Internet Engineering Task Force Interim Meetings, 22 Sep 2021

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From YouTube: IETF-QIRG-20210922-1300

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QIRG meeting session at IETF
2021/09/22 1300

https://datatracker.ietf.org/meeting//proceedings/

A

Right so as people slowly filter in as their reminders remind them of the time uh I'll start by slowly flipping through the irtf note. Well, though,.

A

So welcome to everybody, who's already joined.

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As I do want to draw attention of everybody who has joined to actually pay attention to the slides on the screen and if you're not on the slide view, you need to click on presentation mode on the top screen, as the noteworld does contain.

A

Admin stuff: we need to tell you about.

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A

uh And, as a last slide of the note, well just a reminder that rtf for those- hopefully most of you, will know it is an organization to conduct research, it's about forming collaborations and uh we're not about standardization, like the ietf, our sister organization, and with that the note well out of the way um I'm going to close this, I would like to introduce our uh speaker uh wolfgang dur, so uh valve gang is uh an associate professor at the university of venezuela.

A

uh It works on all aspects of quantum information theory and has contributed to various topics across quantum networks, metrology measurement based quantum computing, decoherence and large scale entanglement and multipart entanglement, especially during his master thesis. He has co-invented the quantum repeater which hopefully most people in this should be aware of, uh and uh he has worked a lot on multipart entanglement, but rather actually than me talking a lot about wolfgang.

A

I will let him talk about uh his work, so I will now uh hand over to wolfgang and thanks for agreeing to this meeting, is there an issue with this screenshot, though it seems.

B

I have a screenshot he's here, yeah before it worked now, I ask for permission and it.

A

B

Say yes and okay, no.

A

So you can always just do that shared slides, they're uploaded.

B

Just switch to the presley slides then, so I also have to ask for permission for this. So, okay.

A

Okay, I'll, let you use that.

B

A

Thank you volga and I'll hand over to you now.

B

Okay. Well sorry,.

A

Just one more thing: uh wolfgang you're, okay with people asking questions during the talk as well.

B

Yes, yes, that that's completely fine, just interrupt me, it's better, that you understand something, and I don't get to the end until that you don't fall asleep. Okay!

B

Well, thanks a lot for the kind invitation, I'm really happy to have the opportunity to present some of the results we we obtained in the last couple of years in the my working group here at the university of innsbruck.

B

um Well, this results are mainly together with jorge miguel ramiro, who is still a phd student with me with alexander pinker, who finished his phd. He's now earning real money and with ferran we're a sabbath and, to some extent of eures of berlin is also involved. So the title of the talk, which I think was actually never really advertised, uh is genuinely optimized entanglement based quantum networks.

B

So what I want to do today is uh really trying to convince you that entanglement based networks really give you some more opportunities than the standard way of thinking about quantum networks and on the other hand, I would try to convince you that we are not really yet at the most general level. So we can really try to make the uh the quantum networks a little bit more general by essentially having a quantum control plane rather than a classical control.

B

So that's the overview, so I will first start with a very basic introduction motivation about entanglement and and how how to use it. Why we really want to have a network. I will tell you about what we understand under an entanglement based quantum networks and in particular, that you can actually optimize these networks uh independent of the of the real physical structure of your underlying physical networks.

B

Then I will show you how to really make your quantum networks genuine quantum uh and then, if I have time, but this is flexible, I can tell you about some other relevant network protocols for long-range communication, some some bits and pieces uh where we try to contribute to this. Okay, let me start with this introduction.

B

So if you look at the classical system, then the bit is sort of the basic unit of information. The classical bit has a value zero one and well that's about it. You can manipulate this bit. You can store it and everything we do when using a computer or sending information through the internet is exchanging and manipulating bits.

B

Now, in the quantum world, things are a little bit more complicated or different, but that's what makes things exciting, namely that these, if you look at the simplest quantum version of the cure bit, it's not only in the state, zero or one, but it can be in sort of a kind of superposition of both at the same time with different weights and actually there's also a phase involved. But that's not so so important. But the important thing is that now we have superpositions of different state, not just the basis states.

B

We can sort of represent this by the block sphere by a vector pointing in one direction in the space of r3, and uh this vector can point actually not only up and down which would correspond to the classical bit values, but in any direction, so it can be in any superposition of the state 0 and this superposition actually makes up for this. uh What is the the true power of quantum physics?

B

Because if you extend this basic principle of a single qubit to more complicated systems like two qubits now you encounter that there are superpositions of states which have a form like this one which I'm I'm I'm showing down here, is psi plus, which is a zero one, plus one zero and these kind of superposition states.

B

They are called entangled states and these entangled states they. They have very nice features and counter intuitive features. If you do measurements on them, you of a single qubit. You get a completely random outcome, independent of what measurement you do. But if you do a measurement on the other particle as well. In the same basis, then you find that the results are either correlated or anti-correlated, depending on which measurement bases you're using and what we've learned in the last couple of years or decade is that these entangled states.

B

They are not only fancy and have some some sort of weird features, but they can act as a resource. We can do something meaningful and powerful with this kind of states.

B

Well, that's just for to complete this there's a nice picture for to visualize an entangled state, namely the singlet state. uh You can visualize it as a rotating coin, where sort of the state of each system has not yet is not yet defined, but once you stop the coin to rotate, which correspond to doing a measurement you and then you look to the coin from one side, this is what ellis does one party does, and the other party looks at the coin.

B

From the other side, then these measurement outcomes, what you see as a measurement value. They are really complementary.

B

You get a different outcome, so whenever one sees head, the other one sees tails, and this is a picture I I, which was coined by my colleague of mine, from the tactics uh but which I find very nice to understand what entanglement is and make me, and well it's quite nice to do to use this at school at high school, for instance, okay, but anyway, um coming back to these applications of these entangled states, well, there's or what this is called. What einstein called something like a spooky action at the distance?

