Towards Quantum Advantage in Sparsified Bosonic SYK Models

TL;DR

The authors propose and analyze a sparsified bosonic SYK model as a tractable testbed for quantum advantage in chaotic quantum systems. By bosonizing the SYK and introducing controlled sparsification, they reduce circuit depths and study OTOCs both in classical simulations and on IBM hardware, revealing a sparsity-driven transition between chaotic and non-chaotic regimes. Key findings include rapid ensemble self-averaging for larger N and the practical challenges posed by noise on current devices, which motivate error-mitigation and hardware-aware sparsification strategies. The work also connects chaos, holography, and quantum simulation, outlining a path toward probing quantum advantage in near-term devices while highlighting substantial hurdles to be overcome. Overall, the study provides a concrete framework and initial results for leveraging chaotic bosonic SYK dynamics to explore quantum advantage and holographic ideas on NISQ-era quantum hardware.

Abstract

We advocate the sparsification of bosonic SYK models as a promising arena for the exploration of quantum advantage. We initiate the study of quantum simulations of the models, both in classical simulators and on quantum devices implemented using superconducting qubits. We point out subtleties in the quantum simulations of highly chaotic systems, which should be addressed in the future search for quantum advantage.

Figures (7)

• Figure 1: Circuit implementing the interferometric protocol to compute the OTOC. The topmost wire corresponds to the control qubit $q_c$ while the lower wire corresponds to the system qubits. The time evolution $U(t)=e^{-i Ht}$ is implemented by Trotterization.
• Figure 2: Comparison of the average value of OTOC for different numbers of ensembles for the full bosonic SYK model.
• Figure 3: Comparison of OTOC for different values of the sparsity parameter $\kappa$ with the full ensemble. 100 different Hamiltonians were used for each ensemble. Note that in order to compare the values for different $\kappa$, we need to rescale time by $1/\sqrt{p}$ with $p$ given in Eq. \ref{['Eq: sparsity parameter']}.
• Figure 4: Comparison of OTOC for different numbers of samples in an ensemble of the sparse bosonic SYK for $N=20$ and $\kappa = 0.1,1,2$.
• Figure 5: OTOC for $N = 8$ with $\kappa = 0.1,0.5,1,2$ respectively. For $\kappa =2$, we have removed the $Jt=0.03$ data point, which falls significantly outside the relevant range and adversely affects the clarity of the plotted results. The circuit depths are listed in Table \ref{['Table:Depth for sims']}.