IEEE QCE 2026 Tutorial

Hybrid Satellite-Ground Quantum Networks and Computing

TUT::QNET::QDC::57: Hybrid Satellite-Ground Quantum Networks and Computing

Yu Wang · Temple University�Lei Fan, Zhu Han · University of Houston�Yuanxiong Guo · University of Texas at San Antonio

Sept 14, 2026 · Toronto, Canada

Schedule of This Tutorial

1

Introduction to Hybrid Satellite-Ground Quantum Networks (10-10:30am)

Motivation, background, and overall system of satellite-ground QN

2

Hybrid Quantum-Classical Computing Framework (10:30-11am)

Key concepts and techniques used by hybrid QC computing to solve optimization problems

3

Entanglement Distribution in Hybrid Satellite-Ground Quantum Networks (11-11:30am)

How to use satellite to provide entanglement for ground quantum networks

4

Entanglement Routing in Hybrid Satellite-Ground Quantum Networks (1-1:40pm)

How to routing entanglement in satellite-ground quantum networks

5

Distributed Quantum Computing via Hybrid Satellite-Ground Quantum Networks (1:50-2:30pm)

How to support distributed quantum computing in hybrid quantum networks

2

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

SECTION 1

Introduction

Motivation, background, and overall system of satellite-ground QN

3

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Outline

1

Quantum Network

2

Quantum Computing and Distributed Quantum Computing

3

Satellite-Ground Communication

4

Satellite-Assisted Quantum Networks

5

Satellite-Ground Quantum Computing

2

UNIQ · Communication-Efficient Distributed Quantum Computing via Unified NIP

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

Quantum Network and Computing

3

Satellite-Ground Quantum Computing

Transmit quantum information between nodes,

using quantum phenomena superposition and entanglement

No bits, but qubits

Bits

Qubits

Bit. [Online]. Available: https://www.computerhope.com/jargon/b/bit.htm

What is a qubit. [Online]. Available: https://www.quantum-inspire.com/kbase/what-is-a-qubit/

Teleportation is real, thanks to quantum entanglement. [Online]. Available: https://www.popularmechanics.com/science/a25699/how-quantum-teleportation-works/

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Quantum Network

Entanglement Generation and Swapping

• Stage 1: Alice and Bob generate an Einstein-Podolsky-Rosen (EPR) pair and send one qubit from their respective pairs to Carol

(a) Entanglement generation

(b) Entanglement swapping

(c) Entanglement established

• Stage 2: Carol performs a Bell-state measurement (BSM) and transmits the result to Bob, i.e., entanglement swapping

• Stage 3: Alice and Bob are entangled

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

• Terrestrial Quantum Network (TQN)
• Utilize optical fiber links
• Exponential increase in photon loss with distance
• Terrestrial repeaters perform entanglement swapping and purification to ensuring high fidelity

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

NP-hard Optimization Problems

e. g. Maximum Likelihood MIMO Detection Using Quantum Computing

Quantum Computing: use quantum mechanics to solve problems too complex for classical computers.

MIMO Detection

Resource Allocation

. . .

Network Slicing

[2] M. Kim, D. Venturelli, and K. Jamieson, “Leveraging quantum annealing for large MIMO processing in centralized radio access networks,” in Proceedings of the ACM Special Interest Group on Data Communication, Beijing, China, Aug. 2019.

[2]

Network Slicing

Network

Function Virtualization

. . .

Quantum Computing:

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Quantum Computer

• Gate Model
• Analog Quantum Model
• Quantum Annealing

• More Qubits
• Faster than classical solvers
• Fit some optimization problems

Maybe we need to use quantum mechanics in our computers.

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

What is wrong in classic computing?

Many Practical NP hard Problems

Total number of combinations exponentially grows

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Known Types of Quantum Computing and Their Applications and Generality.