B

If you do a measurement on one side of an entangled state, you can sort of enforce the other particle at the other side to show to to point in a specific direction. But one has to be careful. uh It's like it's somehow a remote state preparation, but not completely so you can. I you can only choose the direction, but you cannot choose whether the state is showing up or down.

B

So you can control choose the bases, whether you want the z basis or the x basis, but you cannot choose the result of the measurement and you're gonna choose whether it should be the zero or the one state. So this is not useful for communication without any sort of classical side channel. But if you've got this as well, then you can do our most favorite thing in this in this in the quantum networks business, namely teleportation, that we can transmit unknown quantum information.

B

So an entangled state is a resource uh for communicating the state of an unknown cubit, but that's uh that's sort of not coming for free. On the one hand, you need this entangled state and you have to prepare it beforehand, but once you have it, you can communicate whatever other state you have and on the other hand, you need some classical side channel.

B

You need some two extra bits of bits of classical information in order to complete the teleportation process and that's crucial that we have to keep in mind and when we talk about quantum communication, chance and quantum networks, we always have sort of an underlying classical network as well.

B

Okay, but uh throughout all the talk. What I consider is that this classical communication is cheap and we can do it. We can do it fast. We can do it without problems and the quantum communication- that's actually the hub, so we concentrate on the quantum communication, so this was about two qubits and entangled states of two humans. But if you have more systems several qubits, there are other interesting entangled states which you, uh which you can have, and one interesting entangled state of particular interest. Is the so-called ghz state depicted by this sort of spider?

B

So the second plot here, because I I guess you cannot see my pointer and I don't know how to get one but anyway, okay. So this gt state is a sort of the generalization of a bell state where either all cubits einstein. Zero are all cubitized state one. So all of these particles are correlated with each other and uh it's sort of a toy example of of assorting a cat if you wish and this ghc state.

B

This has many other applications that will come to this shortly, and this is a special case of a of a larger class of interesting multi-party entangled states which are called graph states and this graph states. This is what what I will talk about throughout most of this. This talk and this graph states they are defined as a class of multiparty entangled states associated with mathematical graphs. So you have a set of vertices connected by edges and to each graph.

B

You can associate a state by just saying whenever I have an edge, I have an entangling gate between these particles.

B

That's the first definition of this graph states, but equivalently you can describe these graph states in terms of correlation operators, so there are joint eigenstates of correlation operators which are just defined by putting an x on a vertex and c on all the neighbors on all qubits which are connected, and in this way you really define uniquely a class of states which corresponds to all possible graphs.

B

Now the nice thing with these graph states is that, in contrast to general states, you can actually describe these states efficiently and you can prepare these states efficiently, because if you look at the general multiparty state, you have exponentially many coefficients and it's usually very hard to describe these states, but the graph states you can describe efficiently and you can prepare efficiently and the even nicer thing is that there are many examples of interesting states which are in this class of graph states like code words for error, correcting codes like these ghc states, which are resources for metrology like this 2d cluster state, which is a resource for one-way, quantum, computation and so on and so forth.

B

Now these graph states, you can actually manipulate them as well. You can erase certain vertices by doing that measurement. You can join different graphs by merging vertices and you can. You can change the graph by uh doing a so-called local complementation of the neighborhood graph. So there are many ways how you can modify the structure of your state by just doing local operations and actually I've sort of summarized some things you can do.

B

So if you start with two, if you look to the top, if you start with two different graphs, this would correspond to sort of code words for error, correcting codes. You can actually merge them together. Such they form a joint graph. Now the second example, this is the g and c state example, and what you can do from a g c state by measuring all but two particles. You can actually prepare a belt state between these two particles and you can choose which of the bell which of the particles should share against it.

B

So you have some flexibility in sort of sharing different kinds of entanglement. If you start with the bell state- and a generalization of this- is a graph state of six cubic butterfly state, it's called from which you can actually produce two bell states shared between any two of these red particles. So all these different configurations, and more generally, if you have a 2d cluster state, you can actually go to any graph stat just by doing local measurements. You can do this deterministically, and this is what is called one way or measurement based quantum computation.

B

The thing which was coined by or introduced by, paprika and rousendorf quite some time ago, but sort of what you need is a little bit or is a larger 2d cluster states or a graph state corresponding to a rectangular lattice and from there by just doing measurements on the particles and by choosing the proper measurement basis you can choose which state which other state you want to produce.

B

Okay, why? I'm telling you all this? Well uh the one hand we want to sort of generate these graphs that I'm trying to say okay. Well, they are important. They, they are quite general, and there are many many interesting applications. You can do with them. So if we talk about the quantum network, we actually would like to share uh that this network can produce these graph stats that the parties, the nodes in the network, can do interesting things with with this graph stats and what you can do with disentangled states.

B

One thing is teleportation already mentioned, but even more importantly, is the quantum key distribution of quantum key enhancement, actually also that you can do secure communication, you do cryptography based on these entangled states or by sending quantum information. Both things work. You can actually generate these different, multiple graph states and the gst states and other graph states. You can use them for secret, sharing secret voting, some conference key agreement, some security, secure, multi-party applications more from a physical perspective.

B

What is also nice is that you can use ghc states for clock synchronization that you can synchronize different atomic blocks. You can actually enhance the accuracy of of distributed clocks. You can use this for metrology, so quantum metrology.

B

This is the science of doing measurements, precise measurements and if you are interested, for instance, to measure the earth's magnetic field or the earth's gravitational field- uh and you are not interested in just this- that the field at a certain position but at different positions, then, if you distribute certain entangled states, some g and z, type states or others, then you can actually do these kinds of measurements.

B

With help of this distributed multiparty entangled states with an increased accuracy, so you can actually sort of choose the internal states of your sensors, which are different positions in such a way that you can choose which quantity you want to measure whether you want to measure sort of the zeros moment of the field or you want to measure the gradient or you want to measure some fourier coefficients. You can choose by choosing your your state, what you want to measure and actually by using this quantum, entangled states.

