Sparse SYK quantum batteries: Boosting quantum efficiency by reducing complexity

arXiv:2505.17679 · quant-ph, cond-mat.str-el, nlin.CD · Submitted 2025-05-23 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Sparse SYK quantum batteries".

Mira: Here's the gist of the paper. The gist The sparse version of the Sachdev-Ye-Kitaev model shows that reducing its complexity can lead to more efficient quantum batteries, provided the system remains sufficiently chaotic.

Kai: The quest for efficient energy storage and work extraction has been a cornerstone of several technological breakthroughs, dating back at least to the first industrial revolution, with its profound connection to the development of thermodynamics as the backbone for our scientific understanding of Nature Nowadays, as material samples are brought to increasingly lower temperatures and smaller sizes, we are experiencing a nanoscale industrial revolution Here, the challenge of energy storage takes on a quantum mechanical dimension, where centuries-old thermodynamic concepts must be revisited in the light of non-classical resources such as quantum coherence and entanglement Indeed, the interplay between entanglement generation and work extraction from many-body quantum states has spurred a sustained research effort into quantum batteries It is now clear that quantum battery engineering hinges on balancing complexity and controllability This tension motivates the exploration of minimal platforms where access to such observables is amenable to analytical and computational analysis.

Mira: The Sparse SYK Model The authors investigate the sparse version of the SYK model, where interaction terms are removed with a certain probability By pruning a fraction of the couplings, quantum chaotic features—instrumental for efficient energy storage—are retained while mitigating computational and experimental overhead Even more interestingly, our results demonstrate that such sparsification can actually enhance battery performance, provided the system remains sufficiently chaotic.

Kai: The complex SYK (cSYK) model is defined by a Hamiltonian with all-to-all random interactions The sparse version of Eq.

Title and authors: Kai: This paper on "Sparse SYK quantum batteries: Boosting quantum efficiency by reducing complexity" boils down to how they take the full Sachdev-Ye-Kitaev model and prune some of those interactions to make it sparse, and they show that if you keep enough chaos, this reduction actually helps you get better energy storage.

Mira: Yeah, we’re looking at how they defined that sparse version using a random variable xijkl being one with probability p and zero otherwise for each coupling in the complex SYK Hamiltonian. It's about controlling the interaction terms in a many-body system.

Lev: From my side, I see this as trying to solve the problem of computational overhead; when you have all-to-all connectivity, you run into massive bottlenecks when you try to scale up to a larger number of particles, N.

Kai: Exactly what Lev is saying. So they found that by reducing p, which means increasing sparsity, the maximum charging power Pmax actually gets bigger, but only if the system stays chaotic enough.

Mira: That’s because they look at quantum chaos through random matrix theory tools and find a critical sparsity value called p2 where spectral rigidity breaks down. If you stay above that threshold, you get a boost in performance.

Lev: And for running this on real hardware, that p2 is the sweet spot we need to aim for; operating near it seems to maximize the power output before things go weird.

Kai: They also looked at battery efficiency and found that as p gets closer to that critical value p2, the efficiency drops sharply. So you can boost power but have to be careful about efficiency.

Mira: It confirms that this isn't just a protocol trick; it’s a fundamental consequence of the interaction structure itself; you need that underlying chaotic behavior to get the benefits.

Lev: That means we don't have to build these massive, fully connected systems just because they look more complete for theory.

Kai: So the implication here is that sparse quantum systems could be a practical path toward robust quantum batteries without needing impractical complexity.

Mira: It gives us a blueprint for engineering these batteries by focusing on maintaining that chaotic interaction structure rather than just chasing full connectivity.

Lev: And if we can leverage this, it means we might find energy extraction methods that are less sensitive to the sheer size of the system because we're relying on the structural configuration of interactions.

Kai: That points toward developing systems where we don't need infinite connectivity just to see if they work for storing quantum information efficiently.

Mira: It’s a good reminder that understanding how complexity and chaos interact at the nanoscale is really what guides how we design these things.

Lev: So next, let's look at what this specific critical value p2 means for the actual scaling of the stored energy.

The paper's summary: Kai: So they're suggesting that for future work, we should look at how to make these sparse Hamiltonians even more robust, maybe by exploring different types of pruning beyond just a random probability p.

Mira: Exactly what Kai is saying. Since the current model relies on randomly dropping couplings with probability one minus p, the next step would be to see if there's a systematic way to select which terms are most important for maintaining that chaotic behavior.

Lev: I think we need to figure out how much overhead this extra tuning takes; if we get too complicated in selecting the sparse interactions, it might just become as hard to simulate as the full model was.

Kai: Right, the simulation challenge is huge. But Mira’s point is about getting better physics out of that structure; if we can find a more "intelligent" way to prune, we might get even better performance metrics for battery efficiency e(τc).

