Kicked-Ising Quantum Battery

Abstract

Quantum batteries (QBs) have emerged as promising candidates capable of outperforming classical counterparts by utilizing entangled operators. Spin chains, in particular, exhibit unique {charging} properties across diverse settings. Here, we introduce the kicked-Ising model as a QB and analytically characterize its charging dynamics within the self-dual operator regime, valid for arbitrary system sizes and Floquet cycles. Using Clifford quantum cellular automata and momentum-space Floquet analysis with the Cayley-Hamilton theorem, we obtain exact expressions for energy injection, uncovering the influence of boundary conditions and spin-chain parity on charging performance. The kicked-Ising QB achieves maximal charging while exhibiting remarkable robustness against disorder. We further propose an intensified protocol within a fixed time window that enables faster and more efficient energy injection, while non-uniform kick schedules enhance experimental flexibility. Spin correlators analysis further shows that low-frequency driving boosts energy injection, highlighting a clear connection between charging, scrambling, and kick-induced delocalization. Our theoretical framework are supported by tensor-network simulations and finally verified on IBM quantum hardware. Accounting for platform-specific constraints, we demonstrate that the kicked-Ising QB offers a scalable, disorder-resilient protocol and testbed to assess quantum platforms.

Figures (9)

• Figure 1: Kicked-Ising QB charging schematic. A set of coupled spins, driven by an external transverse field applied in kicks at times $t_i\in[0,\tau]$ ($i=1,2,\dots,m$), is used to populate higher-excited states of an initially-discharged QB. Operating in the self-dual operator regime, this model offers a stable and flexible protocol capable to maximally charge a QB, regardless of the uniformity of the kick schedule.
• Figure 2: Normalized injected energies for KIC with $N=104$.a, Using $H_1^{xx}$ as charger [equation \ref{['eq:components_xx']}], analytical results up to $m=N=104$ kicks under PBC. b, Using $H_1^{zz}$ as charger, analytical results up to $m=N$ under OBC. c, Using $H_1^{zz}$ as charger [equation \ref{['eq:components_zz']}], analytical (up to $m=N$) and ibm emtorino results (up to $m=12$) under PBC. Error bars denotes the standard deviation after $100000$ measurements (Methods). d, Using $H_1^{zz}$ as charger, analytical results up to $m=4N$ under OBC. In all panels, analytical (ibm emtorino) results are shown by solid lines (triangular marks). Analytical results were also verified using tensor network methods.
• Figure 3: Population dynamics of KIC QB with $N=14$.a, Using $H_1^{xx}$ as charger [equation \ref{['eq:components_xx']}], population dynamics up to $m=N=14$ kicks under PBC. b, Same as a but under OBC. c, Using $H_1^{zz}$ as charger [\ref{['eq:components_zz']}], population dynamics up to $m=N=14$ kicks under PBC. d, Same as c but evolving the system up to $m=4N=56$ kicks under OBC. For guidance, white lines indicate the normalized injected energy dynamics, see Fig. \ref{['fig:kic']}.
• Figure 4: Charging performance of uniform KIC under the presence of disorder. Using $H_1^{xx}$ as charger [\ref{['eq:components_xx']}], normalized injected energies with $N=20$ for PBC using a disorder ratio $\sigma_J$ equal to $0$ (no disorder), $0.1$, $0.2$ and $0.5$, respectively, are shown from darker to lighter colors, as compared to Fig. \ref{['fig:kic']}a. Similar results are observed for different chargers, system sizes and boundary conditions. Error bars indicate the standard deviation over 100 disorder realizations.
• Figure 5: Normalized injected energies for non-uniform KIC with $N=104$. Kicks are applied randomly in the time window $t_i\in(0,1]$ using a uniform distribution up to $m=20$ ($m=12$) kicks for the MPS (ibm emtorino) results. Solid lines represent the saturation energies. Zoomed inset shows the difference between these values under PBC (orange) and OBC (green). Apart from the MPS solutions, ibm emtorino results are attached for PBC (triangular marks). Rightmost inset shows the same charging dynamics but under an Ising chain (violet), where $E_N/N=0.5$ at time $\tau\sim 0.6$. Error bars correspond to the standard deviation after $1000$ measurements and $n_d=10$ disorder realizations (Methods). The MPS results mostly overlap for both boundary conditions.