B

You can do this in a molecule and last but not least, is distributed quantum computation, because nowadays we are talking about having available some small scale, quantum processors, but in this nisk area, with these noisy intermediate scale quantum devices these processes- they won't be very large. So with this current setups, we can expect something like 10, 20 cubits, maybe 50, but it's not so easy for some of the setups to scale this up to huge systems. But if you have several copies somehow of these setups, several small quantum processors.

B

Well, if you only have them disconnected, that's not very powerful. Actually, it's like having m copies of something and sort of the computational powers m times uh the one of the individual one. But if you manage to connect them to connect these uh these distributed processors, so they can be at different positions in the same lab or they can really be distributed among several cities or among the whole earth.

B

uh Then, if, if, if you do this, then you actually get a quantum processor which consists of the sum of all these qubits, and this is actually exponentially more powerful than the individual ones. Okay, so also from this perspective, to connect these quantum devices to connect the quantum processors, that's also an interesting thing.

B

Okay, now let me come to this entanglement based networks. So, if you think of the standard way of quantum networks, the way you probably think about the quantum networks, you will have quantum devices which are connected by channels and the goal is then to transmit quantum information between these devices. I want to prepare some entangled states which is sort of equivalent, and the usual approach is that you have a classical control plane, which sort of orchestrates everything and this control in this classical control plane.

B

This controls the quantum devices, and then you have to design a protocol to distribute your entanglement and to utilize it, and the main pro main problems in this context are the rooting of entanglement how you get in a given network that you share entanglement between some given two parties and how to do this over a long distance.

B

And quantum repeaters, this is actually something or a way to overcome: channel noise and the way to overcome the no cloning crm.

B

If you, if you want to say so, uh which is basically uh or one variant of the quantum repeater that we introduced some long time ago, actually during my master's thesis, is sort of based on entanglement that you purify entanglement by having several copies of noisy entangled states, you can sort of distill the entanglement into fewer copies, and if you connect, then these sort of short distance pairs of of of high fidelity is still uh you the fidelity decreases.

B

But then you can repeat the process with the longer distance pairs and you get sort of a nested and nested loop of this kind and what can actually show that this is an efficient way of generating entanglement over long distance and then via teleportation to ensure uh corner communication.

B

But what I want to convince you today is that the quantum network is more than just a variant of a classical network that transmits quantum information rather than classical information.

B

And um but okay, I think basically, I said so that the bottom up approach is the usual approach you generate entanglement between end nodes. uh This is similar as in class classical networks. You receive some requests parties a and b say uh well, we want to talk to each other. Please provide us with some entangled states and they these parties. They are connected via different channels and some via some intermediate nodes, and then you have to cook up a protocol how to generate this entanglement. Why are different passes or or whatever?

B

I don't want to go into detail, and but what you should bear in mind that this process of generating entanglement doing this over longer distances and really sort of establishing an entangled link between two parties. That's way more complicated than just doing classical communication between the two, because for classical communication, you just send things along and noise doesn't really harm you very much- and you don't have to worry about about this.

B

There are several passes that you can use it's just that some package eventually needs to to appear at the side b and that's sort of already achieves your communication. Well, with the quantum systems, it's way more complicated, there's a huge overhead in resources which you have to use. uh You have to repeat: you have to use the noisy channel several times.

B

If you want to run, then this entanglement purification and get high fidelities and also you need several rounds of classical communication to make sure that actually the qubit you send arrived on the other side or that your entanglement purification step succeeded so bear in mind that there's a huge overhave to obtain disentangled states, and so if there is some request, some quantum requests on your network, then actually you will have to wait for quite some time before your network.

B

Your underlying physical network manages to establish your entangled link say between here innsbruck and some very far away cities.

B

Okay, so that's the bottom up or the usual approach, I would say- and of course there has been many attempts to uh to design protocols there. I uh many people here the delft group and but also rodney. They contributed significantly to this okay, but what we said is well, let's take a different angle. Take a different point of view make a top down approach which is sort of inspired by this measurement based computation, namely work with entanglement as a resource, and we sort of cook up our network or our entanglement based. Networking is three phases.

B

The first phase is really generating certain multiparty, entangled resource states and well. This is essentially the same as what is done in the standard network, with the difference that we know which state we want to want to get, and we know beforehand. We know from the very beginning which states we want to generate and we have. We can do this not when a request comes in, but already before we can sort of when the network lies idle, we can use it to establish certain entangled states.

B

So there's no time pressure for this, and then um we enter the static phase, so these entangled states they have been distributed among the nodes, the part, the nodes, so the the components of the network, and then they are just maintained and stored. So you need a long-term quantum memory to achieve this, but actually to establish long-distance quantum communication. You already need the quantum memory.

B

It's not just a big deal to have this quantum memory available for longer times, and even if you, if you're, if it's just working for some time, okay, you can refresh the resources which you have okay, but in the static phase. Essentially, you just store and maintain the entanglement entangled states.

B

Well, unless you get some network failures, some some devices drop out or log in and then you have to update your network step, so the resource state which you want to share, because of course you want also new devices to participate in any other critical well and then the final state is the adaptive phase and in this adaptive phase what you do is you manipulate your entangled resource state which you choose properly at the beginning, such that you generate the desired target step. So here is when now the request enters.

B

So this the phase one and phase two we did beforehand and now comes a request now particles now some two nodes say I want to share a bell stick or I want to to share a ghc state with this. With this other two parties, and once this request come, the only thing you need to do is adapt your stored, entangled state. You manipulate your stored integrity state just by local operations, local measurements and some classical communication, and you can, if you have chosen the state properly, you can actually get the desired target state.

B

Basically right away. You only need one round of classical common education, saying where everybody says well. This was the measurement outcome I got and then the target parties can just correct: do some correction operations as in teleportation, and they share the desired target step. You don't have to use your quantum channels anymore at this stage and that's why this approach is really fast at this stage, of course, for building up the entanglement, you essentially have to do the same work as before, but once you need it, you don't have to start from scratch.

