IGF 2021 – Day 0 – Event #119 Quantum Technologies in Poland: Quantum infrastructure and Quantum Computing Open configuration options

The following are the outputs of the captioning taken during an IGF virtual intervention. Although it is largely accurate, in some cases it may be incomplete or inaccurate due to inaudible passages or transcription errors. It is posted as an aid, but should not be treated as an authoritative record.

***

 

>> ZBIGNIEW WAWRZYNIAK:  Good afternoon.  My name is Zbigniew Wawrzyniak.  I am from Warsaw University of Technology in Poland, and we start the session which is called quantum technology in Poland, quantum infrastructure and quantum computation.  Firstly, I would like to introduce my colleague, our moderator, Mr. Adam Piotrowski, who is CEO of Vigo Systems and member of Strategic Advisory Board of Flagship, and our speakers, but the floor is yours, Adam.

>> MODERATOR: All right.  So as Zbigniew Wawrzyniak said, there is plenty of room at the bottom.  He was mentioned possibility that we are going to talk even deeper on the quantum level.  So the quantum technology is usually divided into four regions, fundamental technical, physical research, quantum computing, quantum communication, quantum fencing.

And we are going to have a review today of five panelists, Grzegorz Kasprowicz from Warsaw, Pawal Marc, Lukasz Rudnicki, also, Centre of Theoretical Physics in Polish Academy of Science, and finally, Zbigniew Wawrzyniak who made the first introduction.  Welcome.  Everybody.

We would like to know how far we are from the quantum Internet for the standard use or we are going to use the quantum cell phones or quantum computers, so hopefully our session will give you some introduction to this area.  So first, I would like to introduce our first speaker, Lukasz.

>> LUKASZ RUDNICKI:  (Technical discussion).

So let me be fast and to the point.  So the question I am asked about is about quantum evolution, and it is good to make this introduction about what it means, especially that nowadays people often mention second quantum evolution.

So indeed it's good to have a why to call it evolution and why the second.  So we know that to we first have a look at what was supposed to be the first quantum revolution, and as you can see this very clean description and explanation what is this, it's simply because 100 years ago, people discovered quantum mechanics and then they started learning that using some quantum effects, you can get more than usual.

You can build a laser or a transistor, and you all know that with such tools many things happen in the meantime, so they are essential for modern technology.  Nevertheless as is given in the sentence in the middle, so in such devices quantum mechanics is there.

This doesn't mean that everything which happens inside this controls, let's say on the quantum level, which means every individual let's say particle or photon is quantum, not the case.  Just some quantum effects are used and then this works and being able to provide technology which is based on that was the first quantum approach.

So then immediately we go to the second quantum revolution, which is one or even more steps like further, and maybe here it's explained better.  It says that we deal with single quantum objects.  So the point is that now we are entering the phase in which single quantum objects‑like objects or Photons can be controlled.  This is the big difference which is with the previous situation.

And the ability to do this, this is what people call the second quantum revolution, because in such a case, one can think about the device which is in a way fully quantum because every particular instance inside is quantum, it's controlled quantumly, and everything is according to quantum mechanics and not only pieces of them.

By the way, what you can see here is quantum Flagship from European Union.  This is the biggest initiative in Europe, and also because it describes quite well and with more or less easy language what is the point behind all of this quantum activities.  So you can, if you are anxious, you can go to the Web page and you will find many topics but not too many about what quantum technologies nowadays are, how they should look like.

You can read about principles which come from physics which govern that, but you can also read about possible applications and technologies which are being developed.  For instance, one case which I prepared to show you is in politics of quantum when you open that, there are many applications.  One of them is sensing of activity.  I'm not working on that so I'm not an expert, but from a principle, like I fully understand what is on here and I hope you can understand because it's explained in an accessible language.

The point is that when people are able to control this quantum object, in this case, the environments which you can see behave like an atom, if this object can be controlled precisely, as you can see in the nanometer, so it's all quantum like this can be controlled, can be manipulated, this means that when we are able to do this, we have huge sensitivity to the magnetic field because the magnetic field influences these parameters.

So being able to control the mechanism, we can measure the magnetic field with plea significance much better than with other technologies, let's say.  And then such measurements can be, they are used in nuclear magnetic resonance and step by step we see being able to control something on the quantum regime, we have much bigger possibilities to improve technologies which are in everyday use.