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Gate Level Quantum Computing

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

• Heat the metal to a temperature;
• Lower the temperature;

Annealing a Metal

Simulated Annealing

• Heuristic algorithm;
• Random search method;
• The temperature variable;

Quantum tunneling

Quantum Annealing

• Enables jumping from one classical state to another

– Decreases likelihood of getting stuck in a local minimum

• Width of energy barrier is important, but height is not

Quantum Annealing

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Qubits and Quantum Operation

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Before studying quantum

after studying quantum

Schrödinger Equation

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

• Problem of Hamiltonian:

​

​

​

​

​

• Goal (what the hardware does)
• Minimize σ_i ∈ {-1, +1} subject to provided J_i,j ∈ R and h_i ∈ R coefficients
• In other words, a quantum optimization program is merely a list of J_i,j and h_i
• Classical
• Much easier to reason than a quantum Hamiltonian
• Quantum effects are used internally to work towards the goal
• Sparsely connected
• Possible to map fully connected problems onto the D-Wave’s Chimera graph

Dwave Hamiltonian

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

QUBO (Quadratic Unconstrained Binary Optimization)

These important optimization problems can be transformed into QUBO model:

Quantum Computing:

provide an alternative method to solve some NP-hard problems

• Knapsack Problems
• Assignment Problems
• Task Allocation Problems
• Capital Budgeting Problems
• … (NP-hard problem)

Ising Model

Spins interact with applied field

Neighboring spins interact with each other

Core idea: Encoding the objective function as the eigenvalue of the final ground state of Schrodinger equation, based on Adiabatic Quantum Computing Model

Link Schrodinger with QUBO Model

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

• Considering only the external field:

​

​

• We arbitrarily call σ^z = +1 “TRUE” and σ^z = —1 “FALSE”
• Here are the optimal values of σ^z for different values of h

​

• Observations

– A negative h_i means, “I want σ^z to be TRUE”

– A zero h_i means, “I don’t care if σ^z is TRUE or FALSE”

– A positive h_i means, “I want σ^z to be FALSE”

QUBO Equation

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

• Consider only the coupler strengths:

​

​

• Here are the optimal values of σ^z and σ^z for different values of J_i,j:

​

​

• Observations
• A negative J_i,j means, “I want σ^z and σ^z to be equal”

i j

• A zero J_i,j means, “I don’t care how σ^z and σ^z are related”

i j

• A positive J_i,j means, “I want σ^z and σ^z to be different”

i j

Best answer appear with high probability

but not 100%, which is Achilles’ heel for

many quantum algorithms but not ours

QUBO Equation

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

• Inputs’ energy are set.
• Lowest energy is at or closes to the optima.
• Energy → possibility

• Qubits are entangled.
• At state of many possible answers.
• Couplers & biases applied

A matter of microseconds.

Energy diagram in Quantum Annealing

QUBO Quantum Annealing

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Master Problem

Subproblem

Hybrid GPU and Quantum Computing

using Benders' Decomposition for Mixed Integer Programming

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

Distributed Quantum Computing

3

Satellite-Ground Quantum Computing

• What is Distributed Quantum Computing (DQC)?
• Multiple interconnected quantum processors (QPUs) work together to solve large-scale computational problems
• Why DQC?
• single QPUs have limited qubits
• monolithic large QPU is very hard to build
• a pathway to large-scale quantum computing
• Challenges in DQC
• Qubit allocation/Circuit partition: distribution and management of qubits across multiple QPUs to optimize communication and execution time
• Quantum network function: serve high-quality & low-latency connections among quantum nodes to for remote operations

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

Distributed Quantum Computing

3

Satellite-Ground Quantum Computing

• Entangled qubits enables remote quantum gates and teleportation-based communication
• Qubit allocation requires balancing local processing and remote operations.
• Network topology affects entanglement fidelity and cost of served entangled qubits.

• Quantum circuits describe quantum algorithms
• Single qubit gates + CNOT are universal

Qubit Interaction Graph (QIG) captures all inter-qubit communications

Exactly a graph partition problem, which is NP-hard

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

3

Satellite-Ground Quantum Computing

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

Satellite-Ground Quantum Networking and Computing

3

Satellite-Ground Quantum Computing

Space-Aerial-Terrestrial Quantum Networks (SATQNs)

• SATQN has three layers
• Space quantum network enables long-distance entanglement distribution via free space optical links
• Aerial quantum network supports flexible and rapid deployment using free space optical links
• Terrestrial quantum network offers stable quantum connections via optical fiber links

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

AAN Standardization in 3GPP

3

Satellite-Ground Quantum Computing

2017

Release 14

3GPP TR 22.822

Three Use Cases of AAN

Concept of satellite network access

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

Satellite-assisted Quantum Networks (SATQN)

