Turning High-Level Models into Optimized Quantum Circuits

THE POST-QUANTUM WORLD

Turning High-Level Models into Optimized Quantum Circuits

As we begin training and building up the quantum workforce of the future, it’s clear the precious few developers working in these early days will need some help making the most of their time. We’re starting to see a few players in the quantum development tool market. How does the new offering from Classiq compare? Instead of worrying about gate-level coding, the Quantum Algorithm Design (QAD) platform from Classiq lets developers take high-level descriptions and turn them into quantum circuits that can run on any hardware target. Is QAD the new CAD for the world of qubits?

Guest Speaker: Yuval Boger, Chief Marketing Officer - Classiq  

 

Post-Quantum World Podcast

The Post-Quantum World on Apple Podcasts. 

Quantum computing capabilities are exploding, causing disruption and opportunities, but many technology and business leaders don’t understand the impact quantum will have on their business. Protiviti is helping organizations get post-quantum ready. In our bi-weekly podcast series, The Post-Quantum World, Protiviti Associate Director and host Konstantinos Karagiannis is joined by quantum computing experts to discuss hot topics in quantum computing, including the business impact, benefits and threats of this exciting new capability.

Subscribe


Protiviti Podcast Transcript Transcript

Konstantinos

As we’re training and building up the quantum workforce of the future, it’s clear that the precious few developers working in these early days will need some help making the most of their time. One way to do this is to find tools that let devs go more quickly from high-level concepts to finished quantum circuits. Just what kinds of assistance can a platform called quantum algorithm design provide? Find out in this episode of The Post-Quantum World.

I’m your host, Konstantinos Karagiannis. I lead Quantum Computing Services at Protiviti, where we’re helping companies prepare for the benefits and threats of this exploding field. I hope you’ll join each episode as we explore the technology and business impacts of this post-quantum era.

Our guest today is chief marketing officer for Classiq. They’re doing some pretty cool stuff with algorithmic design, and I wanted to have them on to talk about the tool they developed. So, Yuval Boger, thanks for joining us.

Yuval Boger
Yuval

Thank you very much. Pleasure to be here.

Konstantinos
Thanks. I guess we could just dive right into it. Do you want to tell us a little bit about what you guys do?
Yuval Boger
Yuval

Absolutely. We are a software company, and, with our software teams, we can create quantum circuits that we believe could not be designed otherwise. We call this quantum algorithm design, and some people wonder, “Well, why does it matter, and what does it mean?”

We see all this progress in quantum computers. We know how quantum will have this huge impact on many industries, and we see this race where people are coming up with better and better hardware, more qubits, better coherence, better architecture, and so on, but the problem is that the hardware is useless without software, just like a PC or a Mac or a phone wouldn’t be useful without software running on it. The problem related to that is that today’s quantum software development is very limited. It is very limiting. The reason is, it’s done at the gate level: You specify which qubit goes to which gate, and so on and so on, and that’s OK if you have five or 10 qubits, but it’s not OK if you have a hundred or a thousand qubits. I think people will find it impossible to design and debug circuits this way.

So, when we looked at solving this problem, we looked at how CPUs and other chips were designed. These have millions or billions of transistors, and they’re designed by humans, and many people do that. So, we apply the same principles to quantum: Basically, we ask the user to define a high-level model of what you want the circuit to do and the constraints that you care about. The constraints could be the number of qubits or the level of entanglement, and so on. Our software then synthesizes — within seconds — a quantum circuit that does what you ask for and, to the extent possible, meets the constraints, and now you can change the circuit, or change the constraint, and explore various options.

We think this is revolutionary, for a number of reasons: First, it allows you to create new algorithms with ease. You can focus on what is it that you want to do and not on how the circuit is built. It’s also a huge timesaver, because creating or redesigning a quantum circuit could take weeks, and we can do it in minutes. It scales — you can do it on a hundred or a thousand qubits. The last thing is that you don’t have to be a PhD in quantum physics to design a circuit, just like you don’t have to understand how CMOS gates works if you are a Python programmer. Now you can bring in a financial expert or a supply chain expert, a domain-specific expert, and allow them to focus on what they’re trying to do instead of “How does it work underneath the hood?” Sorry for the long answer, but hopefully, that’s helpful.

