The realization of holographic duality on near-term intermediate-scale quantum (NISQ) hardware requires identifying sparse Hamiltonians that retain essential gravitational features. While previous approaches rely on machine-learning optimization to find such models, we demonstrate that simple magnitude-based pruning of the Sachdev-Ye-Kitaev (SYK) model preserves holographic transport at sparsities ≈5%. By mapping the phase diagram of sparsified SYK (N ≤ 12), we identify a distinct phase boundary where quantum chaos, diagnosed via the Spectral Form Factor (SFF), dissolves, even while traversable wormhole signatures persist. This decoupling suggests that information scrambling can occur without the emergent geometry required for gravity. We validate the gravitational phenomenon of the chaotic phase by observing a quantized Shapiro time delay in the teleportation signal with perturbation, consistent with the emergence of bulk geometry. Finally, we show that this robustness is unique to all-to-all connectivity. Imposing linear local geometry destroys the holographic phase, highlighting non-locality as critical for quantum gravity simulations.
A bstract The Sachdev-Ye-Kitaev (SYK) model is a system of N Majorana fermions with random interactions and strongly chaotic dynamics, which at low energy admits a holographically dual description as two-dimensional Jackiw-Teitelboim gravity. Hence the SYK model provides a toy model of quantum gravity that might be feasible to simulate with near-term quantum hardware. Motivated by the goal of reducing the resources needed for such a simulation, we study a sparsified version of the SYK model, in which interaction terms are deleted with probability 1 −p . Specifically, we compute numerically the spectral form factor (SFF, the Fourier transform of the Hamiltonian’s eigenvalue pair correlation function) and the nearest-neighbor eigenvalue gap ratio r (characterizing the distribution of gaps between consecutive eigenvalues). We find that when p is greater than a transition value p 1 , which scales as 1/ N 3 , both the SFF and r match the values attained by the full unsparsified model and with expectations from random matrix theory (RMT). But for p < p 1 , deviations from unsparsified SYK and RMT occur, indicating a breakdown of holography in the highly sparsified regime. Below an even smaller value p 2 , which also scales as 1/ N 3 , even the spacing of consecutive eigenvalues differs from RMT values, signaling a complete breakdown of spectral rigidity. Our results cast doubt on the holographic interpretation of very highly sparsified SYK models obtained via machine learning using teleportation infidelity as a loss function.
We report the experimental signature of holographically motivated quantum teleportation on a quantum processor, driven by the highly entangled, chaotic dynamics of a many-body system. Specifically, we implement the traversable-wormhole (TW) protocol utilizing a \textit{chaotic} binary sparse
N=8 Sachdev--Ye--Kitaev (SYK) model. This optimized approach dramatically reduces circuit depth for noisy intermediate-scale quantum (NISQ) hardware while rigorously preserving the spectral chaos required for gravitational duality. Diagnosing the teleportation signal via mutual information, we find that while inherent noise in NISQ hardware precludes perfect quantitative agreement with exact numerical simulations, our experimental results provide evidence for the essential qualitative signature: a sign-dependent asymmetry. This work establishes a practical framework for holographic quantum simulations, offering a novel empirical testbed for exploring holographic quantum gravity.
In the Sachdev-Ye-Kitaev (SYK) model, traversable wormhole teleportation fidelity probes the many-body scrambling of holographic black holes. We apply a gravitational-wave-inspired periodic Floquet deformation derived from the lowest-dimensional bilinear
SYK4 sector to the boundary, thereby characterizing the channel response via exact numerical time evolution at
βJ=2. Re-optimizing under the drive isolates genuine physical effects from calibration mismatch, yielding four main results: (i) distinct perturbative and non-perturbative amplitude regimes separated near
ε∼J; (ii) a natural low-pass filter response, with maximum fidelity suppression at
ω≲β−1 and monotonic recovery above the thermal scale; (iii) a scrambling delay, evidenced by a delayed fidelity peak under an inspiral chirp (
Δtscr(fid)=+0.11J−1) and independently confirmed by OTOC measurements to grow monotonically with drive amplitude; and (iv) robust, non-zero fidelity suppression across
N∈{10,12,14,16} Majorana modes. These findings establish that holographic wormholes degrade gracefully under metric-like boundary deformations, providing direct diagnostic signatures for near-term quantum hardware.
