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Quantum charging supremacy via Sachdev-Ye-Kitaev batteries

Davide Rossini, Gian Marcello Andolina, Dario Rosa, Matteo Carrega, Marco Polini

Published Dec 16, 2019• 5 citations
OpenAlex

Abstract

The exactly-solvable Sachdev-Ye-Kitaev (SYK) model has recently received considerable attention in both condensed matter and high energy physics because it describes quantum matter without quasiparticles, while being at the same time the holographic dual of a quantum black hole. In this Letter, we examine SYK-based charging protocols of quantum batteries with N quantum cells. We demonstrate that the optimal charging power of our SYK quantum batteries displays a super-extensive scaling with N that stems from genuine quantum mechanical effects. To the best of our knowledge, this is the first quantum many-body battery model where fast charging occurs due to the maximally-entangling underlying quantum dynamics.

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The exactly solvable Sachdev-Ye-Kitaev (SYK) model has recently received considerable attention in both condensed matter and high energy physics because it describes quantum matter without quasiparticles, while being at the same time the holographic dual of a quantum black hole. In this Letter, we examine SYK-based charging protocols of quantum batteries with N quantum cells. Extensive numerical calculations based on exact diagonalization for N up to 16 strongly suggest that the optimal charging power of our SYK quantum batteries displays a superextensive scaling with N that stems from genuine quantum mechanical effects. While the complexity of the nonequilibrium SYK problem involved in the charging dynamics prevents us from an analytical proof, we believe that this Letter offers the first (to the best of our knowledge) strong numerical evidence of a quantum advantage occurring due to the maximally entangling underlying quantum dynamics.

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We investigate the charging dynamics of Sachdev-Ye-Kitaev (SYK) models as quantum batteries, highlighting their capacity to achieve quantum charging advantages. By analytically deriving the scaling of the charging power in SYK batteries, we identify the two key mechanisms underlying this advantage: the use of operators scaling extensively with system size $N$ and the facilitation of operator delocalization by specific graph structures. A graph-theoretic framework is introduced in which the charging process is recast as a random walk on a graph, enabling a quantitative analysis of operator spreading. Our results establish rigorous conditions for the quantum advantage in SYK batteries and extend these insights to graph-based SYK models, revealing broader implications for energy storage and quantum dynamics. This work opens avenues for leveraging quantum chaos and complex network structures in optimizing energy transfer processes.

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We establish a general implementation-independent approach to assess the potential advantage of using highly entangled quantum states between the initial and final states of the charging protocol to enhance the maximum charging power of quantum batteries. It is shown that the impact of entanglement on power can be separated from both the global quantum speed limit associated with an optimal choice of driving Hamiltonian and the energy gap of the batteries. We then demonstrate that the quantum state advantage of battery charging, defined as the power obtainable for given quantum speed limit and battery energy gap, is not an entanglement monotone. A striking example we provide is that, counterintuitively, independent thermalization of the local batteries, completely destroying any entanglement, can lead to larger charging power than that of the initial maximally entangled state. Highly entangled states can thus also be potentially disadvantageous when compared to product states. We also demonstrate that taking the considerable effort of producing highly entangled states, such as W or k-locally entangled states, is not sufficient to obtain quantum-enhanced scaling behavior with the number of battery cells. Finally, we perform an explicit computation for a Sachdev–Ye–Kitaev battery charger to demonstrate that the quantum state advantage allows the instantaneous power to exceed its classical bound.

