Quantum Networks

From the point of view of quantum coordination the most crucial services of a quantum network are:

• EPR-pair distribution
• multi-partite state distribution

Multi-partite state distribution

Distributing Graph States Across Quantum Networks

Graph state:

• $G=(V,E)$, where vertices are qubits
• Initially all qubits are in $|+⟩$ state, followed by the controlled $Z$ operation (phase flip)

Role of graph states:

• any quantum computation can be done in a "one-way" fashion:

  1. prepare a graph state
  2. perform measurements
  3. perform single qubit operations based on 2

Protocols for Creating and Distilling Multipartite GHZ States With Bell Pairs

Setting:

• to correct and track errors it is necessary to perform joint measurements
• joint measurements in a distributed quantum computing are enabled by GHZ states
• quantum networks should provide this states

Goal: produce GHZ states that at fast rate and with high fidelity

Challenges:

• if GHZ states is produced by fusing Bell pairs, the fidelity degrades exponentially
• distillation or purification

Approach:

Some form of dynamic programming.