Konstantinos

Yes, definitely helpful. Yes, there’s a lot to unpack there. Getting back to the basics, when you guys say quantum algorithm design platform, you’re talking about taking quantum algorithms and implementing them with some kind of constraints on hardware and other needs to actually execute this in the real world. We’re not really talking about designing new algorithms. We’re talking about taking existing algorithms and encoding them into circuits.

Yuval Boger
Yuval

You can absolutely design your algorithms. If you look at the industry today and ask yourself, “Well, how many quantum algorithms are out there?” there are very few.

Konstantinos

Sixty-four.

Yuval Boger
Yuval
Sixty-four. Well, names please. Names, right? The reason is, first, we don’t know what a 1,000-qubit quantum computer looks like, and, even if we had it, we obviously can’t simulate it, and then software tools are so constraining, so we can’t wait to see what people will come up with in terms of new algorithms when they use our platform. But of course, even when you take an existing algorithm like Grover’s search or something else, the algorithm is just the shell, but now you say, “I need an Oracle. I need a particular function to run.” How do you code that? Well, our platform can help you with coding the variable parts of the algorithms that already exist today on the market.
Konstantinos

Yes, it’s getting the information in and out. Of course, that’s a huge part. Do you then anticipate building a library of circuits that people will be able to apply quickly to their needs, or will this always be done more on the fly?

Yuval Boger
Yuval

First, we’re a software company, not a consulting company, so our desire is that customers will build their own algorithms. We’re here to help, but our business is not selling bodies by the hour. The platform shifts with a bunch of useful common algorithms and examples, and you can use them, and you could tailor them to your need, but you can also create new ones. The answer is both.

Konstantinos

Both — OK. So, when you say the platform shifts, is this something you run locally, or is this something you would access purely online?

Yuval Boger
Yuval

Both. Some customers that we have today want to run it locally, for various reasons. Others say, “No, I want the front end or the GUI to run locally, because that’s most convenient for me, and I’ll run the engine — the synthesis engine, the one that takes the model and synthesizes the model circuit — on the cloud. It can work both ways. In terms of the front end, we offer both a VS Code interactive environment as well as, we’re coming out with a Python library that you can then use.

Konstantinos

Yes. I saw you had a PDF that takes you through — at the site, Classiq.io, there was a PDF that explained what it looks like to build. I noticed at the end that you end up pasting the QASM code into the IBM experience. Is that the way that it’s supported for all back-end targets — you then take it and put it into their environments? Would you have something written, then, for IonQ that would go in, or is that always the approach?

Yuval Boger
Yuval
We do copy-and-paste in the application note because Qiskit, in this case, is freely downloadable, and you can try it out, but we support a bunch of backends, whether it’s Q# or Qiskit or others. Think about it as one-click deployment, so, “Here’s the code. Press button, and then you can run it on a simulator, or if you have an account with one of the cloud providers, then you can just run it there,” and we have some of those working today, and I suspect you’ll see more coming in the near future.
Konstantinos

So, you anticipate a time where you select the back-end target and it will send it with some kind of credentials prepopulated, like an API or something like that?

Yuval Boger
Yuval

Absolutely. This is a big issue today, because the architecture of different computers is different and the industry is still early, so you don’t really know who’s going to be the winner — which companies are going to be around in two years or four years. Google’s going to be around, and IBM’s going to be around, but how strong will their quantum computer be, and will you prefer something else? We see this hesitancy with enterprises to say, “Well, what should I go for? Should I take IonQ, or should I take IBM, or should I go for Honeywell, or something else?” We can support multiple backends. One, we give you the ability to estimate the resources that you need — “Do I have a strong enough quantum computer that can run the algorithm that I’m envisioning today?” — and then also, to very quickly deploy it on various back ends with little or no change to the code.

Konstantinos

Interesting. So, do you anticipate that estimator also extending into the calculations per cost? The cloud platforms now — they’re trying that. They’re trying to make you understand what it’s going to cost before you run one of these, and it’s still super nerve-wracking — like, whenever we’re running an experiment, that moment when you’re about to hit execute, it’s like, “Is it going to be a hundred, or 10,000? I don’t know.” You feel like, “Will this destroy my budget? It’s too late. So, are you trying to hook something like that in, or will it still be more on the environments to tell the cost?