B

You have it already prepared, and I should emphasize well sort of this. Top down approach is something like an extreme case. Of course, you can think of hybrid schemes where you just share some a few copies of some entangled entanglement in such a way that you can speed up uh the process for for providing the quantum communication.

B

So it's not that a must that you do with everything in this way. Okay, so another interesting thing is that now this topology of this entanglement based network. This is sort of uh given by the entanglement structure of your shared state, and this is independent of the underlying physical network. So you can build sort of your own optimized network on top of your physical network, and you can design it in such a way that the requests of the network, the functionality of the network, is sort of fulfilled by your resource state.

B

It can be fulfilled without delay. That's what I said already but the question one of the questions which resource state should be stored. What are good resource states and, of course, if you just stare bell states between all pairs of notes or all pairs of devices in your network. Well, that does the job, of course, because you can use these belt pairs for teleportation. You can merge them together to form graph states. You can basically manipulate them.

B

But if you look at this from a storage perspective, well, every node has to store a lot of different values and that's actually quite wasteful, and you can do better by choosing proper multipattern entangled states. Then they allow you for storage advantage, and let me just try to sort of show this a little bit if you have a four node network and the goal is to generate an arbitrary graph states between these four nodes.

B

You can either do this by head by sharing an entangled pairs between every pair of qubits or between all the different nodes, and this in total takes you something like 12 particles to store. Now you can achieve the same functionality by ghc states, a g at c states of for size, four, a gt states of size, three, the green one and the bell pair, and with this you have a little bit less resources, seven qubits only which you need to store, or you can also achieve the same functionality by so-called decorated graph states.

B

Where you take a fully connected graph and you put an additional cubit vertex on each edge and this one allows you then, to decide for each edge by measuring this out, either in the z or in the y basis, when you want to have this edge, if you imagine the y basis or you don't want to have this edge, you erase it and then you do the measurement in the z basis, all of these states. They allow you for this full functionality, but they are sort of made up of different resources.

B

And then the question is what is what are the best ones which give you the minimal error which which give you the minimum storage requirement?

B

And that's what we concentrated on when I talk about optimality, I will talk about the sort of the storage requirement. I don't worry about noise at the moment, but of course one has to take this into account as well. Well, for this entanglement based networks, we actually came up with a stack model uh similar to the oc model. We have a physical layer of a connectivity layer, a link layer and a network layer where you have sort of devices quantum devices associated with the different layers. The physical layers have to channel the connectivity layer.

B

You have a repeater to establish high fidelity, entanglement the link layer is our switches or quantum switches, and in order to connect different networks, you have a router and then, of course, there are different protocols how to establish these entangled states and how you would manipulate them in order to get the desired target configuration say if there comes a request that one one node in one network wants to share in the tangled state with another node in another network, then you have to sort of manipulate these resource states, which you have to design of course.

B

First, uh in order to get these entangled states- and this is these- are things what we did in this in this paper together with alex alex berka, and I I won't go into details with this- I just flash that this different network devices there are resource states. You can try to optimize them.

B

You can design protocols to generate these states to transform these network states to the desired target, state, the state linking protocol region, routing and so on and so forth, and there are also methods to ensure reliability, maybe, as we say a little bit about this um okay, um well, okay, this is just a graphical representation of this, where you have sort of three routers which are sort of form three different or it's one network consisting of three routers and one switch, and they are connected by physical channels, which are these orange tubes, and there is entangled states shared inside these, these routers and the switches in order to ensure their functionality and their entangled states shared between the different devices.

B

And one thing I want to point you to is that if you look at the connectivity in physical terms, which are the orange tubes, this connectivity is different than the entanglement structure of the state's list. I will come back to this later.

B

Okay, I will skip this example. I'm running out of already late a little bit um well regarding the reliability. One problem you have, if you share these entangled states, is that they are actually very uh susceptible to noise. So if you have it, if you take a gfc state and you uh you lose one of the nodes, one of the nodes disconnects or the one particle get lost, then the whole glc state is destroyed.

B

So if you really share a big gfc state among several parties, then by just losing one of the nodes, everything is gap, so you have to think about strategies how to protect this and depending on which of the nodes. If you take this sort of universal structure with different size, jc states, depending on which of the nodes use, it loses a particle either your whole antenna can be destroyed or only part of it, and you can sort of use this by by doing a symmetrized version of this protocol.

B

In order to protect more parts of your entangled states, or you can actually add some shield particles in the sense that if one of the nodes disconnect other parties hold an extra cubit which they can sort of measure, then in order to disconnect this other node in a controlled way, even afterwards, even after it really uh really, the particle is lost and the remaining entanglement stays intact.

B

Okay, but let me switch to these optimized networks to really cooking up your own entangled network and sort of constructing this in an optimal way. This is a work with alex and parker, and uh what I want to emphasize is that usually in the in the club in a standard network, the channels are just given you, you have nodes at certain sites and they are connected by some cables or some uh by some channels and there's not much you can do.

B

You can maybe put a little some some extra root or some extra switch, but uh usually the sort of the physical structure of this network is given and you just have to work with it, and if there is a bottleneck in the network, if you really want to communicate from one side to far away side, and uh if there is sort of only a small link which is used heavily, then this is really sort of restricting your communication. There's no way around this, you have to build some extra physical channel and this might be complicated.

B

On the other hand, if you just want to share some intended states, you can actually choose which entangled states to share, so you can just say. Well, I take these parties a b and c, and I decide these three. They should say. I should share an entangled state and I choose this because I know that these three parties- they tend to talk a lot to each other, so I better have some entangled states prepared for them.

B

So actually what you can do is you can optimize the geometry of your entanglement based network network in such a way that you minimize storage requirements and guarantee the functionality of the network.

B

Okay, now, um the way we think about this, this quantum network, then, is that there is a certain set of functionalities.