3

Satellite-Ground Quantum Computing

• Overcoming distance limits: Satellites enable global-scale entanglement distribution beyond ground-based range.
• Reduced signal loss: Space offers minimal attenuation and interference for more reliable quantum transmission.
• Broad coverage: Satellites connect remote and inaccessible regions lacking ground infrastructure.
• Freedom from obstacles: Signals are unaffected by terrain, buildings, or other terrestrial barriers.
• Global quantum networking: Satellite links are essential for secure, worldwide quantum communication.
• Complementary integration: Satellite systems enhance and extend ground-based quantum networks

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

SATQN Applications

3

Satellite-Ground Quantum Computing

• Time-insensitive applications
• Support long-term stream of entanglements
• Require secure communications
• Steady stream of entanglement over time
• E.g., Quantum key distribution (QKD)

Distributed quantum phase estimation with entangled photons. [Online]. Available: https://www.nature.com/articles/s41566-020-00718-2

Quantum Key Distribution Technology. [Online]. Available: https://www.drishtiias.com/daily-updates/daily-news-analysis/quantum-key-distribution-technology/print_manually

• Time-sensitive applications
• Complete tasks as quickly as possible
• Avoid information decoherence due to noise or delay
• E.g., Distributed quantum computing (DQC)

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

Challenges in SATQNs

3

Satellite-Ground Quantum Computing

Complex Integration

free space optical links and optical fiber links

Decoherence and Errors

noise in quantum channels and imperfections in quantum operations

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

Satellite-Assisted Quantum Networks

3

Satellite-Ground Quantum Computing

Simplified example of a satellite-assisted quantum network.

• The quantum repeaters are depicted as nodes, connected via fiber links.
• Dedicated ground stations (satellite dishes) have both fiber and satellite connections.
• Link colors represent entanglement generation probability, with blue indicating higher probability (shorter links) transitioning to red for lower probability (longer links).

Arxiv: SatQNet: Satellite-assisted Quantum Network Entanglement Routing Using Directed Line Graph Neural Networks

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

Satellite-Ground Quantum Computing

3

Satellite-Ground Quantum Computing

• Quantum Key Distribution (QKD): Satellites send fragile light particles (photons) to ground stations to create unbreakable encryption keys.
• Space-Based Advantage: Photons travel through empty space with very little loss or interference, unlike ground fiber-optic cables that degrade over long distances.
• Entanglement: Low-Earth-orbit satellites generate and split pairs of linked photons, sending one half to the ground and keeping or sending the other elsewhere to connect remote networks.

https://www.linkedin.com/pulse/how-quantum-computing-could-transform-satellite-ground-kiran-kolipaka-oqpgc

Quantum Network

Quantum Computing

Distributed Quantum Computing

​

Satellite-Ground Communications

Satellite Assisted Quantum Networks

INTRODUCTION

Satellite-Ground Quantum Computing

3

Satellite-Ground Quantum Computing

• Global Security: Creating hack-proof communication networks across continents.
• Distributed Computing: Linking separate quantum computers together via space relays.
• Quantum Sensing: Improving environmental monitoring and timing precision from space

Boeing’s Q4S Mission

SPOQC Mission (UK)

IonQ & Skyloom

Infrastructure

EAGLE-1 & SAGA (European Space Agency)

Micius (Mozi) Satellite (China)

SECTION 2

Hybrid Quantum-Classical Computing Framework

Key concepts and techniques used by hybrid QC computing to solve optimization problems

3

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Outline

1

Quantum Optimization Algorithms

Key math foundations and principles

2

Hybrid Quantum Classical Computing

Key concepts and workflow

3

Hybrid Quantum-Classical Application

Simulation Results

4

Conclusion

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Q Algorithm

HyQC

Application

Conclusion

Quantum Quantum Optimization Algorithms

​

Hamiltonian Simulation on Quantum Computer

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Q Algorithm

HyQC

Application

Conclusion

Quantum Optimization Algorithms

*Encode the objective function in the final Hamiltonian of the Quantum System

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Q Algorithm

HyQC

Application

Conclusion

Quantum Optimization Algorithms

*Encode the objective function in the final Hamiltonian of the Quantum System

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Time Dependent Hamiltonian

Q Algorithm

HyQC

Application

Conclusion

INTRODUCTION

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Quantum Adiabatic Algorithm

Q Algorithm

HyQC

Application

Conclusion

Hybrid Quantum Classical Optimization Algorithms

​

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Hybrid QPU-CPU Algorithm Design