Yuval Boger
Yuval

The first thing is to understand the complexity of the circuit, because you have a limited number of qubits, and the qubits have limited coherence, so you don’t want circuits that are too deep.

Some of the things you can play with. For instance, let’s take state preparation, which is the beginning of many quantum algorithms. We allow you to define the values that you want to populate in the qubits and then create a circuit that does that for you, but then we say, “Look, if you are willing to live with lesser accuracy, we can make this a smaller circuit sheller and leave you more coherence time for the rest.” We allow you to design circuits that are feasible today in terms of the width and the depth of them, but I think what you raise is a good idea to estimate the cost out. I would suspect that a Twitter campaign or a Google Ads, very quickly, you’ll be in a situation where you say, “Well, this is my daily budget, and it’s not a blank check — stop when you hit that daily budget,” but, yes, we help with the former, and I think it’s a good idea for us to help on the latter as well.

Konstantinos

I’m assuming you’re doing a whole lot to try and be economical in how you use each qubit. What kinds of techniques are you guys trying? I’ve seen all sorts of things where you break up a problem and you try to do the most you can with the least amount of qubits. Are there any common techniques that you use regularly to make this as efficient as possible?

Yuval Boger
Yuval

The big advantage is that we look at optimization on a system level and not on a local level. What I mean by that is, if you have a compiler, and now they see two consecutive Hadamard gates, they can say, “We can get rid of that — it doesn’t do much.” But when we look at the system level, and with a little bit of help from the user — so, for instance, you could say, “I don’t need this qubit downstream — you could reuse it for something else,” or, conversely, “I actually need to save the result here and use it,” that extra information does allow us to optimize the qubits.

Now, in many of the examples that we do, whether it’s quantum arithmetic or QAOA and so on, sometimes you can say, “OK, what happens if I do have a few extra qubits? How much better, or how sheller, will the circuit be?” Now, if you needed to do that by hand, move from “Here are 10 qubits — I build the circuit,” and now I ask you, “Konstantinos, what happens if you have 15?” you’re essentially almost scrapping the circuit and starting from scratch. With us, it’s just a few seconds. You change the constraints, run the engine, and you’ll see if you like the new option better. We give you the ability to explore the various tradeoffs very quickly and get to a working circuit.

Konstantinos

It sounds like that would help you quickly select other back-end targets if you are presented with a different machine, with a different number of qubits, and to quickly generate. So, you’re not locked in from when you start. When you begin the process, you don’t have to say, “This has to be for the Honeywell H1.” You don’t have to do that, right? You can create it and then pick your target?

Yuval Boger
Yuval

Yes. You’re not locked in. It’s not just a different connectivity. You mentioned Honeywell. They have mid-circuit measurements. Maybe that’s useful in some algorithms. You may say, “This particular computer recommends that you use these gates and not others because of coherence” or other reasons, so we can optimize to that, and you can say, “I prefer that you use these gates” or “Not those,” and therefore, when you say, “Well, how is this going to run on this other hardware provider?” you change the constraints file, and immediately you can generate a circuit that we do our best to meet the new constraints.

Konstantinos

OK. So, you’re thinking of marketing this to the end user — like, someone takes this tool and runs it. How do you compare to, let’s say, Strangeworks or Qatalyst or some of those other – and I wouldn’t say they’re similar, but they are environments where you’re trying to be able to touch all hardware in the end?

Yuval Boger
Yuval

Right. So, if I take the bigger question, “What can companies do if they’re not using Classiq?” First, they can hire consultants, and then, of course, there’s a downside to that: It may be expensive, it may be that they keep or don’t keep the IT or they don’t develop enough quantum expertise in-house, which is probably what they want to do in the first place. With us, it’s not just taking predefined building blocks. It’s taking these building blocks and writing, like, the Oracle that I gave the example before, or creating an entirely new algorithm, and even creating that, you’re not doing it at the gate level, you’re doing it at the system level, so we think we can do it much faster with a larger number of qubits if they’re available, and then the systemwide optimization is something that I don’t believe these other tools do and our platform does.

Konstantinos

OK. Have you already gotten interest from consultants for using this kind of tool? Obviously, in this industry, when a new tool comes out, sometimes consultants want to use it and apply it to customers. I’m not sure how your licensing works. Is there a way to adapt it to different customers, for example, if you are a consultant?

