rdviii
commented
4 years ago Notes from early June:
@Sara @Michal Hajdusek @cocori and I had a meeting (virtual, of course) this morning. We have begun working a little bit on graph state links, as epitomized in Pau Hilaire’s paper (https://arxiv.org/pdf/2005.07198.pdf). This builds on work by Azuma-san (https://www.nature.com/articles/ncomms7787) and earlier work in the Economou group (https://journals.aps.org/prx/abstract/10.1103/PhysRevX.7.041023). (Paul’s paper is pretty self-contained, if you’re just starting to read about this topic it’s fine to start there.) We are trying to work out RuleSets for how to make this happen. A few items from our meeting:
- Terminology: Let’s use “vertex” to mean “photon in a graph state,” so we don’t get confused with “node”, which we use to refer to hardware.
- A quick-and-dirty approach would be to just use Eq. 4 in Paul’s paper to set a probability for link success.
- Our real goal, though, is to simulate the full thing. Actually, it’s really to design a link and the communication protocols to make this happen.
- In Fig. 2, we don’t yet fully understand everything, but we think qubits Q3 and Q1 are operating in parallel, generating their subtrees, and then Q2 is used to merge those subtrees. Is that right? (We’re still reading the paper, so it might be written there somewhere.)
- Oooh, tomography on the link will be difficult. (We looked at a recent paper out of the Jian-Wei Pan group, but not sure it’s of much help here.)
- If end nodes Alice and Bob are having trouble violating a CHSH inequality (or making high-fidelity QKD key or whatever end-to-end check we’re doing), how will they debug that? Do we need link-level tomography?
- I was originally thinking that this choice of using repeater graph states (RGS) could be done in isolation on a single link, without affecting neighboring links. However, we’ve now realized how much this approach is intended to be a multi-hop connection, even though the final output is an end-to-end physical Bell pair. I now think it makes sense to treat the choice of link as something that happens across a network, though there might be a border router that performs interoperability tasks, a la Shota. (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.042338) Thus, RuleSets might need to be multihop, rather than just on the physical link.
- Back when we first began the QuISP journey, we spent a lot of time talking about whether BSA (Bell State Analyzer) nodes are first-class nodes, or if they are just part of the link. Eventually we settled on them being just part of the link: all they have to do is measure the photons and report the results (or failure to receive) to the ends of the link; no node any farther away needs to know anything about the existence of the BSA. Implementing RGS (repeater graph state)-based connections is going to require substantially rethinking this. We are going to have to create a “Generalized Bell State Analyzer” (GBSA) or “Advanced BSA” (ABSA) or something like that. The ABSA (I think I like that name better) has to make decisions in real time, based on prior results. As such, the ABSA will need RuleSets of its own. Moreover, in this connection architecture, the repeater nodes with the matter qubits are completely uninvolved in operation after generating the RGS. In a sense, this flips the network architecture upside down; the nodes with matter qubits are more like midpoint sources and the ABSA is more like the repeater. The ABSA will have to communicate with endpoints to indicate success/failure and Pauli frame corrections. Those RuleSets will have to be developed for the end-to-end (or at least end-to-border-router) connection, so there will be substantial work to be done here... This is going to be more coding and more rethinking of networks than I had originally hoped, but I think it’s tractable and I think we will learn a lot about the feasibility of RGS-based connections as a result.
I think the Figure numbers refer to Paul's arXiv paper: https://arxiv.org/abs/2005.07198
Paul Hilaire 6:24 PM
- I agree with the first points.
- On the Fig. 2, Q3 is used as a quantum emitter that produces photons and Q1 and Q2 are used as "anchors" to "store" the entanglement with the photons produced by Q3. Q2 is used to store the tree branches and Q1 the full arm (full tree + outter qubit). Then you measure them to produce the photons. One should note that with a RuleSet approach, there is a problem as the outter qubit should be measured first to determine then the measurement basis of the other photons in the tree, but the outter qubit is the last one to arrive to the node. This problem can be solved by adding another quantum emitter Q4 that only purpose is to produce the outter qubits and connect them to the graph structure. This way we can force the outter photons to arrive first.
- I don't fully understand what is meant by tomography for this purpose?
- I don't really understand that neither, but if the goal is to improve the Bell pair fidelity, we should add purification to the scheme, which is not really straightforward to implement with all photonic repeaters (at least to me)
- I agree that all-photonic repeaters kind of impose to be used next to other all-photonic repeaters otherwise they are not completely useful. But you can still assume that it can be connected to a larger network if you store the entanglement into quantum memories at interface nodes.
- Also, I've just remembered that in the paper from Mihir Pant (Pant et al. PRA 2017) on RGS, the inner qubits are kept inside the source node and only the outter qubits are sent. This might make the simulation easier to deal with as you can keep the BSA as it is and you reduce the actual number of sent photons (which is good for channel capacity). However, it requires classical signaling (but its repetition rate performance are still not limited by it as for a memory-based quantum repeater) and it requires the inner photons to be stored into the source nodes. These inner photons are substantially different from the Stationnary qubits already developped in QUISP as they can be lost (you need to keep them in a fiber loop until the classical signaling come back to know in which basis they should be measured. That may be an interesting alternative to simplify this simulations (instead of actually sending thousands of photons to produce a Bell pair, you actually send around 15 photons and keep the rest inside the node which maybe faster to simulate). The performances are slightly worse in terms of rate per matter qubits as the inner photons are kept at least twice longer (due to the classical signaling) but I think it is manageable. The channel capacity is "artificially" increased a lot (artificially because you effectively use fibers kept inside the nodes to store the photons...). This was a claim of Pant's paper which I do not completely agree with.
a la Va Tech (or is this a network protocol? Not clear to me yet.)