• Leverage Classical Optimization Frameworks
• Build on proven decomposition and convex optimization methods to ensure scalability, stability, and interpretability
• Identify Quantum-Ready Problem Structures
• Extract discrete, combinatorial, or non-convex components that can be efficiently mapped to quantum processors (QPU) while keeping continuous parts classical.
• Accelerate While Preserving Guarantees
• Integrate quantum modules to speed up computation without compromising theoretical properties such as convergence, feasibility, and optimality.�

QPU

QPU

QPU

On QPU:

Quantum Adiabatic Algorithm

Quantum Hamiltonian Descent

On CPU:

Linear Programming

Convex optimization

Dual Updates

​

​

Q Algorithm

HyQC

Application

Conclusion

Hybrid Quantum Classical Optimization Algorithms

​

Hybrid Quantum Classical Benders’ Decomposition

Zhao, Zhongqi, Lei Fan, and Zhu Han. "Hybrid quantum benders’ decomposition for mixed-integer linear programming." 2022 IEEE Wireless Communications and Networking Conference (WCNC). IEEE, 2022.

Q Algorithm

HyQC

Application

Conclusion

Hybrid Quantum Classical Optimization Algorithms

​

Hybrid Quantum Multi-Cut Benders’ Decomposition

• Quantum algorithm returns multiple solutions after solving the master problem
• Each integer solution produce a subproblem, which further returns an optimality/feasibility cut
• Reduce the number of iterations and speed up the convergence

Zhao, Zhongqi, Mingze Li, Lei Fan, and Zhu Han. "HQC-Bend: A Python Package of Hybrid Quantum-Classical Multi-cuts Benders’ Decomposition Algorithm." In 2025 International Conference on Quantum Communications, Networking, and Computing (QCNC), pp. 591-597. IEEE, 2025.

Q Algorithm

HyQC

Application

Conclusion

Hybrid Quantum Classical Optimization Algorithms

​

Dantzig-Wolfe (DW) Decomposition

Wei, Xinliang, Jiyao Liu, Lei Fan, Yuanxiong Guo, Zhu Han, and Yu Wang. "Hybrid quantum-classical computing via Dantzig-Wolfe decomposition for integer linear programming." In 2024 33rd international conference on computer communications and networks (ICCCN), pp. 1-9. IEEE, 2024.

A. Integer Linear Programming

B. Dantzig-Wolfe (DW) Decomposition

Q Algorithm

HyQC

Application

Conclusion

Hybrid Quantum Classical Optimization Algorithms

​

Dantzig-Wolfe (DW) Decomposition

Wei, Xinliang, Jiyao Liu, Lei Fan, Yuanxiong Guo, Zhu Han, and Yu Wang. "Hybrid quantum-classical computing via Dantzig-Wolfe decomposition for integer linear programming." In 2024 33rd international conference on computer communications and networks (ICCCN), pp. 1-9. IEEE, 2024.

Master Problem

Three cases:

Q Algorithm

HyQC

Application

Conclusion

Hybrid Quantum Classical Optimization Algorithms

​

Dantzig-Wolfe (DW) Decomposition

Wei, Xinliang, Jiyao Liu, Lei Fan, Yuanxiong Guo, Zhu Han, and Yu Wang. "Hybrid quantum-classical computing via Dantzig-Wolfe decomposition for integer linear programming." In 2024 33rd international conference on computer communications and networks (ICCCN), pp. 1-9. IEEE, 2024.

Q Algorithm

HyQC

Application

Conclusion

APPLICATION · CASE STUDY

One SAGIN snapshot couples four resource decisions

Wei, Xinliang, Jiyao Liu, Lei Fan, Yuanxiong Guo, Yanmin Gong, Zhu Han, and Yu Wang. "Quantum-Assisted Resource Management for Data Access in Space-Air-Ground Integrated Networks." IEEE Transactions on Wireless Communications (2025).

Hybrid Satellite-Ground Quantum Networks and Computing | QCE '26

JOINT DECISION VECTOR

x

User association x, y, z

Connect each Mobile User to at most one terrestrial Base Station (TBS), HAP, or LEO. Binary

η

High-altitude Platform(HAP) cache placement η

Store requested items subject to each HAP's capacity. Binary

ξ

HAP location ξ

Choose one of two feasible locations; both links change. Binary

b

Bandwidth allocation b

Allocate continuous TBS-to-MU and LEO-to-MU bandwidth.

MODELING SCOPE

Centralized, snapshot-based, quasi-static channels

Fixed MU / LEO / TBS positions; perfect CSI

Each HAP selects one of two candidate locations

Direct TBS/LEO service competes with HAP service; an HAP cache miss also consumes LEO-HAP relay capacity.