Yuval Boger
Yuval

Absolutely. We do love to work with consulting companies and license the platform either for their internal use, because they want to learn and figure out what they can do and cannot do with quantum, but very quickly taking this to customers and solving the customer’s problem. So, we can either work directly with the customer, but we can certainly take our platform and work with consultants, and we’re doing that today.

Konstantinos

That’s great. It’s funny when you talk about consultants, and I’m sitting here. Obviously, I work for Protiviti, so it’s just entertaining. What kinds of successes have you already had — are there any you could share? Are there any a little publicly announceable, like, some kinds of problems that it would solve?

Yuval Boger
Yuval

We are not announcing customer names at the moment. We’ve certainly done work in financial services. We’re working with a defense contractor, doing some very interesting problems there. That defense company has an algorithm where they wanted to use a hybrid, the classic quantum codes — so, not just run everything on quantum, and of course, they didn’t want to run everything on a classic computer. So, we help them create both sides of the equation — and others as well. As the marketing guy, I am trying to hold back not to tell you all these names of the companies we’re so proud of, but I think the announcements will come very soon.

Konstantinos

Yes, we do have to lead the masses to security sometimes, don’t we?

Yuval Boger
Yuval

Absolutely. Protect people from themselves. It’s surprising how much people trust cloud companies’ apps that you downloaded from God knows where — the iTunes store or wherever — to not do something nefarious, and time and time again, that happens.

We really need to protect the consumers. We really need to protect our economy from what’s happening today. You know the IP that’s been stolen from the United States at this point? This has never happened in the history of the world. The wealth transfers from one country to another — in physics, we talk about phase transition. There will be a point at which so much of that has already happened and no more needs to be stolen to overtake our economy, and then we become the number two, number three global power at that point. That’s a very real thing that’s happening right now. It’s a little bit of a mystery why a lot of it has not been operationalized and commercialized, but again, they’ll reach a threshold where it won’t matter anymore. So much of it will be gone that we will not be able to catch up.

Konstantinos

Yes, that’s fine. You don’t need to talk about the actual people, but it’s fun to see the application, like you just said, hybrid. Normally, if you were to do that with, let’s say, D-Wave, it’s baked into the system — their machine, their hybrid approaches, is a set process. How would you handle that then? If this is talking to quantum back ends, how is it handling the classical side? Do you then hook into something like a neural network? What kind of classical pieces are done?

Yuval Boger
Yuval

This is where our Python library would come in. You can use it to generate a quantum circuit on the fly, run it on a physical back end — say, IBM or the back end of your choice — get the results, and then the Python code, the classical Python code, will look and say, “OK, this is what I need to change — this is what I need to optimize,” and then run that cycle again and again. The response time is not any different than accessing a server on the network, and so you can run these hybrid algorithms with physical back ends very comfortably.

Konstantinos

Nice. So, you’re baking that in, that capability. That’s going to be important. That’s going to be our first real advantage — if you get that hybrid process just right. We’re still limited in machine power right now — we have to do every little trick imaginable. So, with something like IBM, I know their code goes through and rewrites to make sure you’re not doing anything silly, wasteful, anything that’ll kill the process. You guys are adding a little bit of that, too, when you’re refining this, to squeeze everything you can out of each qubit?

Yuval Boger
Yuval

We do the system-level optimization, but then, of course, there is a level that the hardware provider does the best to say, “Well, this is the exact connectivity that I have, so we’re going to swap qubits two and nine because you want to talk with qubit three, and this is how it works for us” or “These gates are implemented in hardware, and here we’re going to have this sequence of gates that implements what you want to do.” So, we leave that to the hardware provider, although, as we spoke about briefly before, we can take their preference of types of gates into our optimization. We can generate code that’s going to be closer to the metal, so to speak, instead of having them to simulate various kinds of gates.

Konstantinos

“To the metal” — there’s a term I haven’t heard used for quantum. It’s very cold metal, I would say.

Yuval Boger
Yuval

It’s a very cold metal, yes.

Konstantinos

It’s a very cold metal. I used to say that all the time, and now it’s like, “I miss that term.” How easy do you make it for beginners? You mentioned customers who want to build in the expertise. What level of experience do you usually recommend for the champion and the company that’s going to try this to have?