B

This network should fulfill, if you have these end users in there these nodes in there, and they want to share some entangled states user one wants to share an entangled state with user seven and that's one use case or one possible functionality, but it can also happen that two of the uh the users want to share an entangled state and there are sort of a bunch of possible possibilities, and each of them can be described again by graph or a graph state. If you wish, and these all these functionalities, this should be guaranteed.

B

So the functionality of the network is sort of given by a set of graph states with certain probabilities.

B

The probabilities that this particular use case, uh or this particular functionality is requested, and this sort of makes up what this or defines what this quantum network should do and in principle, from previous data analysis, you can already determine what is your expected uh sort of um target configurations or quantum communication going on on the network?

B

Okay and what we are interested in is that for a given functionality, what is the minimal resource state to guarantee this functionality either deterministically that each of the use cases can be fulfilled or uh sort of corresponding to this give to these different possibilities? If you, if you talk about the multi-copy regime, but let me stick to the to the deterministic regime where you say: okay, all use cases are equally likely uh and we just have different target configurations.

B

So, but what we can do is we can adjust the topology of our network to the desired target, configuration and recall. We had two tricks of reducing the size, namely one trick, or that there are more. Actually we came up with another.

C

B

uh But the first trick is to say: well: uh the ghc state is actually a resource which can guarantee me a single quantum channel between any two particles in there, and this really saves a lot of resources. If you don't know beforehand which of the two parties want to communicate, and it's just one communication you want to guarantee and on the other hand, the six cubic butterfly state. This can actually guarantee two parallel um communications.

B

uh Two parallels sharing two parallel spells pairs between two different pairs of of notes, and this has been considered by by rodney and then also against isaac, uh but you can sort of generalize this state to larger systems, and what you see is that actually uh by you can save a lot of particles. If you really do it, uh do it like this, so our approach really consists in two steps: we first analyze sort of our our network, our desired functionality via clustering, algorithms.

B

You really want to identify which nodes in the network uh do heavily communicate and which nodes are more or less separated, and for this you can actually use uh classical clustering.

B

We have just have to cook to come up with the appropriate matrix, the cumulative matrix, which sort of gives you the number of links, uh the number of times the link appears and from there you can do a clustering, algorithm and identify sort of nodes in the network which have high traffic and nodes in the network which have lower traffic, and this really gives you the different regions in your network, which you uh sort of connect with each other.

B

So somehow this procedure gives you the topology of the of this entanglement based network, because uh you you make that these these these highly connected uh curates they they share, entangled states of a specific kind, and you can actually do this in a hierarchical way that you can then within some one of these heavily used networks. You can sort of say I take a router which represents this network and then make the same clustering algorithm at the next level. You can do arabic, clustering and then sort of a hierarchic construction of this reason.

B

Okay, that's one thing, and then you you just put bell states wherever you need them and then the second thing is, then, uh that you try to sort of reduce this spell states to multiparty entangled states and this what we do by a merging algorithm, which basically tries to uh rather than having two independent parastates, try to really join them together, like if you go back. If I go back to this glc example, if I have all these different functionalities, which I desire, that you have all these different belt pairs.

B

Well, actually the the clustering algorithm constructs out of this. This ghc state, which gives me the same functionality, and while these plots they just show that this actually works very well. If you look at the bell state approach, so on the on the y-axis is the total number of qubits you need to store and on the x-axis is the number of network nodes, and then we put a sort of randomly chosen target configurations and of different kinds. So that's why we have many different different plots corresponding to different types of networks.

B

Essentially, and if you look at the curves for the gnc states uh for for the bell states, well, actually the resource requirements they they sort of uh scale quadratically with the number of network nodes. Well, if you do the clustering and merging approach, this is the green curve, the lowest one. You really save a significant amount of of of of memory, so you don't need to store that many cubits, okay and, depending on the target structure, that the structure of the target states this this. um This can be even more enhanced.

B

If you look at the top curves okay now uh let me switch gears a little bit and um sort of leave. This entanglement based networks, because what I have to say now also applies to the um sort of standard uh bottom up networks and um we went and come to this, what we call genuine quantum networks.

B

So the idea here is that you perform the different tasks in the network, so the state generation, the state, manipulation the sending the addressing not uh sort of in the classical controlled way, but in a quantum controlled way that you can do everything there in.

A

Wolfgang can I pose you. uh I think tobias has a question.

B

Okay, sorry, I.

A

B

A

Yeah yeah, so sorry, I'm yeah, so I'm kind of bringing that uh tobias. Do you have a question? Would you like to ask it? uh Yes, if you can hear.

D

Me yeah all right. um I have a question to this entanglement based networking thing: can you actually use them for entanglement based quantum key distribution because they need this maximally entangled state in order to be not uh having this problem with the trusted? Repeater thing yeah sure, but that's what.

B

You're sure, if I say I want as a functionality to share a bell state, what I really mean you share a maximally entangled state in a more or less noiseless way, or is it as good fidelity as possible, and then you can of course use this to all these fancy applications. I said at the beginning, including this cryptography.

B

A

Er and mattel: do you have a question.

C

Yeah hi, can you hear me yeah, yeah hi? I was wondering uh in the metrics that you show in uh I think a couple of slides ago, uh where you see the number of qubits that are required to achieve those entangled states. Is it taking account also the way that those, for example, gh ghd state, are generated, uh for example, if I need more qubits to do uh entanglement swapping to to achieve the ghz states, are those qubits taken into account uh as a slope.

B

For the generation, it's just for the storage.

C

I think, because you.

B

Can generate them and then this I don't count at the moment, at least for what I showed you. This is not taken into account. What extra cubes you need at the immediate level, I'm only showing sort of the the qubits for a long time memory, the ones which you need to store, eventually not for building up. That's a different kind of problem or sort of living in a different phase of the network.

C

Yeah great thanks.

B

But of course you have to take this into account eventually as well.

B

Okay, so I don't see any more questions at the moment, so I go on with this genuine quantum networks. So, okay, so, rather than doing everything in a classically controlled way, only one thing, one predefined sin or one single one agrees on. One really does things now in a coherent uh superposition.