Let me also mention that when we look at the funding scheme like worldwide, there is many initiatives like in many countries, which are tied to quantum technologies and funding in next years, even a decade, in Europe we have quantum Flagship which I explained you also.  We also have Quantera, associations of different agencies that you see on the map, and they together support scientists in research projects so you can imagine that Quantera is more research oriented, and they both supplement each other.

What is also left is National Quantum Initiatives.  So in several countries like the U.K., Netherlands, also in Germany, there are national programmes which support quantum technology, like in Germany many people heard about 2 billion Euro for quantum computers.  So this covers the funding of the second quantum revolution in Europe.

The point which I wanted to discuss at the end which I think is of the biggest relevance for our panel today is what happens in Poland, and in particular in widening countries.  Business speaking they are countries that entered the European Union in the last ones and Portugal, because Portugal is a smaller country and that's why it's in this group of countries.  Widening countries are those which in terms of the research and expenses for research and how much funding they get they are a bit of local funding.

And the idea is among those countries and the idea is to increase like the funding and become like a country which is in a better stage because of funding of technology, development, all of that stuff.  Unfortunately, at the current state it doesn't look so well.  So if you look at these three pieces and think about the widening countries, you can imagine that in Quantum Flagship, widening countries are basically absent almost.

This is because one needs to start with very advanced technology.  Somehow it's difficult to enter, but I hope in the next talk we will discuss actually this, how to cross this barrier and how to enter this work starting from a country like Poland.  In Quantera this is more translational, every country contributes and this is why we can have a share.  National Quantum Initiatives, I haven't heard about any big initiative in the widening countries.

Maybe there are some plans like in the Czech Republic, for instance, but at the current stage it's not finalized.  In Poland we don't have such.  I think this is what we can discuss, how we can start from this landscape and how to make it better and get success.

I would like to finish with that.  Thanks a lot.

>> MODERATOR: If there are any questions, please ask them in chat and we will be happy to answer.  I know that there is still lots happening in quantum technologies, and it's projects that are covering several universities and developing international research agenda, but for now, it seems like the quantum computing is taking most of the emotions for the quantum technology.  It's related to unlimited power and computing power of quantum computers, so hopefully they will act as a processor for AI, machine learning, and process of data.

So the first draft report on the computer architecture, but by John Vanamen from 1945 defined the computer as the computer architecture right now.  So how can we define the quantum computer in the real life?  The quantum computers already exceed classical computers.  Can you give us some interesting thoughts about that?

>> MICHAL OSZMANIEC:  It's a great pleasure to be here.  My name is Michal, and I work as a group leader in quantum computing group in Center for physics in Warsaw.  Today I will be trying to convey some messages about what currently what is the current status of quantum computing, and how Polish centers are trying to contribute to this interesting developing landscape.

Let me start with sharing an experimental progress we had in recent years in quantum computing.  So the number of qubits we have is getting larger and larger.  It's improving the number of gates that you, quality of gates is getting better.  You have different platforms like super conducting qubits, ion traps, atoms, also Photonics.

I want to stress that despite what you can maybe hear in popular accounts of the subject, quantum computers are not all power for, like, machines.  They won't solve all problems of humanity, especially in near term.

So the subject became a bit, I mean, you have a lot of marketing these days, a lot of politics involved and it's important to be able to read the fine print.  So, for example this is a Tweet from Ivanka Trump.  It happened years ago when Google announced its quantum supremacy experiment, and you can see that, okay, it is claimed that this experiment, it took three minutes, but in order to simulate this quantum advantage, you need 10,000 Euros in a classical super computer.

But even a few days after the publication, centers of IBM reduced this number to two days and a half, and by now we know that we can actually simulate this experiment pretty well on like a moderate‑size cluster or even faster.

You also have claims like you can maybe break, like soon quantum computers will break encryption in eight minutes.  The fine print being you need around 10 million qubits with error rate that is smaller than the one you currently have.

Same with the time travel thing.  Like, yes, we cannot do time travel even using quantum computers.  Also, I don't, I mean, on a daily basis I work on quantum computers.  I don't believe in the near term they will help us address COVID issue.  So like how do people think about the speedup you can get in quantum computer.