Yuval Boger
Yuval

At some level, of course, you have to know what you’re trying to do. We can take our platform and go to a college, and the college kids will be able to quickly generate a circuit because they don’t have to even understand fully how each gate works. They can focus on the algorithm, just like VHDL or Verilog does that for electronic design. In the teams that we work with, we certainly see the team leader, maybe a PhD in quantum information science, has the experience, but then they want to bring in the domain-specific expert. If they want to solve a supply chain problem, the quantum physicists don’t understand supply chain very well, so they want to bring in the supply chain expert, whether it’s a consultant or the end customer directly.

We believe that our platform makes quantum accessible to a wider range of people. Otherwise, by the way, there are just not enough quantum physicists out there to achieve all the lofty goals that we have with quantum computing. We do see an expert running the team, but then you could have people with lesser degrees of experience actually writing the code.

Konstantinos

On a more philosophical side with the industry and jobs, I have an opinion on this, but I’d like to hear yours: What do you think about the future for quantum coders? I see these tools being developed, like yours, and others that we mentioned. Do you think that within a year, we’ll see more and more of an opportunity for, let’s say, bachelor’s degree coders to hit the ground running because of tools like this?

Yuval Boger
Yuval

I think there are various stages in, say, converting a finance problem into a finance problem that you can solve with quantum computers.

Konstantinos

Yes, absolutely. I know all about that right now, for sure.

Yuval Boger
Yuval

You have to think about how you take advantage of the ability to hold simultaneous values and all the beautiful things in quantum. Once you figure it out — how to take that Monte Carlo simulation and say, “Well, I’m going to run on quantum” — and now you have more of a recipe of “Well, this is what the quantum code needs to do,” then you can have a fresh college graduate, with his head screwed on right, doing the actual coding work.

Konstantinos

That’s exactly how I feel — the same. All computer science was like that. In the early days, it was incredibly complex. You had to understand what was really going on —especially go back to the punch card days — and now it’s become a little more like, you could come in and work on this discrete little piece even if you’re very junior, and contribute to a whole, so I think quantum’s going to be in the same place soon, where you could contribute to that one piece.

How do you see the industry going right now? Do how think that more and more customers are going to be ready to be trying these experiments? Every once in a while, you come across one that is super gung ho and advanced and like, “We really need to be doing this,” and then you’ll still meet those who are like, “No, this is years away,” and no matter what you say to them, they just don’t accept otherwise. How are your feelings on that right now?

Yuval Boger
Yuval

I’m glad to see that everyone seems to be reading the same Gartner report that says, “If you’re not looking into quantum, you’re going to be gone in three or four years, because all your competitors are going to do these great things.” So, what’s happening is that a lot of companies are setting up exploratory teams. They may be three-person teams, they may be 10-person teams, and then they go around and say, “Well, what problems could we solve in quantum? How do we solve them? Let’s start to develop the expertise and prove that there’s something there.”

We work with many of these teams, because I think one of the concerns that these teams have is, “I’ve identified all these problems that I could solve, but if solving a problem takes a year, then, wow, I have to make sure I’m picking the right one,” but if now you have a software platform that makes it much quicker — you can spend two months to solve a problem, move on to the next problem — then within a year’s time, you can tackle various fields and see where can you really get the competitive advantage.

We see a lot of companies in this exploratory phase where they’re trying to build algorithms, trying to process data that they’ve processed on classical computers to make sure that they’re getting similar results, and are looking for that breakthrough, and I think that their breakthrough is going to come from three areas: One, just their experience — “What can you do? What can you not do?” The other thing, the hardware. When the hardware becomes stronger — when you can have more qubits — then you can do more things. Then, of course, I know it’s my job to say that, but without the right software platform, that’s going to be much more difficult to live up to these expectations. So I think all three coming together — the experience, the hardware and software platforms like ours — are going to allow this industry to take off in the next two to three years.