B

So uh do not so I tried to depict this here with uh with what I said before from a ghc state, you can go to either sharing a bell state between two particles or two others, or so or other other twos or other pairs of particles, and rather than sort of choosing one of these possibilities.

B

You actually do this in a coherent way that you that you actually share the superposition of all these different uh possibilities, and for this you need a quantum control plane. You need sort of a quantum register with different weights and different phases, which actually controls everything which is going on and well, I I put some maths here, but actually that's not so not so complicated.

B

So you start with a quantum control register, a superposition with certain weights, and then you try that then you, you sort of prepare a state which is an entangled state which is shared by all the parties which are involved in the protocol, so everybody now holds sort of uh the same state. So the sum of all these cases, it's a generalized g at c state. Essentially so all of the qubits are zero. All of the qubits are in one.

B

If you just have two choices in your control register and everybody shares this step, and now you do all the operations in a controlled way.

B

So for the state preparation, you do some unitary circuit uh controlled on this register, and you do this this on at every place, and by doing so you actually generate okay, there's one more step, then you can actually erase uh most of your control register, except at one party, and then you share a superposition of all desired target states with uh with this control register still attached and then sometimes you may want to get rid of this control register.

B

But I have to say that this is not always possible in some use cases. It is, but it's not generally possible, but that's what you can achieve in general.

B

But, uh okay, that's all nice if the operations are unitary. But what happens if these things, which you want to control, they are actually classical themselves like a measurement measurement, is actually a classical process. You get some classical data from it or sending a photon, that's also a classical process. At the end, you use the gem.

B

You send something wrong, but how can you make all this work also if the processes themselves are classical and actually in general, like a measurement super boost measurement, you want to sort of uh measurement is described by pvm, so some positive value operators- and you have certain outcomes- labels like say by k- and you want to achieve a certain outcome with certain probability.

B

Then you want to get the target step and what you want is a superposed measurement would be something where you either do no measurement with certain probability or uh you do a measurement and get the the the the outcomes according to this probability distribution.

B

So you either do so you want to have a coherent superposition of no measurement being performed and getting that uh sort of a certain outcome in your measurement and the probability distributions should match by the one just doing the measurement. But if you look at this process, actually it turns out that's a non-linear process, so this really seems to be impossible.

B

But uh what you can do is you can mimic the process you can sort of? uh You can get the same output states by actually always doing the measurement either on the system. You want to do the measurement or by some auxiliary system, which you prepared in a certain in a certain state, but you have to know the probabilities of your measurements outcomes for the input state in order that you can sort of prepare the right auxiliary state. If you don't have this information, you cannot do it.

B

But if you have this information, you actually get exactly this desired map. You get exactly this coherent superposition of performing a measurement or not, and actually this is useful for our purpose, because if we manipulate entangled states, we actually do measurements on entangled states and they have a probability distribution which is always flat, so equal probabilities. So we know exactly which kind of states we need to put as auxiliary state in order to mimic this, and then we can have something like a controlled sending or control teleportation.

B

Where you either sort of do a bell measurement on your qubit, you want to send and the part of the bell state or you do a bell measurement on some auxiliary qubit and the plastic, and in both cases you get a completely random outcome and what you end up with is then a superposition of the cubic being transmitted through the others to the other side being teleported, that's the second possibility, or the cubit still being there and just the auxiliary state being destroyed.

B

Okay. This way, you can add quantum control through this teleportation process, and you can also do the same thing with the mergings. The manipulation of graph states actually with. Basically everything.

B

And also with the control transmission, you can uh send a photo not just through one path or another pass, but you can send it in a coherent superposition of one pass and the other pass at the same time, and actually people have realized uh that this allows you to transmit information through channels which each for themselves is useless.

B

It's completely entanglement breaking, but if you have access to both channels at the same time and can sort of send a photo in a coherent superposition through one pass or the other and recombine it at the end, then you can actually transmit information, and this is related to the things that are things which is sort of this castle order or quantum switch.

B

But actually you don't need to sort of different time orders, not this sort of artificial thing, but you can do it with real different channels. In the real me, okay, one more thing we can do with the superpositions is well actually, rather than preparing a certain target state, you can actually prepare a superposition of different target states. For instance, a gfc state shared between any set of three qubits.

B

So if gt states of size three and uh you don't share between a fixed set but between any possibilities, any uh sort of permutation of the three parties, and by doing so actually you find that if you look at this at the each of the possibilities of each of the gfc states, if you do this for a four qubit system, if you, if you lose two of the particles, all of the entanglement is gone. So the state is completely useless.

B

But if you sort of do this with the superposed state in this specific way, I'm writing here and if you then lose two particles. The remaining state is still entangled so by preparing these coherent superpositions of different possibilities, sort of not uh sort of just or not not selecting beforehand, which of these of these three parties should share entanglement.

B

By doing so, you can actually protect your quantum, your quantum states in a better way, and you can also sort of have superpositions of sharing different kinds of states and then deciding later on which of those things you want to use. uh You can think of really uh doing a superposition of different error, correcting codes.

B

Two of different cryptography protocols: there are many possibilities we haven't explored all of them, but I think there's really lots of stuff to do to consider and maybe things where you get an improvement, a surprising improvement similar as the same with the super bowl channels and superposed path. Well, what we did is to to use this idea for a thing which is called cohere or randomized benchmarking, which is essentially benchmarking, a device or a channel in order to learn when you do some some gates.

B

uh So you say you have some small quantum processor which can do a certain set of gates, and then you want to learn.

B

uh How good are these individual gates actually and there's a technique which is called randomized benchmarking, where you apply sequences of random, randomly selected operations and and then you do a certain bunch of measurements specified in a certain measurements, and then there is an efficient way of learning the average fidelity of each of these individual gates by just doing this randomized measurements on uh sort of circuits of varying size, but unfortunately, this benchmarking.

