Quantum simulation of traversable-wormhole-inspired quantum teleportation in a chaotic binary sparse SYK model

The gist The experimental observation of holographically motivated quantum teleportation on a quantum processor, driven by the highly entangled, chaotic dynamics of a many-body system establishes a practical, scalable framework for holographic quantum simulations

Traversable Wormhole Protocol

The traversable-wormhole (TW) protocol is utilized to investigate holographically motivated teleportations by injecting a qubit into the left boundary and reading it out from the right boundary The protocol starts from the initial state Bell⟩P Q ⊗ TFD⟩LR ⊗ 0⟩T, where Q is the message qubit injected into the wormhole, and P and T are reference and target qubits, respectively At inverse temperature β, the TFD state is defined as TFD⟩LR = 1/√Z X n e −βEn/2n⟩L ⊗ n⟩R, where Z is the partition function The protocol injects a qubit into the wormhole at t = −t0 by applying a SWAP operation constructed from the Dirac operator √1/2(ψ1L + iψ2L) [11, 35], following the JW transformation of Ref. [6] Throughout the protocol, the time-evolution operator is U(t) = e −iHtott where Htot = HL + HR At t = 0 we apply the instantaneous fermionic bilinear coupling e iµV, V = 1/qN Hint, (3) where µ is the coupling strength and Hint = i PN j=1 ψjLψjR In the holographic interpretation, with the sign convention adopted here, µ < 0 corresponds to ANEC violation and hence to traversability [9, 11]

Binary Sparse SYK Model

A central obstacle to executing this protocol on nearterm hardware is the dense q-local SYK Hamiltonian, which contains all-to-all interaction terms This high connectivity necessitates prohibitively deep quantum circuits, rendering the simulation highly susceptible to decoherence and noise accumulation on noisy intermediate-scale quantum (NISQ) devices To circumvent this limitation, sparse SYK constructions are strongly motivated The binary sparse SYK model [34] is employed because it preserves spectral signatures of quantum chaos—such as the spectral form factor (SFF) and level-spacing statistics—with efficiency under aggressive sparsification For the binary sparse N = 8 SYK model, we find that the spectral diagnostics remain close to those of the dense model and to the GOE prediction down to K ≈ 10 This specific Hamiltonian is favorable for hardware compilation because it contains many commuting pairs (34 commuting versus 11 anticommuting pairs), which helps term grouping in Trotterized evolution

Hardware Implementation and Working Point

The hardware implementation involves preparing the approximate TFD state variationally using a variational quantum algorithm (VQA) [42] with a fixed ansatz of single-qubit SU(2) rotations and entangling gates, achieving about 92.7% fidelity For real-time evolution, a single-step first-order Lie–Trotter decomposition is used The working point t0 = 1.8 is chosen because the teleportation signal remains large, while the Trotterization error remains tolerable, providing a practical upper bound on the injection time for the hardware implementation This choice of t0 = 1.8 lies inside a finite causal time-ordering window where wormhole-like causal dynamics are preserved over a finite time interval

Diagnostics and Robustness

Traversability is diagnosed by the mutual information IP T (t0, t1) = SP (t0, t1) + ST (t0, t1) − SP T (t0, t1) The protocol exhibits a clear sign-dependent asymmetry quantified by ∆IP T ≡ Iµ0 P T, which is positive in the same time window Size winding diagnostics show that near-perfect size winding is characterized by phase coherence within each size sector, measured by R(l) ≃ 1, together with an approximately linear dependence of arg q(l) on l across different size sectors The chosen Hamiltonian retains the near-perfect size winding near the protocol-relevant time window Furthermore, other disorder realizations in the same ensemble also exhibit qualitatively similar mutual information dynamics, indicating that the mutual information behavior is a generic feature of the ensemble rather than a peculiarity of the chosen Hamiltonian