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The exactly-solvable Sachdev-Ye-Kitaev (SYK) model has recently received considerable attention in both condensed matter and high energy physics because it describes quantum matter without quasiparticles, while being at the same time the holographic dual of a quantum black hole. In this Letter, we examine SYK-based charging protocols of quantum batteries with N quantum cells. We demonstrate that the optimal charging power of our SYK quantum batteries displays a super-extensive scaling with N that stems from genuine quantum mechanical effects. To the best of our knowledge, this is the first quantum many-body battery model where fast charging occurs due to the maximally-entangling underlying quantum dynamics.
The exactly solvable Sachdev-Ye-Kitaev (SYK) model has recently received considerable attention in both condensed matter and high energy physics because it describes quantum matter without quasiparticles, while being at the same time the holographic dual of a quantum black hole. In this Letter, we examine SYK-based charging protocols of quantum batteries with N quantum cells. Extensive numerical calculations based on exact diagonalization for N up to 16 strongly suggest that the optimal charging power of our SYK quantum batteries displays a superextensive scaling with N that stems from genuine quantum mechanical effects. While the complexity of the nonequilibrium SYK problem involved in the charging dynamics prevents us from an analytical proof, we believe that this Letter offers the first (to the best of our knowledge) strong numerical evidence of a quantum advantage occurring due to the maximally entangling underlying quantum dynamics.
A bstract Exponentially fast scrambling of an initial state characterizes quantum chaotic systems. Given the importance of quickly populating higher energy levels from low-energy states in quantum battery charging protocols, this work investigates the role of quantum scrambling in quantum batteries and its effect on optimal power and charging times by means of the Sachdev-Ye-Kitaev model, a maximally-chaotic black hole physics model that has been recently proposed as a quantum battery. We adopt a bare representation with normalized bandwidths to suppress system energy dependence. To our knowledge, this is the first in-depth exploration of quantum scrambling in the context of quantum batteries. By analyzing the dynamics of out-of-time-order correlators, our findings indicate that quantum scrambling does not necessarily lead to faster charging, despite its potential for accelerating the process.
We investigate the charging dynamics of Sachdev-Ye-Kitaev (SYK) models as quantum batteries, highlighting their capacity to achieve quantum charging advantages. By analytically deriving the scaling of the charging power in SYK batteries, we identify the two key mechanisms underlying this advantage: the use of operators scaling extensively with system size NNN and the facilitation of operator delocalization by specific graph structures. A graph-theoretic framework is introduced in which the charging process is recast as a random walk on a graph, enabling a quantitative analysis of operator spreading. Our results establish rigorous conditions for the quantum advantage in SYK batteries and extend these insights to graph-based SYK models, revealing broader implications for energy storage and quantum dynamics. This work opens avenues for leveraging quantum chaos and complex network structures in optimizing energy transfer processes.
A bstract Collective behavior strongly influences the charging dynamics of quantum batteries (QBs). Here, we study the impact of nonlocal correlations on the energy stored in a system of N QBs. A unitary charging protocol based on a Sachdev-Ye-Kitaev (SYK) quench Hamiltonian is thus introduced and analyzed. SYK models describe strongly interacting systems with nonlocal correlations and fast thermalization properties. Here, we demonstrate that, once charged, the average energy stored in the QB is very stable, realizing an ultraprecise charging protocol. By studying fluctuations of the average energy stored, we show that temporal fluctuations are strongly suppressed by the presence of nonlocal correlations at all time scales. A comparison with other paradigmatic examples of many-body QBs shows that this is linked to the collective dynamics of the SYK model and its high level of entanglement. We argue that such feature relies on the fast scrambling property of the SYK Hamiltonian, and on its fast thermalization properties, promoting this as an ideal model for the ultimate temporal stability of a generic QB. Finally, we show that the temporal evolution of the ergotropy, a quantity that characterizes the amount of extractable work from a QB, can be a useful probe to infer the thermalization properties of a many-body quantum system.
We investigate the charging dynamics of Sachdev-Ye-Kitaev (SYK) models as quantum batteries, highlighting their capacity to achieve quantum charging advantages. By analytically deriving the scaling of the charging power in SYK batteries, we identify the two key mechanisms underlying this advantage: the use of operators scaling extensively with system size NNN and the facilitation of operator delocalization by specific graph structures. A novel graph-theoretic framework is introduced in which the charging process is recast as a random walk on a graph, enabling a quantitative analysis of operator spreading. Our results establish rigorous conditions for the quantum advantage in SYK batteries and extend these insights to graph-based SYK models, revealing broader implications for energy storage and quantum dynamics. This work opens avenues for leveraging quantum chaos and complex network structures in optimizing energy transfer processes.
We establish a general implementation-independent approach to assess the potential advantage of using highly entangled quantum states between the initial and final states of the charging protocol to enhance the maximum charging power of quantum batteries. It is shown that the impact of entanglement on power can be separated from both the global quantum speed limit associated with an optimal choice of driving Hamiltonian and the energy gap of the batteries. We then demonstrate that the quantum state advantage of battery charging, defined as the power obtainable for given quantum speed limit and battery energy gap, is not an entanglement monotone. A striking example we provide is that, counterintuitively, independent thermalization of the local batteries, completely destroying any entanglement, can lead to larger charging power than that of the initial maximally entangled state. Highly entangled states can thus also be potentially disadvantageous when compared to product states. We also demonstrate that taking the considerable effort of producing highly entangled states, such as W or k-locally entangled states, is not sufficient to obtain quantum-enhanced scaling behavior with the number of battery cells. Finally, we perform an explicit computation for a Sachdev–Ye–Kitaev battery charger to demonstrate that the quantum state advantage allows the instantaneous power to exceed its classical bound.