Mira: If they can maintain the chaotic features while using fewer total interactions, it means the underlying quantum dynamics are much more resilient than we initially thought.

Lev: That resilience is what matters for hardware implementation; if a sparse Hamiltonian maintains its desirable spectral properties even when you increase the sparsity level further, that’s a real win for scaling down the required components.

Kai: So it’s about finding that sweet spot where complexity drops fast but the quantum advantage doesn't vanish; it's like finding the perfect balance between simplicity and effectiveness.

Mira: And I think this leads into how we can use AI to help us find those optimal sparse Hamiltonians rather than just guessing p2.

Lev: That sounds like a good direction for error correction research; maybe an AI system could help us map out the phase space of interactions that keep the system chaotic and efficient.

Kai: So, if we can leverage AI to design these optimized sparse interaction structures, it moves us closer to a truly practical quantum battery design.

Mira: It’s moving from finding a specific parameter p2 for a fixed model to creating a whole family of sparse models that are inherently high-performing.

Lev: That would be fantastic for hardware because we wouldn't be stuck optimizing one single configuration; we could have a library of efficient Hamiltonians ready to test on different platforms.

Kai: So the next thing we need to watch is how these improved sparse designs translate into actual, measurable energy storage protocols under noisy conditions.

The paper's improvements: Kai: So to wrap up, this paper on "Sparse SYK quantum batteries: Boosting quantum efficiency by reducing complexity" shows that you can get better performance if you keep the system chaotic even when you cut down on interactions.

Mira: It really points toward a practical way for us to build these things without needing impossibly large systems, as long as we respect that underlying chaotic structure.

Lev: For error correction, this means we have a clearer target: don't just aim for full connectivity, but aim for a sparse structure that still retains the necessary spectral rigidity features near p2.

Kai: So it’s not about eliminating complexity entirely, but about finding the right level of complexity—the right amount of interaction—that gives us the best storage and extraction power.

Mira: It gives us a solid framework for designing systems where we can harness quantum resources without succumbing to impractical scaling bottlenecks.

Lev: And that structural insight is going to be important when we look at designing real hardware implementations, because it suggests the advantage comes from how you set up the interactions, not just how big N gets.

Kai: Agreed, so this paper on "Sparse SYK quantum batteries: Boosting quantum efficiency by reducing complexity" gives us a blueprint for building robust systems that are actually feasible to experiment with.

Mira: It really underscores the interplay between complexity, chaos and energy scale at the nanoscale when we’re trying to get these things working.

Lev: I think what this implies is that we should be designing our experiments around finding those critical thresholds, like p2, because that's where the real physics happens.

Conclusion: Kai: So we’re wrapping up on "Sparse SYK quantum batteries: Boosting quantum efficiency by reducing complexity." Basically, they showed that you can get better energy storage if you keep the system chaotic even when you cut down on interactions.

Mira: It really points toward a practical way for us to build these things without needing impossibly large systems, as long as we respect that underlying chaotic structure.

Kai: So it’s not about eliminating complexity entirely, but about finding the right level of complexity—the right amount of interaction—that gives us the best storage and extraction power.

Mira: It gives us a solid framework for designing systems where we can harness quantum resources without succumbing to impractical scaling bottlenecks.

Mira: It really underscores the interplay between complexity, chaos and energy scale at the nanoscale when we’re trying to get these things working.

Lev: I think what this implies is that we should be designing our experiments around finding those critical thresholds, like p2, because that's where the real physics happens.

Kai: Yeah, so tuning the sparsity parameter p near p2 seems like the sweet spot for maximizing both power and efficiency in this model.

Mira: It’s a reminder that we don't need infinite connectivity to get interesting quantum effects in energy storage models.

Lev: And for us, it means focusing on finding those structural configurations where we can achieve this benefit without needing an impossibly large system size.

Kai: Next up, we’ll be looking at some papers on radiative spin caloritronics in nonreciprocal many-body systems.

Dipartimento di Fisica ed Astronomia G. Galilei, University of Padua · National Institute of Nuclear Physics Padova Section

quant-ph, cond-mat.str-el, nlin.CD

Submitted: 2025-05-23

Updated: 2026-10-21

Comments: 12 pages, 14 figures

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 83/100

The gist: The gist The sparse version of the Sachdev-Ye-Kitaev model shows that reducing its complexity can lead to more efficient quantum batteries, provided the system remains sufficiently chaotic.

