Many fundamental properties of a quantum system are captured by its Hamiltonian and ground state. Despite the significance of ground states preparation (GSP), this task is classically intractable for large-scale Hamiltonians. Quantum neural networks (QNNs), which exert the power of modern quantum machines, have emerged as a leading protocol to conquer this issue. As such, how to enhance the performance of QNNs becomes a crucial topic in GSP. Empirical evidence showed that QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes, while theoretical explanations have not been explored. To fill this knowledge gap, here we propose the effective quantum neural tangent kernel (EQNTK) and connect this concept with over-parameterization theory to quantify the convergence of QNNs towards the global optima. We uncover that the advance of symmetric ansatzes attributes to their large EQNTK value with low effective dimension, which requests few parameters and quantum circuit depth to reach the over-parameterization regime permitting a benign loss landscape and fast convergence. Guided by EQNTK, we further devise a symmetric pruning (SP) scheme to automatically tailor a symmetric ansatz from an over-parameterized and asymmetric one to greatly improve the performance of QNNs when the explicit symmetry information of Hamiltonian is unavailable. Extensive numerical simulations are conducted to validate the analytical results of EQNTK and the effectiveness of SP.
翻译:量子系统的许多基本特性被其汉密尔顿和地面状态所捕捉。尽管地面国家准备的重要性(GSP),这项任务对于大规模汉密尔顿人来说是典型的难以解决的。运用现代量子机器力量的量子神经网络(QNN)已成为克服这一问题的主要协议。因此,如何提高量子系统的性能成为普惠制的一个重要议题。经验性证据表明,带有手工艺对称肛门的QNNTZ通常比那些非对称肛门的QNTK系统具有更好的可训练性,而理论解释却没有得到探讨。为了填补这一知识差距,我们在此提议有效的量子神经内核内核(QNTK)网络,并将这个概念与超标度理论联系起来,以量化QNNNT的趋同性能。我们发现,对准性能的推进是其巨大的 EQNTTK系统价值,且不具有低有效层面,要求没有多少参数和量电深到超标度系统,使得QQQ的精确度分析结果能够大大降低损失和快速趋近于EQ的精确度。由ENT的精确度计划进行。