现。也就是说，我们考虑了哈密顿量问题的自动形态群体，这使我们开发了一个在此对称组下的电路结构。在几个地面问题中，在数值上探测了我们新型电路结构的好处。我们发现与文献电路结构相比，我们发现一致的改进（就电路深度，所需参数数量和梯度幅度而言）。
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 circuit structure, 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.
