This project implements distributed quantum Gaussian process regression using Riemannian ADMM optimization for real-world datasets and quantum-generated synthetic data.
├── main.py # Main distributed QGPR with Riemannian ADMM
├── agent_riemannian.py # Quantum agent with Riemannian optimization
├── riemannian_optimizer.py # Riemannian optimization framework
├── real_world_datasets.py # Real-world dataset loaders (SRTM elevation)
├── requirements.txt # Project dependencies
└── README.md # This file
pip install -r requirements.txt# 2D quantum GP synthetic data with default settings
python main.py --input-dim 2 --n-dataset 1000 --n-agents 4
# SRTM elevation dataset (real-world 2D data)
python main.py --real-world-dataset srtm --srtm-region maharashtra \
--dataset-max-samples 1000 --n-agents 4The SRTM (Shuttle Radar Topography Mission) elevation dataset provides real-world 2D spatial data from different geographic regions.
# Maharashtra, India
python main.py --real-world-dataset srtm --srtm-region maharashtra \
--dataset-max-samples 1000 --dataset-normalize \
--encoding chebyshev --kernel-type projected --num-layers 3 \
--num-qubits 4 --outer-kernel matern \
--rho 100 --L 100 --n-agents 4
# Great Lakes, North America
python main.py --real-world-dataset srtm --srtm-region great_lakes \
--dataset-max-samples 1000 --dataset-normalize \
--encoding chebyshev --kernel-type projected --num-layers 3 \
--num-qubits 4 --outer-kernel matern \
--rho 100 --L 100 --n-agents 4
# Oregon Coast, USA
python main.py --real-world-dataset srtm --srtm-region oregon_coast \
--dataset-max-samples 1000 --dataset-normalize \
--encoding chebyshev --kernel-type projected --num-layers 3 \
--num-qubits 4 --outer-kernel matern \
--rho 100 --L 100 --n-agents 4
# Washington Coast, USA
python main.py --real-world-dataset srtm --srtm-region washington_coast \
--dataset-max-samples 1000 --dataset-normalize \
--encoding chebyshev --kernel-type projected --num-layers 4 \
--num-qubits 5 --outer-kernel matern \
--rho 100 --L 100 --n-agents 4Generate data using quantum Gaussian processes for authentic quantum ML research.
# 2D Quantum GP data (default - no classical function)
python main.py --input-dim 2 --n-dataset 1000 \
--encoding hubregtsen --kernel-type projected --num-layers 1 \
--num-qubits 3 --outer-kernel matern \
--rho 100 --L 100 --n-agents 4
# 2D with specific encoding circuit
python main.py --input-dim 2 --n-dataset 1000 \
--encoding chebyshev --kernel-type projected --num-layers 1 \
--num-qubits 3 --outer-kernel matern \
--rho 100 --L 100 --n-agents 4
# Save dataset for later use
python main.py --input-dim 2 --n-dataset 1000 --save-dataset --dataset-name my_qgp_2dThe implementation supports two main dataset types:
Generated using quantum Gaussian processes with parameterized quantum circuits for authentic quantum ML research. The data is truly quantum in nature, not from classical test functions.
Properties:
- Input dimensions: 1D to 6D supported
- Quantum-generated target values using fidelity or projected quantum kernels
- Multiple encoding circuits: Chebyshev, YZ-CX, Hubregtsen, Kyriienko, etc.
- Tunable noise levels for realistic scenarios
Shuttle Radar Topography Mission (SRTM) elevation data providing real-world 2D spatial regression problems.
Available Regions:
- Maharashtra, India: Complex terrain with varying elevations
- Great Lakes, North America: Large-scale water and land features
- Oregon Coast, USA: Coastal topography with elevation gradients
- Washington Coast, USA: Diverse coastal and mountain terrain
Properties:
- Input: 2D coordinates (latitude, longitude)
- Output: Elevation measurements (meters)
- Use case: Spatial regression, environmental modeling
- Features: Real-world spatial correlations, measurement noise
| Feature | Description | Benefit |
|---|---|---|
| Riemannian Optimization | Treats quantum circuit parameters as points on a torus manifold | Better convergence for periodic rotation parameters |
| Distributed ADMM | Consensus-based parameter optimization across agents | Scalable quantum GP with privacy preservation |
| 2D Focus | Optimized for 2D spatial problems | Visualization and interpretability |
| Real SRTM Data | Actual elevation measurements | Realistic GP benchmarks |
| Quantum Kernels | Fidelity & Projected kernels with multiple encodings | Flexible quantum feature spaces |
| Cross-Validation | NLPD-based model selection | Robust hyperparameter tuning |
--n-agents: Number of distributed agents (default: 4)--num-qubits: Quantum circuit qubits (default: 4)--num-layers: Encoding circuit layers (default: 2)--encoding: Circuit type -chebyshev,hubregtsen,yz_cx,kyriienko, etc.--kernel-type:fidelityorprojected--outer-kernel: For projected kernels -gaussian,matern,expsinesquared, etc.--rho: ADMM penalty parameter (default: 100.0)--L: Lipschitz constant (default: 100.0)
--riemannian-method:gradient_descent,momentum, orconjugate_gradient--riemannian-lr: Learning rate (default: 0.015)--riemannian-beta: Momentum/CG parameter (default: 0.9)--gradient-clip-norm: Gradient clipping (default: 1.0)--max-step-size: Maximum step size (default: 0.1)
--partition: Data split method -regional,random, orsequential--test-split: Test set ratio (default: 0.1)--noise-std: Observation noise (default: 0.1)--dataset-normalize: Normalize features and targets
The code generates:
- Convergence plots for ADMM iterations
- Prediction vs ground truth visualizations
- Cross-validation NLPD scores
- Agent-wise performance metrics
- Kernel matrix condition numbers
This implementation is designed for research in:
- Quantum machine learning
- Distributed Gaussian processes
- Riemannian optimization for quantum circuits
- Spatial regression with quantum methods
- ADMM consensus algorithms
If you use this code in your research, please cite:
@inproceedings{gandhi2026distributed,
title={Distributed Quantum Gaussian Processes for Multi-Agent Systems},
author={Gandhi, Meet and Kontoudis, George P},
booktitle={International Conference on Autonomous Agents and Multiagent Systems (AAMAS)},
year={2026},
doi={10.65109/ADPL7324}
}