ABSTRACT The maximum work that can be extracted from a quantum battery is bounded by the ergotropy of the system, which is determined by the spectral properties of the Hamiltonian. In this paper, we employ the formalism of quantum walks to investigate how the topology of the battery and the chirality of the Hamiltonian influence its performance as an energy storage unit. We analyze architectures of battery cells based on ring, complete, and wheel graph structures and analyze their behavior in the presence of noise. Our results show that these structures exhibit distinct ergotropy scaling, with the interplay between chirality and topology providing a tunable mechanism to optimize work extraction and enhance robustness against decoherence. In particular, chirality enhances ergotropy for complete quantum cells, without altering the linear scaling with size, whereas in ring cells, it bridges the performance gap between configurations with odd and even number of units. Additionally, chirality may be exploited to force degeneracies in the Hamiltonian, a condition that can spare the ergotropy to vanish in the presence of pure dephasing. We conclude that topology and chirality are key resources for improving ergotropy, offering guidelines to optimize quantum energy devices and protocols.
ABSTRACT The maximum work that can be extracted from a quantum battery is bounded by the ergotropy of the system, which is determined by the spectral properties of the Hamiltonian. In this paper, we employ the formalism of quantum walks to investigate how the topology of the battery and the chirality of the Hamiltonian influence its performance as an energy storage unit. We analyze architectures of battery cells based on ring, complete, and wheel graph structures and analyze their behavior in the presence of noise. Our results show that these structures exhibit distinct ergotropy scaling, with the interplay between chirality and topology providing a tunable mechanism to optimize work extraction and enhance robustness against decoherence. In particular, chirality enhances ergotropy for complete quantum cells, without altering the linear scaling with size, whereas in ring cells, it bridges the performance gap between configurations with odd and even number of units. Additionally, chirality may be exploited to force degeneracies in the Hamiltonian, a condition that can spare the ergotropy to vanish in the presence of pure dephasing. We conclude that topology and chirality are key resources for improving ergotropy, offering guidelines to optimize quantum energy devices and protocols.
The maximum work that can be extracted from a quantum battery is bounded by the ergotropy of the system, which is determined by the spectral properties of the Hamiltonian. In this paper, we employ the formalism of quantum walks to investigate how the topology of the battery and the chirality of the Hamiltonian influence its performance as an energy storage unit. We analyze architectures of battery cells based on ring, complete, and wheel graph structures and analyze their behavior in the presence of noise. Our results show that these structures exhibit distinct ergotropy scaling, with the interplay between chirality and topology providing a tunable mechanism to optimize work extraction and enhance robustness against decoherence. In particular, chirality enhances ergotropy for complete quantum cells, without altering the linear scaling with size, whereas in ring cells, it bridges the performance gap between configurations with odd and even number of units. Additionaly, chirality may be exploited to force degeneracies in the Hamiltonian, a condition that can spare the ergotropy to vanish in the presence of pure dephasing. We conclude that topology and chirality are key resources for improving ergotropy, offering guidelines to optimize quantum energy devices and protocols.