Key concepts

Sparse SYK Model: This is a simplified version of the complex Sachdev-Ye-Kitaev model where most interaction terms are randomly removed with probability 'p'. This allows researchers to study quantum chaotic features while significantly reducing the computational and experimental difficulty associated with fully connected models.
Quantum Chaos: This refers to the chaotic behavior observed in a quantum system, which is crucial for efficient energy storage. In this context, it is analyzed using tools from random matrix theory to understand how the energy levels of the system behave under different levels of interaction complexity.
Critical Sparsity ($p_2$): This is a specific threshold value for the sparsity parameter 'p' where the system transitions from being fully chaotic to losing spectral rigidity. The authors found that battery performance is significantly enhanced when tuning the system close to this critical point, indicating a delicate balance between complexity and chaos.

Terminology

Robustness — 1× in this paper · explained in 6 episodes
SYK Model — 1× in this paper · explained in 2 episodes

Summary

The gist The sparse version of the Sachdev-Ye-Kitaev model shows that reducing its complexity can lead to more efficient quantum batteries, provided the system remains sufficiently chaotic.

Introduction and Motivations

The quest for efficient energy storage and work extraction has been a cornerstone of several technological breakthroughs, dating back at least to the first industrial revolution, with its profound connection to the development of thermodynamics as the backbone for our scientific understanding of Nature Nowadays, as material samples are brought to increasingly lower temperatures and smaller sizes, we are experiencing a nanoscale industrial revolution Here, the challenge of energy storage takes on a quantum mechanical dimension, where centuries-old thermodynamic concepts must be revisited in the light of non-classical resources such as quantum coherence and entanglement Indeed, the interplay between entanglement generation and work extraction from many-body quantum states has spurred a sustained research effort into quantum batteries It is now clear that quantum battery engineering hinges on balancing complexity and controllability This tension motivates the exploration of minimal platforms where access to such observables is amenable to analytical and computational analysis.

The Sparse SYK Model

The authors investigate the sparse version of the SYK model, where interaction terms are removed with a certain probability By pruning a fraction of the couplings, quantum chaotic features—instrumental for efficient energy storage—are retained while mitigating computational and experimental overhead Even more interestingly, our results demonstrate that such sparsification can actually enhance battery performance, provided the system remains sufficiently chaotic. The complex SYK (cSYK) model is defined by a Hamiltonian with all-to-all random interactions The sparse version of Eq. (1) is simply implemented by introducing, for each coupling, an additional random variable xijkl being equal to 1 with probability p and 0 otherwise.

Quantum Chaos and Sparsity

The quantum chaotic character of the SYK model reflects on specific features of its energy spectrum, which can be analyzed by means of tools from random matrix theory (RMT) The nearest-neighbor gap ratio quantifies the repulsion between energy levels at scales of the mean level spacing Consistently with predictions from RMT, r remains approximately constant for large p, while a sharp drop is observed as soon as p approaches a critical value of sparsity usually labelled p2, signaling the dramatic breakdown of spectral rigidity The critical sparsity values p2 are highlighted in a darker shade: p2 = 0.1263 for N = 6, p2 = 0.0279 for N = 8, and p2 = 0.0097 for N = 10.

Implementing the Battery and Performance Metrics

A quantum battery is intended as a collection of N quantum cells The charging protocol is governed by HˆB(t) = Hˆ0 + λ(t)Hˆ1 (3), where λ(t) = 1 when 0 ≤ t < τc, and 0 elsewhere. The average charging power is defined as P(τc) = EN (τc)/τc, where the stored energy EN (τc) is given by Eq. (5) In Fig. 3, we report the maximum charging power, Pmax = max τc P(τc), as a function of the sparsity parameter p for N = 8 Remarkably, by reducing p (i.e., increasing sparsity), we observe a significant enhancement in the maximum power, which reaches its peak near the critical threshold p ≈ p2.

Battery Efficiency and Scaling

A key quantity is the battery efficiency e(τc) = EN/2(τc) / ergotropy In Fig. 4, we report our numerical results concerning the battery efficiency as defined in Eq. (6) for different values of the sparsity parameter, with different comments now in order As p approaches the critical value p2 (dashed vertical lines), spectral rigidity breaks down and loss of chaotic features lead to a sharp decline in the efficiency. The results confirm that sparse Hamiltonians still exhibit non-trivial scaling, suggesting that the observed enhancement is a fundamental consequence of the underlying interaction structure rather than a protocol-dependent artifact.

Experimental Considerations

Implementing a sparse model may enable experimentalists to overcome significant bottlenecks displayed by the full version Even within ultracold atomic gases, implementing the fully connected SYK would require 4 ·10 cubed lasers just for the N = 16 fermions A similar N is achieved by considering mesoscopic graphene flakes at strong disorder and magnetic field, by considering the electrons in the lowest Landau level Implementing a sparse version represents an appealing alternative.

