SYK Holography Simulation Framework

This repository contains the reference implementation for the paper "Geometry of Traversable Wormholes and Quantum Chaos in Magnitude-Pruned SYK Models".

It provides a high-performance, tensor-optimized framework for simulating Sachdev-Ye-Kitaev (SYK) quantum many-body systems. The codebase focuses on holographic properties, including wormhole traversability (OTOC), spectral form factors (SFF), and chaos indicators (Gap Ratio) across different sparsity levels and geometries.

Installation

git clone https://github.com/leotam/sparse_syk_gravity
cd sparse_syk_gravity
pip install -e .

Docker (Recommended)

For optimal performance, especially for the GPU-accelerated experiments (Figure 5), we recommend using the NVIDIA cuQuantum container.

Pull and run the container:

nvidia-docker run --gpus all -it --rm \
    --entrypoint /bin/bash \
    -v $(pwd):/workspace/syk-research \
    nvcr.io/nvidia/cuquantum-appliance:25.11-cuda12.9.1-devel-ubuntu24.04-x86_64

Usage

The simulations are driven by a single CLI entry point: run_experiment.py.

Figure 1: Compression Benchmark

Evaluates the robustness of the traversable wormhole protocol as the Hamiltonian is sparsified.

time python run_experiment.py benchmark --ensemble 40

Figure 2: Phase Diagram

Sweeps system sizes ((N=4) to (12)) and sparsities to map the "Holographic Phase" boundary where the wormhole remains open.

time python run_experiment.py phase_diagram --ensemble 40

Data is saved to v2syk_phase_data/ and allows for resuming interrupted runs.

Figure 3: Linear Geometry

Simulates a 1D chain geometry (Linear SYK) to test teleportation fidelity in non-all-to-all connected systems.

time python run_experiment.py linear --ensemble 32

Figure 4: Shapiro Delay

Measures the time delay of the signal as a function of the perturbation strength (simulating the gravitational Shapiro delay).

time python run_experiment.py shapiro --sparsity 0.1 --ensemble 1000

Figure 5: GPU Gap Ratio

Calculates the adjacent gap ratio to detect the transition from chaotic (GUE) to integrable (Poisson) statistics.

time python run_experiment.py gpu_gap --ensemble 8

Hardware Note: The results in the paper for Figure 5 were generated using 2x NVIDIA RTX A6000 GPUs. The rest is run on a 48 core, 128GB RAM machine.

Project Structure

• src/physics: Core logic for Hamiltonian generation, Majorana algebra, and time evolution.
• src/experiments: Standalone modules corresponding to each figure in the paper.
• src/config.py: Thread safety configurations and physics constants (J=1.0, beta=4.0).

If you want a fast smoke test run:

time python run_experiment.py benchmark --ensemble 2 --sparsity 1.0
time python run_experiment.py phase_diagram --n_values 4 --ensemble 2 --sparsity 1.0
time python run_experiment.py linear --ensemble 2 --sparsity 1.0
time python run_experiment.py shapiro --ensemble 2 --n_majoranas 8
time python run_experiment.py gpu_gap --gpus 0 --n_values 16 --ensemble 1 --sparsity 1.0

FIGURE 1: SYK COMPRESSION BENCHMARK (Ensemble=2)
Sp 100.0% | Terms: 495/495 | Peak: 0.0309 | SFF Ratio: 1.37

Generating Figure 1...
Saved figure to figures/figure1_benchmark.png

FIGURE 2: PHASE DIAGRAM SWEEP
Running N=4 Sp=1.0...
Generating Figure 2...

FIGURE 3: LINEAR GEOMETRY SWEEP
Running 10 simulations...
[Parallel(n_jobs=-1)]: Using backend LokyBackend with 48 concurrent workers.
[Parallel(n_jobs=-1)]: Done   2 out of  10 | elapsed:    0.7s remaining:    2.8s
[Parallel(n_jobs=-1)]: Done   5 out of  10 | elapsed:    0.7s remaining:    0.7s
[Parallel(n_jobs=-1)]: Done   8 out of  10 | elapsed:    0.7s remaining:    0.2s
[Parallel(n_jobs=-1)]: Done  10 out of  10 | elapsed:    0.9s finished

FIGURE 4: SHAPIRO DELAY (N=8, Ensemble=2)
Simulating Strength 0.00...
Simulating Strength 0.39...
Simulating Strength 0.79...
Simulating Strength 1.18...
Simulating Strength 1.57...

============================================================
FIGURE 5: GPU GAP RATIO SCALING
GPUs: [0] | N_Values: [16] | Ensemble: 1
============================================================
Running 1 tasks...
Total Runtime: 5.36s
Saved figures/figure5_gap_scaling.png

License & Citation

This code is released under the Apache 2.0 License. If you use this software in your research, please cite our work:

@article{MagSYK,
  title={Geometry of Traversable Wormholes and Quantum Chaos in Magnitude-Pruned SYK Models},
  author={Tam, Leonidas and Woodside, Barrett},
  journal={Zenodo},
  year={2025},
  doi={10.5281/zenodo.18037727},
  url={https://doi.org/10.5281/zenodo.18037727}
}