Message Passing Distilation

Using the Free Qubit Trigger

In the world we live in, we are only able to directly affect and know about objects/information in our proximity. To be able to provide a network with entanglement, as a chain repeater does, we would need to employ a message passing protocol that let's other nodes in the network know what our node needs or what it can provide.

This is why, in this example we will go over one way to do exactly that: We will set up a protocol that provides nodes with entanglement on request, and purifies said entanglement. You might notice that in this example we (for now) omit swapping. That is because to understand the protocol and the code we need to take it step by step and start froma 2 node network.

The communication processes between 2 nodes of the same edge are set up in setup.jl, and are the following (and can be found mor indepth in the next section):

• the free_qubittrigger, which is added to one single node from each edge of the network to prevent overlocking, and signals a free local slot when one is found
• the entangler which replies to the free_qubittrigger and finds a pair for the node that it replies to
• and the purifier which waits for the entangler to entangle enough pairs for it to be able to perform purification.

Each of the three listens on a channel tied to each of the network's edges.

This example is split into 4 files that are set up this way for easier delimitation of what this simulation does. We have:

• setup.jl : sets up the simulation and the three processes above
• 1_entangler_purifier_console.jl : records a the simulation and saves it as a video
• 2_wglmakie_fullstack.jl : shows the interactive simulation in a web browser
• cssconfig.jl : css style and configurations used by 2_wglmakie_fullstack.jl

One goal of this example is to not only understand a way of passing messages to request entanglement, but to also initiate one to quantum entanglement purification.

In the given example we select and compare two types of circuits: 2 to 1 (Single Selection) and 3 to 1 (Double Selection). We notice that the 3 to 1 circuit outperforms the 2 to 1 circuit in terms of final vs initial fidelity, but the probability for a 3 to 1 to actually succeed in creating a high fidelity pair is lower than a 2 to 1's. This can be observed to it's best extent when enabling the recycle purif pairs option on the web simulation.

The web simulation

The web simulation is split into two panels that display the same simulation, but have different auxiliary plots and sliders for the user to play with. They are explained in the simulation's main page and also in the docs.

We chose to split the simulation as such for the users to focus on the important parts of each step of the protocol rather than needing temselves to figure out what each slider is tied to.

Chart flow of the protocol

Entanglement (simple channel)

sequenceDiagram
    Alice-->>Alice: FIND_FREE_QUBIT
    Alice->>+Bob: FIND_QUBIT_TO_PAIR
    Bob->>Bob: WAIT_UNTIL_FOUND
    Bob-->>-Alice: ASSIGN_ORIGIN or UNLOCK (if not found)
    Alice->>+Bob: INITIALIZE_STATE
    Bob->>-Alice: GENERATED_ENTANGLEMENT
    Alice->>+Bob: GENERATED_ENTANGLEMENT_REROUTED (process_channel)
    Bob->>+Bob: Lock self (localy)
    Bob->>+Alice: LOCK Alice
    Alice->>Alice: Wait for process to pick up

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Purification (on process channel)

sequenceDiagram
    Bob-->>+Bob: LOCK and and repeat above diagram until length(indices) == purif_circuit_size
    Bob->>-Bob: Perform purification measurement and send it to Alice

    Bob->>+Alice: PURIFY(local_measurement)
    Alice->>Alice: Perform purification measurement and compare to Bob
    Alice->>Bob: REPORT_SUCCESS
    Alice->>-Alice: Release locks and clear registers based on success
    Bob->>Bob: Release locks and clear registers based on success

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Coupled purification after entanglement

sequenceDiagram
    Alice-->>Alice: FIND_FREE_QUBIT
    Alice->>+Bob: FIND_QUBIT_TO_PAIR
    Bob->>Bob: WAIT_UNTIL_FOUND
    Bob-->>-Alice: ASSIGN_ORIGIN or UNLOCK (if not found)
    Alice->>+Bob: INITIALIZE_STATE
    Bob->>-Alice: GENERATED_ENTANGLEMENT
    Alice->>+Bob(process_channel): GENERATED_ENTANGLEMENT
    Bob(process_channel)->>Alice: LOCK Alice
    Bob(process_channel)-->>Bob(process_channel): LOCK and WAIT FOR length(indices) == purif_circuit_size
    Bob(process_channel)->>-Bob(process_channel): Perform purification measurement and send it to Alice

    Bob(process_channel)->>+Alice(process_channel): PURIFY(local_measurement)
    Alice(process_channel)->>Alice(process_channel): Perform purification measurement and compare to Bob
    Alice(process_channel)->>Bob(process_channel): REPORT_SUCCESS
    Alice(process_channel)->>-Alice(process_channel): Release locks and clear registers based on success
    Bob(process_channel)->>Bob(process_channel): Release locks and clear registers based on success

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Important

if graphs are too large/too little on retina screens specifically on macos, go to cssconfig.jl and modify

retina_scale = 1 # modify to 2 instead of 1