B

This is limited to certain classes of operations and uh sort of two specific groups- clifford group, for instance- and you have a scaling problem. So if you really want to benchmark larger gate, sets operating or not just a single qubit, but on many.

C

B

This is really scaling bad, so what we said is well, rather than let's take our idea from this coherent superposition, rather than sort of doing several independent tests of randomly selected gates circuits. So usually you would do select a certain sequence of gates. You would apply this and then you do some measurement.

B

You repeat this repeat this several times for this specific set of of gates, and then you select another set of gates and do the same thing again and yet another set of gates randomly selected, but rather than doing this in this sequential way, you can actually do this in a coherent, superposition, so sort of testing. All these different gate sets at the same time, and actually what we found is, if you do this, it's not only that you get an improved efficiency, so faster convergence of this of this procedure.

B

But it's also that you get that that you can actually test larger gate sets actually uh general gain sets, and the thing is that you can achieve this by having sort of an external device which provides you with this, uh producing these coherent superpositions and the gates you test. They are still the same. So that's one use case of this coherent, superpositions.

B

Okay, so I'm not sure how well I'm doing this time. I think I'm pretty late already, so maybe this last thing is other protocols I wanted to mention. I just give you two three buzzwords without going into any details.

B

So one thing is about raw long-range, big quantum data transmission, and this has to do with uh how you realize your long-range communication, and if you do this with the standard repeater the standard quantum repeater we introduced back in 98, I think or if you do it with other types of modern types of repeaters with encoded or sending encoded information or distributing encoded entangled states. So all these approaches they essentially they scale somehow with the distance only polynomially or logarithmically, but this scale is the distance.

B

What we came up with is a way to avoid this and actually do uh quantum communication of large amounts of quantum data in such a way that they require the resources they don't scale at all with the distance. So if you count sort of the number of qubits you have actually to transmit through a noisy channel and then make a relation to the number of qubits you actually get successfully, throw which way succeed in transmission, then um this is.

B

This is approaching a constant and the key idea behind this is a measurement based implementation of doing all the operations which are required for error correction or for entanglement purification.

B

There is a trick, which is this measurement based what we call measurement based quantum communication that you in order to manipulate a state, you can sort of teleport it through a certain entangled state, and by doing so you not only transmit the information, but you actually perform a certain operation.

B

Like you perform an encoding operation, you perform a step of an entanglement purification protocol and what you do is sort of given, by the shape or by the type of entangled state you teleport through, and that's the basic trick, what we use and this trick. This really has the advantage that you get a a really good error uh sustainability. That is uh your your resource states. If they can be very, very noisy up to 10 percent of noise per particle, and still these processes work.

B

Okay, based on this, you can sort of cook up a quantum communication scheme based on the usage of finer size, hashing, and then you really get something with fine outside. That is a constant scaling distance.

B

um We worked on more entanglement purification protocols using a high dimensional register to learn information which actually turned out to be more efficient than some recent work which we just published in prl this year. So if you are interested in this, uh you can just look up the paper, and the final thing I was saying is it's another work where uh which is also accessing like a nice concept?

B

Well, where you can sort of store the information in the quantum network, not in a localized way at individual nodes, but in a delocalized way that you sort of distribute your information holographically among the whole network, and the advantage of this is that it's it's better protected. So if some nodes fail, only a small amount of information is destroyed and on the other hand, uh it's also that not all the information is accessible.

B

So if you want to sort of store the information in a secure way such that several parties, so maybe all of them have to come together and work together to get the information and if you just have individual parties trying to to get it, they just can get some small amount of information. And these two things.

B

This is what you can achieve with uh this delocalized information storage in this uh in this quantum networks- and you can actually do this in a in a natural way by doing basic protection, not in an active error correction way, but really choosing some sort of encoding where you stick your states or w states, and then you really get uh sort of a large, um so little accessible information and many nodes can can fail, and only little of your of your information is destroyed by this.

B

And actually you can uh generalize this to really come up with networks. Where you have your information stored in parts of your network, not in a single node but another certain subset of of nodes, and that you can actually transport it through the network, and then you can localize. Also the information, then at a given node, which you choose or that you can say it should be in a certain region and all this manipulation can take place by uh by only doing single qubit operations.

B

So it's really a measurement based based okay, and with this I'm at the end. I just want to remind you of the two headlines. I had, on the one hand, the entanglement based networks, which sort of shift the challenges to build quantum networks and give you new possibilities and new features. You can optimize networks, you can prepare resource states beforehand.

B

You know what you should prepare and, on the other hand, these genuine quantum networks, where we actually go away from the classical control plane and make everything in this quantum networks, genuine quantum and also have a quantum control plane and then achieve also some quantum addressing and stuff like this, and the questionnaire is what else other than these small things I showed you. Can we do with this additional power?

B

Okay, then, thanks for listening and I'm open for for questions happy to take some.

A

Thank you very much for that talk wolfgang. uh So if there are any questions, uh please ask them officially. The meeting time is over and I do think mitaiko will kick us out in 10 minutes, but we are open for questions as far as long as wolfgang wants to stay so tim or rodney. Do you have a question since you opened up first, or should I start with the queue.

E

Studio back on to surface sort of a shadow chair here go go, go ahead through the people, but I'll.

A

E

Some questions later: okay,.

A

uh Tim, would you like to go first.

F

Yeah, yes, please can you hear me, can you yeah? Can you sorry? Oh yeah, that's great yeah, sorry um yeah. um I have a question about this long range big day. Quantum data transmission, I'm afraid my connection got a bit choppy when you talked about this. um I was wondering you made the claim that there is no scaling with distance, and I was wondering what you meant by this, as in in terms of time or in terms of error in terms of resources.

B

So the scaling of the number of qubits which are involved in in total.

B

If you look at the standard repeater schemes, you get some polylogs scaling in the distance and also for uh polynomial l for the standard repeat, and if you take the the one of yang and and looking you have a polyloc scaling, but all and then the error correction also has a polylog scaling, but uh it's really constant. So if you really take this, uh what I mean here is the involved qubits, which which I get divided by then the qubits I I get out at the other, the reversing sorry yeah, some rate.