The traversable wormhole protocol in coupled Sachdev-Ye-Kitaev (SYK) systems produces a transmission signal C(t) widely interpreted as evidence of holographic dynamics. Recent work has questioned this interpretation, showing that similar signals arise in generic thermalizing systems. We address what the signal actually probes by systematically destroying quantum chaos in the SYK model via random coupling deletion, while monitoring the transmission signal across the chaos-to-integrable transition. Using exact diagonalization of the doubled SYK model at N=10 with 50 disorder realizations per sparsity, supplemented by Krylov-subspace extensions to N=20, we find that the ensemble-averaged peak height varies by less than 1.1% across a 50-fold sparsification range, even as the underlying spectrum transitions from Gaussian-unitary-ensemble to sub-Poisson statistics. A 1,200-instance sweep over the inter-system coupling mu confirms that the signal is controlled by mu alone, with no dependence on internal chaos. We further verify that the thermofield double state retains its thermal structure under sparsification despite substantial changes to the state vector, providing a structural explanation for the invariance. These results indicate that the transmission signal diagnoses inter-system coupling fidelity rather than holographic dynamics, and that future quantum-simulation experiments require independent chaos diagnostics to substantiate gravitational claims. As a practical consequence, the invariance implies that 98% of the Hamiltonian's coupling terms can be discarded (with variance rescaling of the survivors), reducing the gate count per Trotter step by approximately 50x at N=10 and bringing larger traversable-wormhole simulations within experimental reach.
The reconciliation of unitary quantum mechanics with the smooth geometry of General Relativity remains a central challenge in quantum gravity, epitomized by the Firewall Paradox. In this work, we investigate the emergent geometry of the black hole information manifold using a metric-preserving machine learning framework. We simulate a 1D quantum black hole using the Sachdev-Ye-Kitaev (SYK) model and reconstruct its bulk geometry via an autoencoder constrained by the Quantum Bures Metric. Our analysis reveals a strong negative correlation between the thermodynamic entropy and the box-counting dimension of the emergent manifold, with finite size scaling consistent with perfect anti-correlation in the thermodynamic limit. Crucially, control experiments reveal that this correspondence is chaos-dependent: integrable free fermion systems show dramatically weaker correlations, while spatially local Heisenberg chains exhibit intermediate behavior. This establishes chaos as a key requirement for strong entropy-topology correspondence, distinguishing maximally chaotic from integrable thermal quantum states. We observe no topological phase transitions across the thermal crossover, supporting the hypothesis that high-entropy chaotic thermalization drives geometric smoothing, consistent with the ER=EPR conjecture.
We study a sparse Sachdev-Ye-Kitaev (SYK) model with
N Majoranas where only $\ensuremath{\sim}kN$ independent matrix elements are nonzero. We identify a minimum $k\ensuremath{\gtrsim}1$ for quantum chaos to occur by a level statistics analysis. The spectral density in this region, and for a larger
k, is still given by the Schwarzian prediction of the dense SYK model, though with renormalized parameters. Similar results are obtained for a beyond linear scaling with
N of the number of nonzero matrix elements. This is a strong indication that this is the minimum connectivity for the sparse SYK model to still have a quantum gravity dual. We also find an intriguing exact relation between the leading correction to moments of the spectral density due to sparsity and the leading
1/d correction of Parisi's U(1) lattice gauge theory in a
d-dimensional hypercube. In the $k\ensuremath{\rightarrow}1$ limit, different disorder realizations of the sparse SYK model show emergent random matrix statistics that for fixed
N can be in any universality class of the tenfold way. The agreement with random matrix statistics is restricted to short-range correlations, no more than a few level spacings, in particular in the tail of the spectrum. In addition, emergent discrete global symmetries in most of the disorder realizations for
k slightly below one give rise to
2m-fold degenerate spectra, with
m being a positive integer. For
k=3/4, we observe a large number of such emergent global symmetries with a maximum
28-fold degenerate spectra for
N=26.