We introduce a counter-diabatic (CD) approach for deriving Hamiltonians modeling superchargable quantum batteries (QBs). A necessary requirement for the supercharging process is the existence of multipartite interactions among the cells of the battery. Remarkably, this condition may be insufficient no matter the number of multipartite terms in the Hamiltonian. We analytically illustrate this kind of insufficiency through a model of QB based on the adiabatic version for the Grover search problem. On the other hand, we provide QB supercharging with just a mild number of global connections in the system. To this aim, we consider a spin- 1/2 chain with n sites in the presence of Ising multipartite interactions. We then show that, by considering the validity of the adiabatic approximation and by adding n terms of (n−1)-site interactions, we can achieve a Hamiltonian exhibiting maximum QB power, with respect to a normalized evolution time, growing quadratically with n. Therefore, supercharging can be achieved by O(n) terms of multipartite connections. The time constraint required by the adiabatic approximation can be surpassed by considering a CD expansion in terms of the gauge potential for the original Hamiltonian, with a limited O(n) many-body interaction terms assured via a Floquet approach for the CD implementation.

中文翻译：

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通过反绝热动力学对量子电池进行增压


我们引入了一种反绝热（CD）方法，用于推导建模超级充电量子电池（QB）的哈密顿量。增压过程的必要条件是电池单元之间存在多方相互作用。值得注意的是，无论哈密顿量中有多少个多部分项，这个条件都可能是不够的。我们通过基于 Grover 搜索问题绝热版本的 QB 模型来分析说明这种不足。另一方面，我们只需要系统中少量的全局连接即可提供 QB 增压。为此，我们考虑存在伊辛多方相互作用的情况下具有 n 个位点的自旋 1/2 链。然后我们证明，通过考虑绝热近似的有效性并添加 n 个 (n−1) 位点相互作用项，我们可以实现一个哈密顿量，该哈密顿量相对于归一化演化时间呈现出最大 QB 幂，随 n 呈二次方增长。因此，增压可以通过多方连接的 O(n) 项来实现。通过考虑原始哈密顿量的规范势的 CD 扩展，可以超越绝热近似所需的时间约束，并通过用于 CD 实现的 Floquet 方法确保有限的 O(n) 多体相互作用项。