Key coupling: HAP location changes access and backhaul; caching changes relay demand and user cost.

Q Algorithm

HyQC

Application

Conclusion

APPLICATION · MATHEMATICAL MODEL I

Rates, location, and caching define the utility

Wei et al., Eqs. (2)-(16), pp. 3-5; m(i) denotes the item requested by MU i.

Hybrid Satellite-Ground Quantum Networks and Computing | QCE '26

BANDWIDTH-CONTROLLED ACCESS RATES

With channel and power fixed during the snapshot, these rates are linear in the optimized bandwidth b.

h: channel efficiency

HAP LOCATION CONTROLS TWO LINKS

The same ξ_k selects the MU-HAP access rate and the LEO-HAP backhaul rate.

r: achievable rate 

RATE MINUS ACCESS AND CACHE-MISS COSTS

utility = delivered rate - association cost - HAP cache-miss cost

NETWORK OBJECTIVE

WHY P1 IS A MINLP

Products x·b and z·b gate bandwidth by association; y·η, y·ξ, and y·η·ξ couple HAP association, caching, and location.

Q Algorithm

HyQC

Application

Conclusion

APPLICATION · MATHEMATICAL MODEL II

Linearization exposes a Benders-ready MILP

Wei et al., Eqs. (16a)-(20)

Hybrid Satellite-Ground Quantum Networks and Computing | QCE '26

PHYSICAL FEASIBILITY IN P1

ASSOCIATION + SATELLITE CAPACITY

CACHE + BANDWIDTH BUDGETS

CACHE-MISS BACKHAUL FLOW

EXACT BINARY-PRODUCT LINEARIZATION

Representative exact hull for u = yη

The same 3-constraint pattern enforces v = uξ and w = yξ.

AUXILIARY BINARY GROWTH

Increase Binary Varaibles

Reformulated MILP Model

QPU master: X binary

CPU LP: Y = bandwidth

Q Algorithm

HyQC

Application

Conclusion

APPLICATION · ALGORITHM

HyBD sends only the discrete master to the QPU

Hybrid Satellite-Ground Quantum Networks and Computing | QCE '26

The classical Benders loop stays intact; quantum annealing acts as the binary master oracle and sample generator.

1 Build QUBO master

binary X + encoded ω + accumulated cuts

2 Sample on QPU

retain top σ feasible candidate solutions X'

3 Solve σ LPs on CPUs

recover bandwidth Y and dual point or ray

4 Add σ cuts

update upper/lower bounds and repeat

Q Algorithm

HyQC

Application

Conclusion

APPLICATION · SIMULATION AND HARDWARE RESULTS

Hardware tests match CBD with fewer Benders rounds

Hybrid Satellite-Ground Quantum Networks and Computing | QCE '26

Benders rounds to convergence

TEST CASES tuple = {MU, TBS, HAP, LEO, data}

Case 1

{25, 5, 1, 1, 8}

621 reported logical binaries

Case 2

{25, 5, 2, 1, 5}

774 reported logical binaries

Case 3

{25, 3, 2, 2, 5}

749 reported logical binaries

D-Wave Leap + classical LP solver | Same optimal objective as CBD in the tested cases | RAND is lower

Case 3​

​

Q Algorithm

HyQC

Application

CONCLUSION

Hybrid Quantum Classical Computing

Hybrid Satellite-Ground Quantum Networks and Computing | QCE '26

   Conclusion

• Select the right role for each processor
• QPU: hard tasks; CPU: convex optimization;
• Decomposition provides the bridge
• Benders and Dantzig–Wolfe decomposition create a structured interface between quantum and classical computing
• Multiple QPU samples can generate multiple cuts in one iteration and reduce the number of decomposition rounds
• The SAGIN case study demonstrates the workflow
• hybrid method reached the same optimal objective as classical Benders decomposition while requiring fewer Benders rounds

