Quantum Networking

Quantum Network Architecture

A quantum network connects quantum processors via quantum channels (optical fibers or free-space links) to distribute entanglement and enable quantum communication.

Network layers:

• Physical layer: fiber/free-space links, single-photon sources and detectors
• Link layer: entanglement generation between adjacent nodes
• Network layer: entanglement routing and swapping
• Application layer: QKD, distributed quantum computing, blind quantum computation

Entanglement Distribution

Distributing entanglement over long distances faces photon loss in optical fibers:

where dB/km for telecom fibers. At 100 km: . At 300 km: .

Quantum repeaters overcome this by creating entanglement over shorter distances and swapping.

Entanglement Swapping

Entanglement swapping extends entanglement over longer distances:

1. Source creates Bell pairs: and
2. Perform Bell measurement on and
3. After measurement, and become entangled (even though they never interacted)

This is the key operation for quantum repeaters and long-distance quantum networking.

Network Protocols

Key quantum networking protocols:

• Entanglement generation: create Bell pairs between adjacent nodes
• Entanglement swapping: extend entanglement over multiple hops
• Entanglement purification: improve fidelity of noisy entanglement
• Quantum teleportation: transfer quantum states using entanglement
• Superdense coding: send classical bits using entanglement + qubits

Real-World Quantum Networks

• Tokyo QKD Network: metropolitan QKD with trusted nodes
• Beijing-Shanghai backbone: 2000 km QKD with trusted relay
• European Quantum Communication Infrastructure (EuroQCI): pan-European QKD network
• IBM Quantum Network: cloud access to quantum computers

Current networks use trusted nodes — true end-to-end quantum security requires quantum repeaters.

Python: Entanglement Distribution

import numpy as np

def entanglement_distribution(distance_km, fiber_loss_db_km=0.2):
    # Estimate entanglement distribution success probability.
    total_loss_db = fiber_loss_db_km * distance_km
    survival_prob = 10**(-total_loss_db / 10)
    return survival_prob

def entanglement_swapping_fidelity(F1, F2):
    # Compute fidelity after entanglement swapping.
    return F1 * F2 + (1-F1) * (1-F2) / 3

for d in [50, 100, 200, 500]:
    p = entanglement_distribution(d)
    print(f"{d} km: survival prob = {p:.4f}")

F = 0.95
print(f"Swapping fidelity ({F}, {F}): {entanglement_swapping_fidelity(F, F):.4f}")

Quantum Network Protocols

The quantum internet protocol stack:

Each layer builds on the previous, abstracting hardware details for higher-level protocols.

Entanglement Distribution Rate

The entanglement distribution rate depends on:

For metropolitan networks (~50 km): Hz For long-distance (~500 km): Hz (without repeaters) With quantum repeaters: polynomial in distance

Summary

This topic covers the fundamental concepts and applications in quantum computing. Understanding these concepts is essential for advancing in the field and applying quantum techniques to real-world problems. The mathematical framework provides the foundation for analyzing quantum algorithms and hardware implementations.

Key takeaways include the importance of quantum coherence, the role of entanglement as a resource, and the tradeoffs between different quantum computing architectures. As the field progresses from NISQ to fault-tolerant devices, these foundational concepts will continue to underpin new developments and applications.

Further study should include hands-on implementation using quantum programming frameworks, analysis of recent research papers, and exploration of the connections between quantum computing and other fields such as machine learning, optimization, and simulation.

Quantum Network Capacity

The capacity of a quantum network:

where is the entanglement rate of edge .

For a linear network with identical links: where is the number of nodes.

For a complete graph: (all links can be used simultaneously).

Network design must balance entanglement generation, storage, and consumption rates.