Conclusions

Our work underscores the potential of sparse quantum systems as a viable path toward the goal of implementing robust quantum batteries, offering a blueprint for harnessing quantum resources without succumbing to impractical complexity We have first shown that, starting from the fully connected SYK model, quantum chaotic features persist down to a critical value (p2) of the sparsity parameter, a threshold where spectral rigidity breaks down Remarkably, we show that moving closer to p2 from above positively affects the battery performance. Ultimately, this approach also sheds light on the fundamental interplay between complexity, chaos and energy scale at the nanoscale.

Acknowledgements

The authors acknowledge financial support from the Project PARD 2024 “Role of disorfigure in work extraction and energy storage for SachdevYe-Kitaev quantum batteries” within the Project ”Frontiere Quantistiche” (Dipartimenti di Eccellenza) of the Italian Ministry for Universities and Research, and from the European Union-Next Generation EU within the “National Center for HPC, Big Data and Quantum Computing” (Project No. CN00000013, CN1 Spoke 10 - Quantum Computing). The authors thank M. Di Liberto for the concession of Virtual Machine at CloudVeneto, and F. Campaioli for stimulating discussion

Code Availability

All the codes employed in this paper are publicly available [47]. They have been developed thanks to the open-source Python framework QuTiP.

Supplemental Material

The Jordan-Wigner transformation maps the complex SYK onto a spin-1/2 model providing a more convenient numerical platform The spectral form factor (SFF) provides a robust measure of spectral rigidity and is commonly defined in terms of the analytically continued partition function Z(τ) as follows As an exemplary case, we compute the SFF for N = 8, as reported in Fig. 6 Evidently, the fully connected case p = 1 (solid blue line) displays the expected dip–ramp–plateau structure characteristic of quantum chaotical systems As sparsity increases (i.e. as p decreases), we observe a suppression of the ramp and a lifting of the plateau. The population dynamics are provided by Eq. (11) where pk(t) = X i⟨k, i⟩Ψ(t) squared / 2 As first noticed in [23] regarding the fully connected cSYK model (i.e., the p = 1 case), such a charging protocol induces a peculiar non-local dynamics in energy space. The stored energy EN (τc) is given by Eq. (12) as a function of τc, i.e., the duration of the charging protocol, and normalized to the number of battery cells Remarkably, by lowering p (i.e. by increasing sparsity) we see a significant increase in the energy we are able to stored in the battery. The DKL(J Jsp) measures the statistical distance from the fully-connected model via the Kullback-Leibler divergence

Figure 5 Analysis

The scaling of ⟨⟨∆τ⋆Hˆ2α⟩⟩, namely ∆τ⋆Hˆ2α averaged over disorder [23], with N, evaluated at the optimal time τ⋆, for which P(τ⋆) = Pmax The left panel shows the scaling behavior related to Hˆ1. In the fully connected limit (p = 1, blue circles), the observable exhibits an approximately linear growth with N, closely matching the ∼ N reference scaling. Conversely, a markedly different trend emerges in the sparse regime (p = p2, green circles): the quantity grows significantly faster than linearly, revealing a clear super-linear enhancement. Since this boost is driven solely by the tuning of the sparsity parameter p, it is identified as a non-genuine quantum advantage.

Improvements for AI systems

Reduce computational overhead in quantum simulations by pruning interaction terms from large all-to-all models, as this is done to mitigate significant practical bottlenecks regarding system size associated with fully connected SYK couplings.
Design quantum battery charging protocols that operate near the critical sparsity value p2, because the maximum charging power Pmax reaches its peak near the critical value p approx p2, where the system transitions from a chaotic to a nonchaotic regime.
Develop energy storage algorithms that leverage reduced complexity by employing sparse Hamiltonians, as this approach shows EN (τc) saturating approximately p p2, a confirmation that the battery performance are predicated on retaining at least some degree of its quantum chaotic behavior in the fully connected (p = 1) case.
Create AI systems capable of quantifying genuine quantum advantage by analyzing scaling behaviors such as the quantity grows significantly faster than linearly, revealing a clear super-linear enhancement when tuning the sparsity parameter p to p2.
Implement robust energy extraction methods that are less sensitive to implementation size by utilizing sparse charging Hamiltonians, as this suggests a non-genuine quantum advantage, arising from the structural reconfiguration of the interactions rather than the intrinsic nature of the operators.

Abstract

In the context of energy storage at the nanoscale, exploring the notion of quantum advantage implies walking on the thin line at the boundary between quantum mechanics and thermodynamics, which underpins our conventional understanding of battery devices. With no classical analogue, the Sachdev-Ye-Kitaev (SYK) model has emerged in the last years as a promising platform to boost charging and storage efficiency thanks to its highly-entangling dynamics. Here, we explore how the robustness of this setup by considering the sparse version of the SYK model, showing that, as long as chaos is not completely broken, reducing its complexity may lead to more efficient quantum batteries amplifying the charging power.