SECTION 3

Entanglement Distribution in Hybrid Satellite-Ground Quantum Networks

How to use satellite to provide entanglement for ground quantum networks

3

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Outline

1

Introduction

Motivation, background, and problem setup

2

System Model and Problem Formulation

Key concepts and definitions used throughout

3

Proposed HQCDW Algorithm

Main techniques covered in this tutorial

4

Evaluation

Applying the methods, evaluation highlights

5

Conclusion

Takeaways, open problems, and resources

2

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

INTRODUCTION

Satellite-based Entanglement Distribution

• Limitations of ground-based quantum entanglement distribution
• Exponential photon loss in fiber (roughly 0.2 dB/km)
• Decoherence accumulates with distance (more swapping, more noise))
• Geographic and infrastructure constraints
• An alternative way: satellite-based entanglement distribution
• Bypass many environmental factors, enable the creation of long-distance entangled links with higher fidelity
• Single “hop” replaces many repeater nodes
• Overcome the geographical constraints of ground-based systems
• Downward atmospheric path is shorter and more favorable

​

4

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

INTRODUCTION

Satellite-based Entanglement Distribution

[1] Yin et al., “Satellite-based entanglement distribution over 1200 kilometers,” Science, vol. 356, no. 6343, Jun. 2017

[2] Hiemstra et al. "The European satellite-based QKD system EAGLE-1." Free-space laser communications XXXVII. Vol. 13355. SPIE, 2025.

[3] Merolla et al. "High-performance 1560 nm entangled photon source for high secure key rates QKD satellite-based communications." International Conf. on Space Optics—ICSO 2022. Vol. 12777. SPIE, 2023.

[4] Mazzarella et al., “QUARC: Quantum research CubeSat—A constellation for quantum communication,” Cryptography, vol. 4, no. 1, p. 7, 2020

[5] Hutterer, et al. "QUBE-II - Quantum Key Distribution with a CubeSat". 73rd International Astronautical Congress, IAC 2022

4

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

EAGLE-1 & SAGA (European Space Agency) [2&3]

Micius (Mozi) Satellite (China) [1]

QUARC (UK) [4]

QUBE II (Germany) [5]

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

INTRODUCTION

Optimization of Entanglement Distribution from Sky

• Selecting an optimal satellite configuration for satellite-based entanglement distribution
• [1] Khatri et al., npj Quantum Inf., 2021
• [2] Panigraphy et al. INFOCOM workshop, 2022
• [3] Wei et al. IEEE Network, 2025
• Satellite assignment x_i,j to maximize the weighted utility
• Constraints on GS receivers (R_k), satellite transmitters (T_i), fidelity threshold (F_j^th)

​

​

​

​

�

• Solutions: Greedy^[1], MIS-based^[2] (only for special cases), MaxFlow-based^[3] (for more general special cases), LP-based (opt but large time-complexity)

4

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

INTRODUCTION

Motivation & Contribution

• Limitations and challenges of previous works
• a heuristic greedy algorithm and ignores some resource constraints
• only consider some specific settings by converting the problem into either a maximum weight independent set problem or a maximum weight bipartite matching problem
• without possible terrestrial swapping (which can improve feasibility of the problem)
• Our work investigates a joint satellite assignment, resource allocation, and path selection scenario to build quantum entanglements for ground stations by leveraging satellite-based entanglement distribution and terrestrial quantum swapping.
• X. Wei, L. Fan, Y. Guo, Z. Han, Y. Wang, Entanglement from Sky: Optimizing Satellite-based Entanglement Distribution for Quantum Networks, IEEE/ACM Trans. on Networking (TON), Volume: 32, Issue: 6, Pages: 5295-5309, Dec. 2024.

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Fig. 1. The satellite-based entanglement distribution and terrestrial quantum swapping architecture.

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

MODEL AND PROBLEM

System Model

• Network Model
• satellites (SAT): 𝑀 = {1, · · · , |𝑀|}, 𝑠𝑚_𝑖: quantum memory of SAT 𝑖, 𝑡𝑟_𝑖: number of transmitters of SAT 𝑖.
• ground stations (GS): 𝑁 = {1, · · · , |𝑁|}, g𝑚_𝑘: quantum memory of GS 𝑘, 𝑟𝑟_𝑘: number of receivers of GS 𝑘.
• ground station pairs (GSP): 𝑂 = {1, · · · , |𝑂|}
• Channel Model� spontaneous parametric down-conversion (SPDC)
• space-to-ground transmittance:
• free-space transmittance:
• atmospheric transmittance:

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

MODEL AND PROBLEM

System Model

• Entanglement Model
• Either via satellite-based entanglement
• Or via GS swapping (limited to two-hop)

​

​

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Fig. 1. The satellite-based entanglement distribution and terrestrial quantum swapping architecture.

