Quantum advantage in batteries for Sachdev-Ye-Kitaev interactions

TL;DR

This paper analytically investigates how quantum advantage in charging quantum batteries can be achieved with sparse SYK interactions, showing that disorder can lead to power scaling as the square of the number of cells.

Contribution

It provides a simple model and analytical results demonstrating the conditions under which quantum advantage scales favorably in fermionic systems with disorder.

Findings

Quantum advantage scales as N^{(α-q)/2 + 1} for certain SYK interactions.

Disorder can enable power scaling as N^2 in quantum batteries.

Analytical expressions relate connectivity and interaction parameters to quantum advantage.

Abstract

A quantum advantage can be achieved in the unitary charging of quantum batteries if their cells are interacting. Here, we try to clarify with some analytical calculations whether and how this quantum advantage is achieved for sparse Sachdev-Ye-Kitaev (SYK) interactions and in general for fermionic interactions with disorder. To do this we perform a simple modelization of the interactions. In particular, we find that for $q$-point rescaled sparse SYK interactions the quantum advantage goes as $\Gamma\sim N^{\frac{\alpha-q}{2}+1}$ for $q\geq\alpha\geq q/2$ and $\Gamma\sim N^{1-\frac{\alpha}{2}}$ for $q/2>\alpha\geq 0$, where $\alpha$ is related to the connectivity and $N$ is the number of cells. This shows how we can get $\Gamma\sim N$, i.e., an average power that scales as $N^2$ thanks to the disorder.