Presentation Outline
- Introduction & Motivation — 6G challenges & SDN limitations
- Background — Quantum Computing & QAOA fundamentals
- Methodology — QUBO formulation & quantum circuit design
- Experimental Setup — IBM Qiskit simulation environment
- Results & Discussion — Routing optimization outcomes
- Conclusion & Future Work
I. Introduction & Motivation
Why Quantum Computing for 6G Networks?
The 6G Challenge
- Increased throughput demands
- Ultra-low latency requirements
- Massive connectivity for IoT
- Stricter reliability (URLLC)
- NP-hard routing in ultra-dense deployments
Key Insight: Traditional SDN architectures face scalability
and fault tolerance challenges as network complexity grows exponentially
toward 6G.
IoT
Autonomous Vehicles
URLLC
NP-Hard
Software-Defined Networking (SDN)
Advantages
- Separates control plane from data plane
- Flexible & programmable management
- Microservices-based decomposition
Limitations
- Scalability bottlenecks
- Performance overhead
- Security concerns
Solution: Integrate Quantum Computing at the SDN
controller level to tackle combinatorial routing optimization
— the Q-SDN framework.
Hybrid Quantum-Classical SDN Architecture
Fig. 1: Hybrid quantum-classical SDN architecture — combining quantum & classical computing at the controller level for 6G ultra-dense networks
II. Background
Quantum Computing & QAOA Fundamentals
Quantum Computing Basics
- Qubits exist in superposition of |0⟩ and |1⟩
- Entanglement links qubits over distances
- Enables parallel processing of multiple outcomes
- Potential breakthroughs in cryptography, optimization, material science
Why QC for Networking?
Combinatorial complexity of routing continues to increase. QC exploits quantum effects (superposition & entanglement) to boost computational power for NP-hard problems.
Combinatorial complexity of routing continues to increase. QC exploits quantum effects (superposition & entanglement) to boost computational power for NP-hard problems.
QAOA — Quantum Approximate Optimization
- Subset of Variational Quantum Algorithms (VQA)
- Suited for NISQ (Noisy Intermediate-Scale Quantum) devices
- Hybrid quantum-classical algorithm with parameters $(\beta, \gamma)$
- Encodes optimization into a Hamiltonian & seeks ground state
$$|\Psi(\boldsymbol{\beta},\boldsymbol{\gamma})\rangle = \hat{U}(H_C,\gamma_1)\hat{U}(H_M,\beta_1)\cdots\hat{U}(H_C,\gamma_p)\hat{U}(H_M,\beta_p)|\psi_0\rangle$$
where $p$ = circuit depth, $H_C$ = cost Hamiltonian, $H_M$ = mixer Hamiltonian
QAOA Components
$U(H_C, \gamma)$
Encodes the optimization problem. Shapes the energy landscape where solutions correspond to energy levels.
Encodes the optimization problem. Shapes the energy landscape where solutions correspond to energy levels.
$U(H_M, \beta)$
Facilitates state exploration. Mitigates local optima by guiding the system through the energy landscape.
Facilitates state exploration. Mitigates local optima by guiding the system through the energy landscape.
Fig. 3: QAOA scheme — Quantum Circuit Representation
III. Methodology
From Network Graph to Quantum Solution
Overall Framework Pipeline
Fig. 2: Procedure for mapping the routing problem onto a gate-based quantum computer
Network Graph
→
Problem Formulation
→
QUBO Model
→
QAOA
→
Optimal Route
Step 1: Problem Formulation
Network as Directed Graph $G(V, E, W)$
- $V$ — network nodes (routers, switches)
- $E$ — communication links
- $W$ — edge weights (latency, cost)
Cost Function
$C(x) : \{0,1\}^n \rightarrow \mathbb{R}$
Minimize total travel distance/latency subject to constraints
Objective: Find $x^*$ such that $C(x^*) \leq C(x)$
for all $x \in \{0,1\}^n$, minimizing cost across the entire solution space.
Variables:
• $n$ = number of qubits (dimensionality)
• $x$ = bit string representing a potential solution
• Each qubit $\leftrightarrow$ one binary decision variable
• $n$ = number of qubits (dimensionality)
• $x$ = bit string representing a potential solution
• Each qubit $\leftrightarrow$ one binary decision variable
Step 2: QUBO Formulation
$$\min_x \; x^T Q x + C^T x$$
- $x$ — binary vector (0s and 1s)
- $Q$ — symmetric matrix (pairwise qubit interactions)
- $C$ — linear coefficients vector
Flow Conservation (Kirchhoff's Law):
$$\sum_{\text{incoming}} f = \sum_{\text{outgoing}} f$$
No accumulation of flow at any intermediate node.
$$\sum_{\text{incoming}} f = \sum_{\text{outgoing}} f$$
No accumulation of flow at any intermediate node.
Step 3: Objective with Penalty Terms
$$\min\left(\sum_{(i,j)\in E} w_{ij}X_{ij} + P\left(\sum_{j:(i,j)} X_{ij} - \sum_{j:(j,i)} X_{ji} - 1\right)^2 + P\left(\sum_{j:(i,j)} X_{ij} - \sum_{j:(i,j)} X_{ji}\right)^2\right)$$
Penalty $P$: Enforces constraints via quadratic penalty terms.