Ergotropy as Permutation Work: A First-Principles Unification of Quantum Battery Scaling Laws and a Universal Spectral Bound This research establishes a fundamental reinterpretation of ergotropy—the central figure of merit for quantum battery performance—as a combinatorial sorting distance derived from the Hardy-Littlewood-Polya Rearrangement Inequality. By shifting the foundation from traditional thermodynamics to spectral graph theory, the author proves a Universal Ergotropy Bound: \Delta(T) = J[\lambda_{max}(A_T) - \lambda_{min}(A_T)] where A_T is the adjacency matrix of the battery's coupling topology T. This single spectral theorem provides a unified framework that recovers all three major scaling laws previously reported in literature: O(1) for ring topologies, O(N) for complete graphs, and O(\sqrt{N}) for wheel graphs. Key Contributions: New Scaling Regime: Predicts and proves an O(\log N) scaling for hypercube topologies, a regime previously unidentified in quantum battery research. Decoherence Dynamics: Derives the exact ergotropy evolution equation under graph-structured dephasing using the graph Laplacian. Optimal Topology: Establishes the Ergotropy-Decoherence Tradeoff and proves that the hypercube is the uniquely optimal topology for the energy-coherence product. AI Inference Conjecture: Proposes a formal mapping between neural network layers and quantum batteries, providing a first-principles justification for why sparse architectures (e.g., Transformers, MoE) are thermodynamically mandated for energy efficiency. All results are proven from first principles, connecting significant mathematical constants (such as 4J, 2, and \sqrt{N}) to deep structures in condensed matter physics, quantum information, and information theory
Going beyond isolated system dynamics, we examine how local and spatially correlated reservoirs influence the work extraction in quantum batteries. By employing a one-dimensional spin-1/2 model coupled to baths via dephasing and amplitude-damping noise, we demonstrate that correlations in reservoirs can significantly enhance battery's performance compared to local noise. In the dephasing scenario, we prove that correlated reservoirs produce a finite amount of extractable work, or ergotropy, during the transient regime when a two-cell battery is initialized in a product state while local noise yields vanishing ergotropy at all times, despite nonvanishing stored energy in both cases. Numerical simulations confirm that this advantage persists across larger system sizes and for both entangled and product initial states. We also find that the dynamics of quantum coherence closely mirror those of ergotropy, highlighting coherence as a key resource underlying the enhanced performance of quantum batteries. Further, we observe that the fraction of stored energy extracted from quantum batteries displays a sharper contrast between the correlated and local reservoirs. Moreover, for dephasing noise, this fraction remains independent of system size, whereas in the amplitude damping case, it exhibits a clear system-size dependence within the transient regime, highlighting distinct operational behaviors under different noise models. In addition, we reveal that when the battery dynamics is governed by an effective Hamiltonian with long-range interactions, it yields higher ergotropy compared to short-range interactions, emphasizing the advantages of reservoir engineering for efficient device design.
The realization of scalable quantum battery architectures requires concern not only with how much energy can be stored, but also with how energy is transported, distributed, and converted into extractable work across connected battery nodes. While previous studies mainly focused on collective charging in multi-cell quantum batteries, the topology-dependent transport law and the corresponding work-oriented performance of quantum battery networks remain largely unexplored. In this work, we investigate quantum battery networks with engineered reciprocal and nonreciprocal couplings and compare different connection topologies, including cascaded and parallel architectures, within a unified transport framework. In the nonreciprocal regime, the optimal coupling follows distinct scaling laws for the two connection topologies, namely Jopc∝N for cascaded transport and Jopp∝N−1/2 for parallel charging in the large-N limit. In reciprocal cascaded networks, a parity-dependent spectral response produces an odd-even transport effect that is absent in the nonreciprocal and parallel configurations. We further analyze the role of thermal and squeezed reservoirs and show that thermal noise mainly increases passive energy, whereas squeezing enhances ergotropy and thus the useful fraction of stored energy. These results shift the emphasis from charging enhancement to transport engineering and provide architecture-level design principles for quantum battery networks.
Abstract Quantum batteries utilize quantum effects to enhance energy storage and work extraction quantified by ergotropy. However, degradation of stored energy due to environmental noise remains a key limitation. For a single qubit, we show that repeated amplitude damping and bit-flip noises lead to ergotropy loss, while repeated phase-flip noise permits partial preservation of work. Extending this protocol to a two-qubit Heisenberg XYZ system with Dzyaloshinsky–Moriya interaction (DMI), we find that strong DMI widens the energy gap and stabilizes chiral correlations. Therefore, ergotropy persists in DMI-dominated regimes for coherent initial states, demonstrating that chiral spin interactions serve as a microscopic resource for noise-resilient quantum batteries.
This study explores the energy storage dynamics of a quantum battery (QB) modeled using a dipolar spin system with Dzyaloshinskii-Moriya (DM) interaction. We examine the performance of this system in terms of ergotropy, instantaneous power, capacity, and quantum coherence using a two-qubit model. By solving the system's time evolution under cyclic unitary processes, we analyze how external parameters such as temperature, magnetic field, and DM interaction influence the charging behavior and quantum resources of the battery. The findings demonstrate that quantum coherence and DM interaction significantly enhance the energy storage efficiency and power output of the quantum battery, offering promising strategies for designing high-performance quantum energy storage devices. Furthermore, we investigate the performance of quantum battery under the influence of a common dephasing environment, which limits the long-term work-extraction capability of dipolar quantum batteries.