Superextensive charging speeds in a correlated quantum charger

Long-range interactions within a quantum charger induce a collective steady-state charging mode that depends superlinearly on the size of the charger, exceeding the performance of noninteracting, parallel units.

Introduction and Motivation

A critical engineering objective for developing quantum technology is controlling energy flow in quantum devices. Floquet engineering provides a practical tool to bridge this communication gap by allowing quantum systems to act as pumps that transfer a quantized amount of energy per period under strong periodic drives. The paper generalizes this concept to interacting many-body quantum systems, demonstrating that the presence of interactions can parametrically enhance the performance of the charger. The central objective is to investigate whether interactions can enhance the performance, showing that "the transferred energy W can scale as W ∝ N(1+δ) (1) over a broad range of system sizes N, with δ > 0, when interactions are present."

Model and Methodology

The quantum charger is modeled as a long-range interacting spin chain subject to two classically oscillating fields, defined by the time-dependent Hamiltonian:

H(t) = H0 + V1(ω1t + ϕ1) + V2(ω2t + ϕ2).

The dynamics are treated in a Floquet picture where quasi-stationary Floquet states ψα⟩ are defined through the eigenvalue equation U(T)ψα⟩ = e(-iϵαT)ψα⟩ of the time-evolution operator U(t) for a single Floquet period T. The integrated pumping power (work) from each drive is given by Wi(t) = iωi⟨ψ(0)U†(t)∂U(t)/∂ϕiψ(0)⟩, and the work output per cycle for Floquet states is Wi,α(T) = ωiT ∂ϵα/∂ϕi.

Superlinear Charging Effects

The analysis focuses on all-to-all couplings (Jij = J). For the LMG model realized by this setup, the work scales quadratically up to a characteristic system size N∗, after which it crosses over to linear scaling. Specifically, "for small system sizes, the maximum work Wi(T) associated with the optimal work state shows a quadratic scaling ∝ N squared [Fig. 2(a)]. In this regime, the charger effectively transfers the interaction energy I = P i,j Jij = JN squared from one drive to the other. For larger system sizes, we observe a crossover to linear scaling, ∝ N." This superlinear effect is confirmed even in the steady state when considering optimal Floquet states.

High-Frequency and Low-Frequency Limits

The superlinear scaling is understood in the high-frequency limit (JN, h ≪ ω), where the work scales quadratically, W ∝ N squared. The effective Hamiltonian expansion shows that superlinear behavior can emerge at second order in 1/ω, provided that both drives have the same frequency (p = q = 1), in agreement with Fig. 4(a). In contrast, in the low-frequency limit (ω << JN, h), a semiclassical argument shows that the nonlinear contribution to the work Wi,NL vanishes in the low-frequency limit.

Stabilization and Experimental Accessibility

While work states are not quasi-stationary and require resetting after each period, they can be coherently stabilized by echo pulses. A periodic protocol involving an instantaneous pulse Vecho = e(i∆ϕSz e(i∆θSy)) is proposed to approximately reset the system in a unitary manner. This echo-induced stabilization of work states generates the optimal work output in the steady state, and the echo work Wecho exactly cancels the work by the two drives as shown in Fig. 6(b), restoring the energy balance W1 + W2 + Wecho = 0. Furthermore, classical spin-coherent states approximating optimal Floquet states are found to closely reproduce the quantum optimum in the collective pumping regime.

Conclusion and Future Directions

The work demonstrates that interactions induce collective charging where energy pumping is superlinearly amplified with system size, persisting up to a critical system size N∗. The key finding is that nonlinear pumping persists up to a critical system size N∗, where the drive becomes strong and the charger splits into independent subsystems. Future work should explore the resilience of the proposed charger against dissipation and disorder, and relate this effect to time crystals. The paper concludes that while not required for superlinear charging, interference can significantly enhance the work output by utilizing work states. The superlinear charging occurs in the high-frequency limit and is most efficient for drives with small, commensurate frequency ratios. This effect does not enable efficient frequency conversion.

The gist: Long-range interactions within a quantum charger induce a collective steady-state charging mode that depends superlinearly on the size of the charger, exceeding the performance of noninteracting, parallel units.

Based on this scientific paper, here are specific improvements that can be made to AI systems by leveraging the principles of a quantum charger:

1. Promote Superlinear Energy Transfer in Quantum Computing Architectures:

2. Enable Enhanced Energy Conversion in Quantum Transducers:

3. Develop Novel, Robust Many-Body Qubit Control Schemes:

Here is a detailed breakdown of what these improved AI systems can achieve:

1. Promote Superlinear Energy Transfer in Quantum Computing Architectures

The paper demonstrates that long-range interactions within a quantum system (modeled as an interacting spin chain) can induce a collective steady-state charging mode where the energy transfer power scales superlinearly with the system size, specifically as:

W ∝ N(1+δ) (with δ > 0)

The AI systems derived from this principle could be used to design quantum processors that maximize energy throughput.

The improved AI system can perform:

The AI can optimize the coupling topology and interaction parameters of a many-body qubit array (e.g., an Ising or Lipkin-Meshkov-Glick model) such that the steady-state energy transfer rate between two drives (representing different control pulses) scales superlinearly with the number of qubits in the processor. This would allow for significantly higher energy pumping efficiency compared to noninteracting systems, effectively maximizing computational throughput per unit time by treating the processor as a collective energy converter rather than a collection of independent units.

2. Enable Enhanced Energy Conversion in Quantum Transducers

The paper highlights that Floquet engineering, especially in the high-frequency limit, allows quantum systems to act as pumps that transfer quantized energy between drives (quantum chargers). Furthermore, the analysis shows that superlinear charging is most efficient for comparable drive frequencies and can be probed experimentally.

The improved AI system can perform:

The AI can design optimal time-dependent driving protocols (Floquet engineering) for quantum devices intended to act as transducers between different physical media (e.g., microwave fields to optical photons, as suggested by references [74]–[79]). By utilizing the superlinear charging effect, the AI can engineer a system that converts energy from one drive frequency into another with substantially higher efficiency and power scaling than current non-interacting designs, leading to more robust and powerful quantum transducers.

3. Develop Novel, Robust Many-Body Qubit Control Schemes

The research identifies work states—eigenstates of the work operator—which exhibit superlinear scaling but pump significantly more work than standard Floquet states. Crucially, these work states can be stabilized in the steady state using an echo protocol (applying a time-reversed pulse after each cycle).

The improved AI system can perform:

The AI can autonomously design complex quantum control sequences for many-body systems (like spin chains) to maintain a high-performance, superlinear energy pumping state. This includes designing the necessary periodic echo pulses that coherently stabilize work states in the steady state, ensuring continuous operation without requiring external reset protocols. This enables the creation of more stable and efficient quantum devices capable of sustained, high-rate energy manipulation in non-equilibrium regimes.

We define a quantum charger as an interacting quantum system that transfers energy between two drives. The key figure of merit characterizing a charger is its charging power. Remarkably, the presence of long-range interactions within the charger can induce a collective steady-state charging mode that depends superlinearly on the size of the charger, exceeding the performance of noninteracting, parallel units. Using the driven Lipkin-Meshkov-Glick model and power-law interacting spin chains, we show that this effect persists up to a critical system size set by the breakdown of the high-frequency regime. We discuss optimal work output as well as experimentally accessible initial states. The superlinear charging effect can be probed in trapped-ion experiments, and positions interacting Floquet systems as promising platforms for enhanced energy conversion.