Let me talk about factoring.  The problem is the factor natural numbers into prime factors.  So, for example 21 is a product of 3 and 7, and we have this famous Shor algorithm that takes care of solving this problem for large numbers, it takes cubic time with the number of bits of a number.  But the best classical algorithm has this exponential scaling for the same task.

And here I plotted for you comparison in the logarithmic scale between those two algorithms so best classical takes some number of elementary steps, Shor is much faster.  Actually for the sizes comparable to the number of bits you can in RSA, the speedup is immense, I factor of like H of the universe, right.

So it's this exponential difference in complexity.  So why haven't we broken RSA yet.  For this it's not only the number of qubits matters but also the quality and how they are connected.  So it's true that you need exponential number of classical bits to describe the state of NQubits, but once you have errors the quantum system deteriorates and the magic of the quantum necessary is lost.

And, therefore not only the number of qubits matters, but you need to keep errors suppressed and currently we are on the verge of maybe entering the region in this kind of space of useful applications of quantum computers.  So in the near term, we won't be able to run full‑fledged quantum algorithms.

We need to resort to heuristic a bit ad hoc methods that don't have probable guarantees of working.  So applications can be optimization, quantum chemistry or machine learning, and people work intensely on that.  In order to run those rigorous full‑fledged algorithms like Shor algorithms that simply large quantum systems you need to enter this regime where you have hundreds of thousands of qubits.

So we are not there yet.  So that's the landscape of quantum computing nowadays, and now I want to pass quickly to offer I view of the activities we have in Poland in this field.  So we have this consortium of three institutes, Center for theoretical physics, institute for theoretical and applied computer science, and university, so our product is funded by foundation for, and we focus on near term quantum.  We work on near term algorithms, quantum learning, quantum error correction.

I wanted to highlight just three, like, three outcomes of our research.  So first, our colleagues from Krakow they come out with the fastest state of the art, classical simulator of quantum computer.  That will be soon implemented within Qiskit, a library developed by IBM.

In Warsaw we propose an alternative scheme for quantum supremacy that uses some advantageous properties but in the interest of time let me pass the most applied of the areas we work on namely quantum error mitigation.

Assume you have some complicated quantum device that is ran some algorithm and you are getting some outcome, some output signal, but because you have knowledge on this device, this signal is corrupted, it's noisy.  If you knew what the noise was, you can unfold it, you can reverse its effect to recover the perfect, let's say, outcomes or algorithm.

There are problems with this approach because you have exponential complexity when you want to describe this knowledge, when you want to characterize a device, even if you want to process the, through the classical processing.  Now, in this work we, let's say, partially solved those issues.  So we decided to look for patterns and structure in the errors that occur in those devices.

We use characterization techniques to speed up the like efficiency of the characterization, and you can see here like real experimental results like, so, we use our techniques on IBM devices on some applied, on some concrete problem and you see how our methods improve the algorithm.

To conclude, I wanted to repeat again that present day quantum computers don't offer any practical advantage over quantum computers, although there are many, we are in this point in time when many interesting directions for both industry and academia.  So on the applied side, on the science side, it's, I think, thrilling to try to evolve new algorithms for those devices.  So you have to learn how to efficiently learn how they operate, so characterization and benchmarking would be very important thing.

So how to, like, in my opinion make quantum computing stronger?  So, of course, some better funding would be it's always welcome as we have suggested, but in my opinion also education in quantum computing, better access to hardware and strengthening links between academia and industry.  So that's it from me.  Thank you.

>> MODERATOR: I see no questions.  But showing the roots hidden under the ground it's a very critical to take over from science to industry to really address the application domains and implement standards or I'm really curious to see how it develops, but I see a large branch that were on your ‑‑ large brands on your presentation, Google, IBM, I know there are many others like Honeywell working.

There a place for smaller companies to enter the game.

>> MICHAL OSZMANIEC:  Currently it's dominated by bigger companies but on European side, there is a Finish company let's say Europe tries to invest in its own quantum computers.  Actually, like, I think the amount of money we need to put to have actual quantum computer forces, like, either to have large scale investment or to have very serious involvement of the Government.

And actually many of the companies you mentioned they do enjoy support of the Government also in the U.S., for example so I think that this is what will be happening.  This is what is happening in Europe currently.

>> MODERATOR: All right.  I would like to hear your experience on combining of quantum hardware and software for demonstrate technologies.