Set as $P = \sum_{i,j} w_{i,j} + 1$ to prevent violations.
- $w_{ij}$ = link latency (cost)
- $X_{ij} \in \{0,1\}$ = link selection
- Constraints squared & added to objective
- Result: unconstrained quadratic binary problem
Quantum Circuit Implementation
Fig. 5: Representation of QAOA Quantum Circuit (H1–H3) — 12 qubits
$R_Z$ gates Linear terms (diagonal rotations based on $\gamma$)
$R_{ZZ}$ gates Quadratic terms (qubit interactions)
$R_{ZZ}$ gates Quadratic terms (qubit interactions)
$R_X$ gates Mixer Hamiltonian (Pauli-X, based on $\beta$)
H gates Initial equal superposition
H gates Initial equal superposition
IV. Experimental Setup
Simulation Environment & Configuration
Simulation Environment
Tools & Platform
- IBM Qiskit SDK for quantum simulations
- Microservices-based SDN controller (MSN)
- Based on Ryu SDN framework decomposition
- Classical optimizer: COBYLA
Configuration
- QAOA depth: $p = 1$ (single layer)
- 12 qubits per routing instance
- Penalty: $P = \sum w_{i,j} + 1$
- Optimizer: COBYLA (29 iterations)
Goal: Minimize routing latency between host pairs while satisfying flow conservation constraints.
Network: 10 nodes, directed graph with 12 binary decision variables. Link weights represent latency in milliseconds.
Network Topology
Fig. 4: Network topology — 10 nodes with link latencies (ms)
Routing Scenarios:
• H1 → H3: Source node 0 to destination node 9
• H7 → H8: Source node 5 to destination node 3
Edge weights represent link latencies (not representative of real-world — designed to test QAOA)
• H1 → H3: Source node 0 to destination node 9
• H7 → H8: Source node 5 to destination node 3
Edge weights represent link latencies (not representative of real-world — designed to test QAOA)
V. Results & Discussion
Proof-of-Concept Routing Optimization
Routing Example 1: H1 → H3
| Path (Nodes) | Binary Encoding | Cost | Probability |
|---|---|---|---|
| 0-1-4-9 | 100100100000 | 27 | 0.000942619... |
| 0-1-3-9 | 101001000000 | 38 | 0.000770757... |
| 0-2-5-6-8-9 | 010010010101 | 106 | 0.000742073... |
| 0-2-5-6-7-8-9 | 010010011011 | 114 | 0.000640327... |
Optimal path: 0-1-4-9 with cost = 27 (minimum latency). Found in only 29 COBYLA iterations with $\beta$ = -0.2403, $\gamma$ = -5.6069.
Routing Example 2: H7 → H8
| Path (Nodes) | Binary Encoding | Cost | Probability |
|---|---|---|---|
| 5-2-0-1-3 | 111010000000 | 52 | 0.000348017... |
| 5-2-0-1-4-9-3 | 110111100000 | 71 | 0.000148433... |
| 5-6-8-9-3 | 000001010101 | 92 | 1.544e-05 |
Optimal path: 5-2-0-1-3 with cost = 52. Penalty $P = 182$. Optimal $\beta$ = -1.1491, $\gamma$ = -6.0246.
Key Findings
Strengths
- QAOA correctly identifies low-latency paths
- Accommodates flow constraints via penalty terms
- Only 29 iterations with single-layer QAOA
- Feasible on current NISQ hardware
Current Limitations
- Limited qubit capacity constrains network size
- Noise in NISQ devices affects accuracy
- Single-layer depth ($p=1$) limits solution quality
- Small topology (proof-of-concept only)
VI. Conclusion & Future Work
Summary & Research Directions
Conclusion
Hybrid Architecture
Combined quantum-classical SDN framework for real-time routing in 6G networks
Combined quantum-classical SDN framework for real-time routing in 6G networks
QUBO Modeling
Successfully mapped routing as a QUBO problem solvable via QAOA
Successfully mapped routing as a QUBO problem solvable via QAOA
Feasibility Demonstrated
IBM Qiskit simulations confirm QC can identify feasible optimal paths
IBM Qiskit simulations confirm QC can identify feasible optimal paths
Scalable Methodology
Extendable to larger, multi-constraint settings with hardware advances
Extendable to larger, multi-constraint settings with hardware advances
Future Work
- Broader topologies — Scale to larger, real-world network graphs
- Multi-objective optimization — Include throughput, reliability, energy efficiency
- Noise mitigation — Evaluate error-mitigation for near-term quantum devices
- Distributed quantum controllers — Multiple QPUs for network segments
- Deeper QAOA circuits — Increase $p$ for better approximation quality
- Hybrid approaches — Combine with AI/ML-based adaptive routing
Thank You
Quantum-Enhanced Software-Defined Networking:
A Communication Perspective
IEEE INFOCOM 2025 Workshop
Contact: heurpe, jomondel@iteam.upv.es
swaraj_shekhar.nande, riccardo.bassoli, frank.fitzek@tu-dresden.de