Quantum walks as a tool to design robust quantum batteries: the role of topology and chirality

TL;DR

This work addresses how quantum batteries can store and release energy most efficiently by leveraging quantum walks on graphs. It shows that battery topology (ring, wheel, complete) determines ergotropy scaling (complete: linear in $N$, wheel: $\sim\sqrt{N}$, ring: size-independent) and that chirality—the inclusion of complex phases in off-diagonal couplings—can boost extractable work and protect it against decoherence by inducing degeneracies. The authors develop ideal charging/discharging protocols and analyze performance under several noise models (pure dephasing, Haken–Strobl, stochastic quantum walks), revealing that even minimal ring cells ($N=3,4$) can exhibit robust ergotropy due to degeneracies, while complete cells maximize energy scale. Collectively, topology and chirality emerge as design principles for robust, scalable quantum batteries with implications for practical quantum-energy technologies 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. 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.

Figures (10)

• Figure 1: Schematic representation of a quantum battery. On the left the graphical representation of the whole battery, which consist in an arrangement of Q-Cells. On the right the focus on the structure of the topology of the Q-Cells analyzed: (1) Wheel Q-Cell, (2) Complete Q-Cell and (3) Ring Q-Cell.
• Figure 2: Schematic representation of the charge-discharge cycle of a quantum battery, where each panel corresponds to a different battery state. Left panel (a): Fully charged battery (described by the pure eigenstate $\ket{\psi}=\ket{\phi_{N-1}}$); Left (b): Ground state of the battery (described by the pure eigenstate $\ket{\psi}=\ket{\phi_{0}}$). Right panel (a): Fully charged battery (described by the pure eigenstate ${\rho}=\ket{\phi_{N-1}}\bra{\phi_{N-1}}$). Right (b:) State of the battery after a non-ideal evolution (corresponding to the density matrix ${\rho}(\tau)$). Right (c): Passive state of the battery (corresponding to the state ${\zeta}$ introduced in Eq.\ref{['eq:passive_state']}). Right (d): Ground state of the battery (described by the pure eigenstate ${\rho}=\ket{\phi_{0}}\bra{\phi_{0}}$).
• Figure 3: Graphical representation of the Wheel Q-Cell composed of $N=9$ discrete elements for a skeleton quantum battery.
• Figure 4: Graphical representation of the Complete Q-Cell composed of $N=10$ discrete elements for a circulant quantum battery.
• Figure 5: Graphical representation of the ring Q-Cell composed of $N=8$ discrete elements for a circulant quantum battery.