quantum-transport-clustering

name: quantum-transport-clustering description: "Qlustering: Unsupervised clustering via steady-state quantum transport in GKSL-governed quantum networks. Data encoded as input states, cluster assignments inferred from terminal output currents. Use when: quantum machine learning, unsupervised quantum clustering, GKSL master equation applications, open quantum network learning, quantum data clustering, or algorithm-hardware co-design for quantum ML."

Qlustering — Quantum Transport for Unsupervised Clustering

Analog quantum computation framework for unsupervised clustering using steady-state quantum transport in open quantum networks (arXiv: 2605.10844).

Core Idea

Cluster data by encoding it as quantum states in an open quantum network and reading out cluster assignments from steady-state terminal currents — no full state tomography required.

GKSL Master Equation

The quantum network evolves under the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation:

dρ/dt = -i[H, ρ] + Σ_k γ_k (L_k ρ L_k† - ½{L_k†L_k, ρ})

Where:

• ρ: density matrix of the quantum system
• H: Hamiltonian encoding the data structure
• L_k: Lindblad operators for dephasing/dissipation
• γ_k: coupling strengths

Workflow

Step 1: Data Encoding

Map classical data points to quantum input states:

• Each data point → a specific input state configuration
• Feature distances → Hamiltonian coupling strengths

Step 2: Quantum Transport Dynamics

• Initialize the network with data-encoded input states
• Let the system evolve under GKSL dynamics
• System reaches steady state naturally (no active control needed)

Step 3: Current Readout

• Measure terminal currents (particle flow rates at output nodes)
• Cluster assignments are inferred from current magnitudes/patterns
• High current to terminal T_i → data point belongs to cluster i

Step 4: Classical Post-Processing

• Map current patterns to discrete cluster labels
• Validate against known labels (if available)

Key Advantages

1. Tomography-free: No full state reconstruction needed — only measure terminal currents
2. Hardware-native: Current readout is a natural observable in quantum transport setups
3. Robust to dephasing: Stable performance across wide range of dephasing strengths
4. Hybrid workflow: Classical data prep + quantum dynamics + classical readout

Benchmarks

• Synthetic datasets: competitive with classical methods
• QM9 (molecular dataset): effective clustering
• Iris dataset: competitive performance
• Stable across dephasing strength variations

Design Principles

1. Algorithm-hardware co-design: Match encoding to available hardware observables
2. Transport over state: Use particle flow (currents) as the computational output, not quantum states
3. Open system advantage: Decoherence/dephasing is a feature, not a bug — helps convergence to steady state
4. Minimal measurement: Only terminal currents, not full density matrix

When to Use

• Unsupervised clustering on quantum hardware
• When state tomography is too expensive
• Hybrid classical-quantum ML pipelines
• Quantum networks with accessible transport measurements