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

MODEL AND PROBLEM

System Model

• Satellite-to-Ground Entanglement
• The fidelity of entangled photon pair after transmission can be approximated by

​

​

​

​

​

​

• Terrestrial Quantum Swapping
• The fidelities of the new states after swapping are defined below ^[2]

​

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

[1] N. K. Panigrahy, P. Dhara, D. Towsley, S. Guha, and L. Tassiulas, “Optimal Entanglement Distribution using Satellite Based Quantum Networks,” in IEEE Conference on Computer Communications (INFOCOM) Workshops, Virtual, May 2022.

[2] A. Zang, X. Chen, A. Kolar, and J. Chung, “Entanglement Distribution in Quantum Repeater with Purification and Optimized Buffer Time,” in IEEE Conference on Computer Communications Workshops, New York, NY, May 2023.

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

MODEL AND PROBLEM

Problem Formulation

• The joint satellite assignment, resource allocation, and path selection problem.

​

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Objective: maximize the overall utility of all traffic GSPs

Satellite assignment or

Terrestrial quantum swapping

if a swapping path is selected, then two entanglement links along this path must be established based on the satellite assignment.

the fidelity of entanglement links after transmitting or swapping is larger than the fidelity threshold.

hard problem to solve

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

HQCDW Algorithm

HQCDW ALGORITHM

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

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Fig. 3. Proposed HQCDW framework for joint satellite-based quantum entanglement distribution and terrestrial quantum swapping.

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

HQCDW Algorithm

HQCDW ALGORITHM

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

4

① Linearization

② general form

③ reformulation

④ linear combination of extreme points

⑤ DW decomposition

Block

structure

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

Partial Linearization & Three DW Subprobelms

HQCDW ALGORITHM

Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

4

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

EVALIATION

Evaluation Setting and Baselines

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Network architecture

Comparison methods

• Steepest Descent (SD) [3]: SD is a solver for binary quadratic models by D-Wave Systems with the best move determined through a local minimization.
• Random Steepest Descent (RASD) [3]: RASD combines random sampling and steepest descent, with the algorithm using random sampling to generate initial states for SD.
• Classical Optimizer (COPT): COPT solves the original problem (5) by using a classical optimizer (e.g., Gurobi, Scipy) in a classical CPU computer.
• Classical DW Decomposition (CDWD): CDWD decouples the original problem using DW decomposition and solves all problems with a classical optimizer.

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

EVALIATION

Evaluation – Objective Value

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

This highlights the effectiveness and robustness of using DW decomposition to tackle larger network scales.

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

EVALIATION

Evaluation – Solver Accessing Time: QUBO-DW2

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

This analysis highlights the advantage of using the DW decomposition to overcome constraints imposed by the maximum number of qubits in the quantum machine.

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

EVALIATION

Evaluation – Solver Accessing Time: DW3 & PL

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

This analysis highlights the advantage of using the DW3 and PL to overcome constraints imposed by the maximum number of qubits in the quantum machine.

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

EVALIATION

Evaluation – Qubit Usage

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

This result highlights the benefits of DW decomposition (also partial linear) for larger-scale problems.

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

EVALIATION

Evaluation – Qubit Usage

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

The benefits of DW with three subproblems are further

Introduction

Model and Problem

HQCDW Algorithm

Evaluation

Conclusion

CONCLUSION

Conclusion

• Satellite-based entanglement distribution provides a great �alternative way to support ground-based quantum networks
• However, finding optimal satellite assignment is a challenging �optimization problem in hybrid satellite-ground networks!
• We studied a joint satellite assignment, resource allocation, and path selection for entanglement distribution within a satellite-ground network
• We proposed a hybrid quantum-classical Dantzig-Wolfe decomposition technique by leveraging both quantum and classical computing to effectively solve large-scale network optimization challenges and balance qubit usage
• Experiments provided compelling evidence of the efficiency and robustness of the proposed methods, with a stable solver accessing time and consistent results compared to classical optimizers

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Hybrid Satellite-Ground Quantum Networks and Computing | QCE ’26

Thank You & Questions

Lei Fan, Yuanxiong Guo, Yu Wang and Zhu Han · lfan8,zhan2@uh.edu, · yuanxiong.guo@utsa.edu, wangyu@temple.edu�Lab / Group Website · https://sites.google.com/view/lorelab/home, https://guoyuanxiong.github.io/,

https://cis.temple.edu/~yu/wanglab/ and https://wireless.egr.uh.edu/