Gravitational Wave-Induced Scrambling Delay in SYK Wormhole Teleportation

Abstract

Traversable wormhole teleportation in the Sachdev-Ye-Kitaev (SYK) model links quantum channel integrity to black hole interior dynamics, using teleportation fidelity to probe holographic scrambling. We subject the SYK boundary to a gravitational-wave (GW)-inspired periodic Floquet deformation, mimicking a leading-order metric-strain perturbation from the JT-gravity dictionary. We characterize the channel response via exact numerical time evolution with disorder averaging at $βJ = 2$. The drive produces a coherent, frequency-selective fidelity suppression, yielding four main results: (i) two amplitude regimes separated near $\varepsilon \sim J$ (perturbative sensing vs.\ strong-drive); (ii) the channel acts as a low-pass filter, most sensitive at $ω\lesssim β^{-1}$ with monotone recovery above the thermal scale; (iii) an inspiral chirp drive delays the fidelity peak by $Δt_{\rm scr}^{(\rm fid)} = +0.11\, J^{-1}$, corroborated by an out-of-time-order correlator (OTOC) diagnostic ($Δt_{\rm scr}^{(\rm OTOC)} = +0.20\, J^{-1}$), establishing a genuine scrambling delay; and (iv) the effects persist across $N \in \{10, 12, 14, 16\}$ Majorana modes, indicating no systematic finite-size suppression. These results establish that holographic teleportation channels degrade gracefully under GW-inspired boundary deformations, with direct implications for near-term quantum processor implementations of traversable wormholes.

Figures (9)

• Figure 1: Schematic of the GW-perturbed wormhole teleportation protocol(GW-WITP)
• Figure 2: Trotter integrator convergence ($N=12$, $\beta J=2$). (a) Teleportation fidelity $\mathcal{F}$ vs. step size $\delta t$ using the first-order Lie--Trotter (LT) integrator for six representative parameter points: the unperturbed protocol, monochromatic drives at $(\varepsilon,\omega)=(0.20\,J,\,1.50\,J)$, $(0.50\,J,\,0.50\,J)$, $(1.50\,J,\,1.50\,J)$, $(0.20\,J,\,3.14\,J)$, and the inspiral chirp of Fig. \ref{['fig:chirp']}. Fidelity is stable across $\delta t = 0.0500$--$0.0125\,J^{-1}$. (b) Absolute difference $|\mathcal{F}_{\rm LT} - \mathcal{F}_{\rm Strang}|$ vs. $\delta t$ (log-log); the midpoint-evaluated Strang integrator achieves $O(\delta t^2)$ convergence, approximately $40\times$ lower error than LT at the same step size. (c) LT convergence increment $|\Delta\mathcal{F}|$ compared to the statistical noise floor $\sigma_{\rm dis}/\sqrt{N_{\rm avg}}$ for each test point; all physical points ($\varepsilon\leq 1\,J$) lie below the noise floor.All main-text results use $\delta t = 0.05\,J^{-1}$; the adaptive scheme $\delta t = 0.05/(1 + 0.5\varepsilon)\,J^{-1}$ is used at $\varepsilon > 1\,J$ (Fig. (\ref{['fig:amplitude']})), and step-size halving was verified to keep $|\Delta\mathcal{F}|$ below the noise floor across the full scanned range $\varepsilon \in [0, 2.5\,J]$.
• Figure 3: Disorder-averaged teleportation fidelity $\mathcal{F}$ versus GW strain amplitude $\varepsilon$ at fixed drive frequency $\omega=1.5\,J$ ($N=12$, $\beta J=2$, $N_{\rm avg}=20$). Shaded bands denote $\pm\sigma_{\rm dis}/\sqrt{N_{\rm avg}}$. The classical benchmark $\mathcal{F}=0.25$ is shown for reference. Across the scanned range $\varepsilon\in[0,2.5J]$, the channel remains well above the classical limit while exhibiting a smooth, monotone suppression with a visibly accelerating rate above the sensing-to-strong-drive crossover near $\varepsilon \sim J$. Inset: Fractional quantum advantage $R(\varepsilon)=(\mathcal{F}(\varepsilon)-0.25)/(\mathcal{F}_0-0.25)$, measuring the fraction of the unperturbed quantum channel capacity retained under the GW drive. $R$ remains above $90\%$ throughout the entire sensing regime $\varepsilon\lesssim J$, dropping below this threshold around the onset of the strong-drive regime $\varepsilon\gtrsim J$ (dashed vertical line). Quantum-advantage teleportation is maintained across the full sensing regime relevant to the results of this paper.
• Figure 4: Teleportation fidelity $\mathcal{F}$ as a function of GW driving frequency $\omega$ at fixed strain amplitude ($N=12$, $\beta J=2$). Two physically distinct frequencies are marked: the thermal scale $\omega_T = \beta^{-1} = 0.50\, J$, which separates the quasi-static and dynamical driving regimes, and the MSS chaos scale $\omega_L = 2\pi/\beta = 3.14\, J$ (large-$N$ chaos timescale). Fidelity suppression is maximum in the quasi-static limit $\omega \to 0$ and decreases monotonically with $\omega$, consistent with a low-pass crossover at $\omega_T$. The sensitivity is not peaked within $[\omega_T, \omega_L]$; $\omega_L$ marks the empirical recovery scale rather than a band edge. The monotone frequency dependence establishes a low-pass response of the calibrated teleportation channel to GW-inspired boundary deformations.
• Figure 5: Time-domain comparison of the injected GW chirp waveform $h(t)$ (left axis, normalised) and the induced SYK boundary strain energy $H_{\rm GW}(t)$ (right axis, in units of $J$) as functions of time $t$ during the teleportation protocol. The boundary energy tracks the injected waveform in both phase and amplitude, demonstrating that the SYK boundary faithfully encodes the temporal structure of the GW drive. The temporal correlation between $h(t)$ and $H_{\rm GW}(t)$ (or $S_R(t)$) directly underlies the fidelity distortion.