Hamiltonian Qkd Routing

---
name: hamiltonian-qkd-routing
description: "Quantum-inspired Hamiltonian optimization for QKD network routing using effective Hamiltonian modeling, Quantum Monte Carlo annealing, and stochastic Tensor Network State compression. Activation: QKD routing, Hamiltonian optimization, tensor networks, quantum annealing, network orchestration."
---

# Hamiltonian-Based QKD Network Routing Optimization

Quantum-inspired optimization framework for adaptive multi-demand routing in Quantum Key Distribution (QKD) networks from arXiv:2605.27425 (May 2026). Combines effective Hamiltonian modeling, Quantum Monte Carlo annealing, and stochastic Tensor Network State (TNS) compression.

## Core Methodology

### Problem

QKD networks require routing that jointly optimizes latency, secret key generation rate, congestion, finite capacity, and operational security constraints under dynamic traffic conditions.

### Key Insight

Represent the communication network as a **stochastic interacting graph** whose routing configurations evolve under an effective Hamiltonian containing latency, keyrate, congestion, risk, and capacity terms.

### Two Complementary Approaches

1. **Stochastic Metropolis Annealer**: Incremental local Hamiltonian updates explore the optimization landscape
2. **Stochastic Boundary-MPS Tensor Network**: Compresses low-energy routing sector through thermal branch selection

## Numbered Steps

1. **Model network as stochastic graph**: Nodes = network devices, edges = quantum channels with keyrate capacity
2. **Define effective Hamiltonian**: H = α·latency + β·keyrate + γ·congestion + δ·risk + ε·capacity
3. **Initialize routing configuration**: Random or heuristic starting assignment of traffic flows
4. **Metropolis annealing**: Propose local changes, accept/reject based on energy difference ΔH and temperature schedule
5. **TNS compression (parallel)**: Represent low-energy routing sector as boundary-MPS tensor network
6. **Thermal branch selection**: Select branches with highest thermal probability for routing decisions
7. **Converge and deploy**: Extract optimal routing configuration from lowest-energy state

## Pitfalls

- **Temperature schedule**: Too fast → trapped in local minimum. Too slow → impractical for real-time routing
- **Hamiltonian weights (α, β, γ, δ, ε)**: Must be calibrated to network-specific priorities
- **TNS bond dimension**: Too small → loses routing configurations. Too large → computational bottleneck
- **Dynamic traffic**: Re-optimize when traffic patterns shift significantly; stale solutions become suboptimal

## Applications

- Large-scale QKD network orchestration
- Statistical-physics-inspired network optimization
- Tensor-network compression for routing problems
- Future quantum-native routing systems

## Verification

- Framework establishes scalable bridge between QKD orchestration, statistical-physics optimization, tensor-network compression, and quantum-native routing
- Validates on dynamic traffic conditions with multiple simultaneous demands