>> GRZEGORZ KAPROWICZ: I will figure out which of my four screens to share.  Okay.  Good evening, my name is Grzegorz Kaprowicz I work at the Warsaw University of Technology.  I would like to tell you about our success story in quantum computing cooperation over Internet and community that joined forces to do something important.

And I would like to tell how to make money on quantum computing without building your own quantum computer.  So here is the agenda.  I don't want to go into details about technology, but just to give you the perspective.

The quantum computer consists of freezer and box.  The box is important because it supplies to many topologies, only optical quantum computers don't sit in the frig, but many including ion traps sit in some form of freezing.

We have optical electronics, modulators, et cetera, the general opinion is the quantum computer is as good as the control box and the algorithms that control it.

The bigger quantum lab resembles wires and boxes connected using blue tape, and I'm not joking, there is lots of connections and solutions that are simply working by chance.  And in every lab, there are engineers inventing the wheel and developing the system that perfects their needs.  There are those that have magic boxes without proper documentation.

So the next that comes and builds next generation over and over again.  To make cooperation between the labs easier and to use necessity of reinventing the wheel, a few research labs joined and formed ARTIQ.  It is a bottom up initiative around open source created by physicists or physicists which with helps of entrepreneurs.

There are many beautiful open projects on GitHub, but most of them have failed.  Why?  There was a lacking strong commercial partner who was able to review the design on the boxes and sell it on the shelf, and it needs to be cheap, so cheap that it doesn't make any sense to produce.  The economy of scale does the job.

So we, the community created various modules.  Each module is a product, each includes electronics, mechanics, software, drivers also documentation of its result.  Then two companies in Poland put a lot of effort and money to commercialize it.  The project is still alive.  We got funding from sources and the device is under development.

Some new modules, for example, control the laser spectrum, some qubits vibrations.  So the cooperation of nearly 100 people from around the world is possible due to Internet, GitHub, Zoom and many other tools.  Actually, the pandemic proved that such a project can continue without any problem.

Many of us never met each other because the conferences are also virtual and we proved it's possible to build the tie technical hardware in such a way.  Instrument station, without loses nuances of compatibility, and the other approach to the ARTIQ is that it can be operated by physicists without the need of hiring high end engineers to knowing the nuances of the language or development foundation.

And using Python you can use the system.  And here is our team, part of it, some small part of it, some groups are founders, some ‑‑ funders, some are clients, some are using hardware, others write software.

So this is a project that is community founded.  So it works in a way that if one institution wants to have certain models.  It pays money to the company or to the university to develop the development, but in return it gets all of the other work funded by other institutions.  This is how this looks like.

How to earn money?  Build a quantum computer.  There is too much hype around this in the field.  I have an impression that every person who knows how to opens his own start up.  That's not the path.  We are electronic engineers not physicists.  There was a popular statement long time ago in a gold rush, so during a gold rush sell a quantum system.

These are examples of the systems we develop.  Some are simple, some are complex.  Some may say that you are also doing it in the lab sometimes, for example to blink left, but most of the hardware we created likes like this.

It rounds at 16 gigahertz, it took a lot of time to design and verify it and build prototypes and do it again.  This is a commercial product.

So to conclude, here are some examples of our hardware in places around the world, but let's talk about a bit about the business model behind it.  There can be four general business models for hardware.  It can be any combination of openness and commercial.  One of the problems in quantum community is ability to pair particle systems.  Either one can build its own system and often it happens or to pay the company to build it.

Once he or she needs to change something, she has to pay again.  So that's why open source makes a lot of sense.  From client perspective, it's a win/win situation, one gets exactly what is needed and modified.  You can produce it when some company charges too much, this appears on the market or makes the product obsolete, but what about the entrepreneur?

What are the advantages.  The company starts with the prototype of the product, and this product was created a compromise between many clients so the company knows there is a market.  It doesn't have to do market research, invest a lot in R and D.

It needs just to commercialize it.  And it gets a lot of support from the community, so it doesn't have to hire engineers to provide support.  And the product can be a lot cheaper due to this savings.  Let's conclude.

So we created a complex system which for the moment has devices in the pipeline that are currently in development.  We use bottom up approach in a completely remote way using Internet tools.

I think even Chinese people are commercialize it.  Most products are available off the shelf.  We have a lot of in the fooled of quantum computing.  So keep tuned.  Thank you.