Conclusion

The paper concludes that within a binary sparse SYK regime that remains chaotic, the characteristic TW-protocol signal survives execution on present-day quantum hardware This work represents the first quantum-hardware realization of the TW protocol utilizing an explicitly chaotic Hamiltonian Looking forward, a compelling theoretical extension is the investigation of commuting [49] and d-commuting SYK models The robust binary sparsification framework established here can be generalized to other quantuminformational probes, including out-of-time-order correlators (OTOCs) and Krylov complexity This offers a highly viable path toward executing complex phenomena, most notably the Hayden–Preskill protocol [51–54]

Acknowledgements

The authors thank Jeongho Bang and Kyoungho Cho for valuable discussions, helpful correspondence, and for providing access to the quantum processor This work was supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT & Future Planning(NRF-2021R1A2C1006791), the Korea government(MSIT)(RS-2025-02311201), (RS-2024- 00445164) and the framework of international cooperation program managed by the NRF of Korea(RS2025-02307394), the Creation of the Quantum Information Science R&D Ecosystem(Grant No. RS-2023- NR068116) through the National Research Foundation of Korea(NRF) funded by the Korean government(Ministry of Science and ICT). This research was also supported by GIST research fund (Future leading Specialized Research Project, 2026, and the Regional Innovation System & Education(RISE) program through the (Gwangju RISE Center), funded by the Ministry of Education(MOE) and the (Gwangju Metropolitan City), Republic of Korea(2025-RISE-05-001)

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The gist The experimental observation of holographically motivated quantum teleportation on a quantum processor, driven by the highly entangled, chaotic dynamics of a many-body system establishes a practical, scalable framework for holographic quantum simulations

Traversable Wormhole Protocol

The traversable-wormhole (TW) protocol is utilized to investigate holographically motivated teleportations by injecting a qubit into the left boundary and reading it out from the right boundary The protocol starts from the initial state Bell⟩P Q ⊗ TFD⟩LR ⊗ 0⟩T, where Q is the message qubit injected into the wormhole, and P and T are reference and target qubits, respectively At inverse temperature β, the TFD state is defined as TFD⟩LR = 1/√Z X n e −βEn/2n⟩L ⊗ n⟩R, where Z is the partition function The protocol injects a qubit into the wormhole at t = −t0 by applying a SWAP operation constructed from the Dirac operator √1/2(ψ1L + iψ2L) [11, 35], following the JW transformation of Ref.

1. Improved AI systems can perform holographically motivated quantum simulations by utilizing binary sparse Sachdev–Ye–Kitaev (SYK) models to simulate traversable-wormhole (TW) protocols, which dramatically reduces circuit depth for noisy intermediate-scale quantum (NISQ) hardware while rigorously preserving the spectral chaos required for gravitational duality.

2. The improved system can empirically test holographic quantum gravity by observing a sign-dependent asymmetry in the mutual information between the reference and target qubits, which is diagnosed as a sign-dependent asymmetry in experimental results, even when inherent noise in NISQ hardware prevents perfect quantitative agreement with exact numerical simulations.

3. The AI can generate hardware-efficient Hamiltonians for TW protocols by systematically identifying a binary sparse SYK Hamiltonian that is both sufficiently shallow for near-term quantum devices and robustly chaotic, using spectral diagnostics like the Gaussian-filtered SFF and level-spacing distribution to ensure consistency with random-matrix theory (RMT) predictions.

4. The system can execute complex quantum information transfer protocols by implementing the TW protocol on superconducting IBM quantum processors, achieving a measurable sign-dependent asymmetry more explicit[ly] and exhibiting a clear peak near the teleportation time, which is consistent with exact results, thereby providing the first quantum-hardware realization of the TW protocol driven by an explicitly chaotic Hamiltonian.

5. The improved system can ensure causal signal integrity by verifying that the chosen hardware working point lies inside this window [of wormhole-like causal dynamics over a finite time interval], confirming that the system preserves the causal ordering of injected signals and exhibits behavior consistent with first-in–first-out behavior.