B

I see the ones you have.

A

Yeah thanks, okay and next in the queue is liang zhang.

G

Thanks for the very nice talk with a lot of interesting ideas, yeah, so I I really like the part you talk about the january in quantum network, so so I think that one potential application will be related to, like a quantum run, access memory, which is kind of querying. The different addresses in a super position.

B

Yes, well, we haven't thought about this, but this really sounds like like a good idea to have a look at yes,.

G

Yeah so yeah, I think it will be interesting to extend that to the quantum network context. Yeah.

B

Thank you. Well, actually, I have to say sort of this sort of this different time order. So these these things of having a things in a quantum controlled way, that's not entirely new. I think it's new in the network picture, but uh people have started uh discussing this in this context of this temporal order or the quantum switch in different contexts, but uh not, I think not in this.

B

It is quite general terms we try to put this, so I don't uh claim that we reinvented that we invented the wheel, and I guess also rodney thought about these kinds of things already a long time ago, at least informally, he told, but thanks lang for the for this suggestion.

A

Any more questions.

A

No, I I do have one for myself, uh which is that, uh so you showed the scaling of resources, uh especially for for these entanglement based networks, um and you showed that at scale much better than bell pairs, the on-demand one. What I'm curious about is um have you tried scaling with? Have you looked at how it scales with increasing uh request demand?

A

So, as you push the network with more and more demand from end nodes, is the scaling since the scaling? I was I'm wondering if, because the scaling with resources is so good, does it also? Does it also mean that scaling with the size? The number of requests is also just as good.

B

uh Well, okay, but we looked at many different uh scenarios, so we looked at this tonight where you have only very few requests or parallel requests.

B

I have to say I think, that's the important thing if you're, if you only have single requests or a single bell pen, each of the requests or if you have several or multiple uh bell paths which you want to have which you want to share uh simultaneously and of course there is a- is a difference of which kinds of requests you uh you consider there and, um of course, the optimal thing you you get, uh the optimal improvement you get with only very few requests if each of the requests is just a single belt here, because you know rather than having all the possible belt pairs where each of the parties needs to store n minus one qubits, because it has to store a belt pair between any of the other ones.

B

You can just store a single gfc state, so that's really sort of very favorable from our perspective and if you put more and more sort of parallel traffic there, of course our improvement is going down and uh it's also going down. If you are going, if you're taking your probabilities into account, so this is really for this deterministic uh use.

B

If, if you really have multiple uses, if you have, if you say uh my network should actually be able to uh provide sort of uh billions of of these spell states uh simultaneously, then it turns out that at the end of the day, it's best to just store the bell states, but in the regime, where you have a smaller number of uh of of sort of requested uh states there, you really get this uh this. This big improvement. It's it's well, big! It's! It's still only polynomial, but in practical terms.

B

I think this can mean a lot if you really need a quantum memory of just 50 qubits or a quantum memory of several hundred or thousands.

A

Yeah, so it could be that uh if you're a network operator you actually first, you prepare all these gazette states ahead of time and whilst the demand is below a certain threshold, that's how you deal with it and you save resources.

A

But you do would have a fallback mechanism to switch back to bell pairs if it's above a certain threshold and by basically that point you're.

B

Just above capacity, yes,.

A

Okay, that's interesting! Thank you. Any other questions.

A

Another question.

F

I found the the uh entanglement-based content network is very interesting, but I must say I didn't fully understand the um the part where you talk about optimization and um my question is um um now suppose that uh we we completely follow what you, uh what you propose then, should we in practice um perform uh optimization over uh purification protocols and uh protocols to produce uh ghc states etc. Should we should this be different from if we follow a a quantum network that produces bell pairs on request only.

B

I would say that uh if you know, if you have different targets, there's a different, optimization.

A

B

And okay, I I hear feedback now uh this distracting okay,.

D

B

So that um so, depending what you want to produce, you will use a different protocol to generate it, but I'm not worrying about this part at the moment. Of course, you have to build these resource states eventually, and you have to optimize these uh these protocols also, but this is in the first phase in this sort of build-up phase.

B

What I'm looking at is really at the end is storage requirements, I'm only saying, okay, I don't worry how you would generate this, and I think that also for this generalization there is an improvement, uh because these states they might be less entangled or you have certain or different target states you want to generate, and you can really optimize beforehand how you would use your given physical network to produce just these states, but this optimization is really for the storage. So how much?

B

uh How much qubits you need to store for longer times such that you get the desired functionality of the network. This is where we showed this. This disadvantage for the building up of these resource states. This we haven't discussed in this in this first works, but I expect that also, there is a there's, an advantage.

F

Clear, that's what I didn't fully uh uh understand. Yeah thanks thanks.

A

uh Any last questions, because I do, I think miteko might kick us out so.

E

Yeah, I think we'll lose our connection here momentarily won't. We.

A

Yes, I I don't actually know how forceful it is so.

C

A

If there is, is there any last question final question, we.

E

Should thank we've already lost uh a few of the participants, but we should thank uh wolfgang for the for this uh amazing talk. There's al there's such an incredible work going on in wolfgang's group and in that.

A

E

A

Yeah, uh so in that case, with no more questions, uh I'd like to wrap up. Thank you again volgang. uh If there are any follow-up questions there will be on the mailing list, I'm not sure, if you're on it, but if you're not on it I'll make sure to relay their questions to you.

A

Okay, so so focus on this. If anybody has any uh questions, just shoot them at the mailing list so that we can all benefit uh from the exchange and with that I'd like to wrap it up, then, and thank everybody else for attending as well. Thank you all.

B

Well, thanks a lot for your patience.

E

B

E

E

I'm going to sign off and go to bed myself.

A

E

A

B

Thanks a lot for inviting me.

A

Yeah no problem thanks for watching, so I'm also going to disconnect then okay, bye-bye bye, then.