>> MODERATOR: Thank you.  So it was started in Italy.  And in Great Britain so we next evolution starting in Poland?

>> GRZEGORZ KASPROWICZ: Just use our system.

>> MODERATOR: It will become popular.

>> GRZEGORZ KASPROWICZ: It's over 2,000 pieces last year, I think, so, yes.  Getting more.  More.  Yesterday, I saw, there is action in Flagship, there is an action in project where they build 1,000 quantum computers, and I noted they are using my hardware.  I was so proud.

>> MODERATOR: That's always great when you are seeing your users everywhere.  All right.  With this kind of quantum computing, you can break any kind of encryption codes, so probably will have new holes in E‑commerce or private networks someday.

>> GRZEGORZ KASPROWICZ: I don't think it would ever happen because already guys are implementing post quantum algorithms.  You can take the least developed PQC algorithm, implement it in hardware and even when the quantum computer gets ready to break the existing encryption standards, we won't use them anymore.  I don't think they would be able to break our encryption.  So in many years nobody would use it.

>> MODERATOR: Remember that there is already a lot of stored data which is still critical.  So encrypting this data is also very valuable.  So ‑‑

>> GRZEGORZ KASPROWICZ: You can imagine secrets from World War II which are still critical, yes.

>> MODERATOR: All right.  So post quantum computing, but there is also quantum cryptography and distribution of quantum key solutions.  Can you give us some overview about the quantum key distribution system?

>> PAWAL MARC:   I am having a problem with Zoom.  I cannot unmute this software.  Okay.  My name is Pawal Marc, and I would like to share with you some information about quantum key distribution.  I will start from beginning because in theory quantum key distribution is a promise or idea in which we can design the quantum channel and we can exchange for this quantum channel our secret messages.  And we are sure that nobody can eaves drop it because it is covered by physical, it means if we design quantum channel, the quantum state cannot be repeated or cloned due to the fact that we cannot reproduce the unknown quantum state.

In theory, we have Alice and Bob which exchange the information, and they want to keep it in a secret.  They always know that somebody can listen to this talk, and they invent some special algorithm of how to cover this information to first share the special key which will be used for encryption and decryption of this message.

Here we have the example of this exchange of the key.  This is protocol BB84, like a base, which was developed in 1984, but it is pretty simple to show how the quantum key distribution works.  So Alice sent to Bob previously generated random number qubits or bits, zeros and ones, and it all of the bits can be caught in two bases.  Let's say we have polarization base coding so we code Photons in state of polarization, so we have two bases, one base shows your qubits which are vertical aligned, and horizontal will be zero.

The second basis, we have two qubits, one will be minus 45, the 0 will be 45 like here, for example.  So when Alice caught this qubits in her randomly chosen bases, Bob has feet 20 detectors which are polarization sensitive, Bob measures all of the qubits, and they can concur, Alice and Bob, using normal channel which can be listened for anybody.

If they agree that some of the bits are rated good by Bob's measurement scheme, so they saved the key and finally they can find the proper length of the key which will be used in accord of the date.  They can trust me this data without caring if the eaves dropper can hear this because any time an eaves dropper starts to listen to this channel, it's quantum state will be destroyed.

However realistic devices has some imperfections.  We have also limits in case of light sources and detectors.  So this imperfection always can cause that someone can listen to us and try to hack this information and finally record encode this data without knowing because this is the most important that we or if Alice and Bob exchange the information, they will be sure that somebody can start to hack their talk.

So in practical application, the source is usually used photo sources, it could be weak coherent state, thermal, single Photon or entangled Photon.  They code in polarization or in phase.  The phase coding is more common than polarization, and both have to be kept in polarization and phase decoding scheme and proper photo detector.

As a photo detector we use little use single photo detector and the channel we use optical fiber or free space.  The quantum hacking which can be in design or optimized by an eaves dropper can be directed to the source of light and to if we use phase encoding scheme, the source can be tagged by some special procedure, for example Photon number splitting, phase remapping or non‑random phase.  Or we can attack the hacker by double click, fake state, time shift and detector control.  Other attacks, it's a Trojan horse attack.  If the eaves dropper is in one side or only one to Alice and Bob and this back scatter information can be read and this information can be encoded information.

Now, we are starting to our project which is funded by the National Center for Research and Development.  This is the part of the Safir program of this agency, and we direct this project first for design the system for optical fiber.  We want to build this caricature which could be implemented because one of the consulting partners company, and we also try to focus our development to change security standards which are only directed to code and encode information.

We didn't see yet any standards in case of protecting optical fiber, for example.  And we designed a sensor which is, which can be applied to see if some eaves dropper can start to hacking our optical fiber.  We start from two designs.  We design the quantum key distribution system based on optical fibers, and we work in quantum random number generator, which is another story in quantum technology because we usually, if we want to encode information, we need to go to quantum random generator.

Now, we are using only mathematics and some special algorithms which are able to build random number enough long to code information.  And that's all I would like to say for you about quantum key distribution.

>> MODERATOR: Thank you for the introduction for the quantum key distribution.  Always when there is a new way of communicating, there is hacking experience, and I know there are already people all around the world trying to hack the insertions and I know that there is always new technologies to prevent hacking, so it's always a race.

>> PAWAL MARC:  I agree with Michel that there is more management in showing that quantum computer starts to break all of these codes, then reality because even now we have quantum key distribution which works with the speed about 10 megahertz.  So this is, I think this speed is not interested for community because we are working with gigahertz speed, not with megahertz, but we will see.  There are some implementations we can buy, for example ‑‑ maybe not, for example.  We can buy some system that are available in the market.

>> MODERATOR: All right.  Thank you very much, and so can you give us a final summary?  Are we there yet with the quantum Internet, quantum computers or are we far away?

>> ZBIGNIEW WAWRZYNIAK: Good afternoon, so I will try to summarize the problems of quantum communication infrastructure.  So first of all, we can tell that the second quantum revolution is in the early stages of development, and there is a most significant scientific innovation of acting, how the data should be compiled, analyzed and utilized.

>> MODERATOR: It's not full screen.

>> ZBIGNIEW WAWRZYNIAK: Okay.  I'm sorry, just a moment.  This is the aspect of second quantum revolution, and we can tell that the technology development will bring major changes in all segments of society, but no one can predict it certainly whether the Blockchain, Artificial Intelligence and quantum computing and other heuristic occurrences will benefit mankind.

So next question about technical aspects, and for realistic usage of classical supercomputing and quantum computing, it's necessary to make sec cue quantum communication infrastructure, and in this integration of quantum photography and quantum product and system is important to make a, to improve this in communication, in conventional communication infrastructure.

Then if we look at the communication infrastructure, we see that the important thing is to prepare QCI, and in fact it's not just QKD but also the others, so we can expect that the evolution come into quantum Internet connecting devices like quantum computers, simulators, sensors, quantum networks and then to build a quantum resources securely all over Europe.

And practical aspects, there is two phones with building quantum cryptography or increased security.  This is the smallest quantum generator, and at the very small keep 2.5‑millimeter there is a random number generating, QRNG, and this makes encryption and security services like banking, mobile payment and so on is the safest commercially available phone in the world of this type.

Quantum computing areas is rather very wide, and there are many branches, but the most important thing are the quantum traps, and in fact trap is the most interesting idea with making such an infrastructure, and then we should say about some system aspect, software, classical computation and what is important is to prioritize business to impact potential in use cases.

So another important questions are parameters coming from technology, I mean number of qubits, qubits lifetime, a great way to gate fidelity, operation time and so on, and whole ecosystem of quantum computers, I mean services, applications, and quantum computer hardware and then the most important aspect for us, also support for such a quantum company.  So the landscape is like this.  There is not in this research but the full landscape is much more complicated, so only two quotations that quantum technology is not a general purpose technology and quantum computing cannot solve all of the problems at the moment, but the main aim of the quantum revolution is to bring together scientists from academia, engineers, industry and future users into quantum technologies.  Thank you very much.

>> MODERATOR: Thank you very much.  We are not yet there, but there is already first products on the market.  They were developed in Europe, and then commercialized in Korea, but let's hope we are going to have global companies selling those quantum tools for everybody to be used for better society.

Thank you for everybody, for attending our session.  And have a good event.

>> ZBIGNIEW WAWRZYNIAK: Thank you for moderating our session, we have less than one minute left.  You can ask us using the chat.  We try to answer your questions.  Thank you very much.

>> MODERATOR: Thank you.