Konstantinos

Yes, I think we’re exactly on the same page there. That’s how I view it. It’s funny, because when you talk to the Gartner guys on the phone, I get accused of being too optimistic. It’s like, “Wait, but you just told people that they have to be looking into this.” They think I’m too much of a quantum champion, but I really am. I believe in the industry. I agree, I don’t think it’s great to be a fast follower in this industry. I think you do have to start really with the feelers out there, and I’m not just saying that because of what I do. I think that the opportunity to innovate and to come up with some IP of your own and be the first out of the gate — even if it’s just for a few months — you’ll have some distinct advantage. That’s huge in terms of dollars and cents and identifying yourself to your customers as an innovator. I think that’s important.

Yuval Boger
Yuval

Absolutely. For all the badmouthing that I did earlier on consultants, consultants bring real value here, because what you see is a breadth of companies, and you say, “Well, this has worked here and this hasn’t worked there, and based on our experience, we think you could start with this problem,” and then, of course, your expertise in doing many of these projects allows people a very nice on-ramp to start developing their own internal capability. So, forgive me if I was a little bit too harsh on consultants.

Konstantinos

Absolutely not. It makes for funny content, I think. I’ve been in consulting for a very long time — I’ve seen all sides of it — but, yes, that is where the most gratifying parts of it are: being able to deal with a lot of customers and seeing all their views on things, and being able to give them that high view looking down on everything at once and what we see, so it helps to make some of those important decisions. I enjoy that part of it. Obviously, it sounds like you’re helping a lot of customers. It’s funny — when you describe what your tool does and how you help companies, in a weird way, you sound like a consultant, so it is funny right there. So, what are you guys working on now? Do you have any big changes that you’re trying to implement with the tool? Any coming versions that you might want to hint at?

Yuval Boger
Yuval

I think that we are always looking to expand the circle of customers that we work with, starting with two or three saying, “This is several months ago. This is not ready, and this is not ready. Tell us what you need.” Now that our platform is becoming more mature, we can increase the circle of customers that work with it. As we get closer and closer to a public release where you can just download it from the internet and start using it, we’re still in the closed beta mode, but now we feel comfortable that we can bring in additional design partners, additional customers, and they can get real benefit out of the platform. And, of course, we benefit from their input and suggestions.

Konstantinos

Yes, it looks like you could do a demo now and try it out. I’m not sure what your pricing model is. I don’t know if you want to talk about that on a podcast or not. That’s totally up to you.

Yuval Boger
Yuval

Our pricing model is an annual software license — not that different from a CAD tool that you would use for electronic circuit design or mechanical design.

Konstantinos

Yes, that sounds good. It lends to the idea that this will be around in a year or two — meaning the industry. It’s not going anywhere. This is the decade of quantum. Let’s face it — it just is. I know I want to try it. I definitely do. Do you want to tell us a little bit about your podcast?

Yuval Boger
Yuval

Sure. My podcast is now in the fourth or fifth episode. It’s called The Qubit Guy’s Podcast. That’s one of the signs that the industry is early, because I was able to grab the Qubit Guy handle on Twitter and other places. We try to bring in people who have interesting things to say. We had an analyst. We had a consultant, God forbid. We have other guests, and we try to talk not so much about the news of the day — this acquisition, or this qubit count — but about other things that have a longer shelf life and give people an opportunity to think about where the industry is going and what they should do about it.

Konstantinos

Cool. Before we start to wind down, what have you seen lately in the industry that gives you hope that we might hit advantage really soon? Is there anything that has caught your attention?

Yuval Boger
Yuval

We see an increasing number of customers that are looking into this. We see more and more money that’s being poured from both a government standpoint as well as a venture capitalist standpoint. So many smart people are putting in money, then they must be right — at least, I hope so. We see some very clever articles or algorithms on how to do things either completely with quantum or in the hybrid sense, so there’s a ton of fascinating academic work that’s going on. And for me, it’s really a fun time to be in an industry that’s figuring out where it goes next and all these new things — so many things that haven’t been done before — and I highly recommend joining the quantum computing industry if you can.

Konstantinos

Yes, and because you guys work with software, I don’t believe that advantage is going to be achieved only because of hardware. I really don’t. I think that first little bit, that first cusp, is going to be because someone’s going to have that more clever way of doing something with what we have, too. So, environments like this, like yours, where we can play around and optimize circuits, that’s hugely important to this. Like I said, I’m looking forward to playing this myself.

So, it’s Classiq.io if you want to learn more, and I’ll, of course, put links to everything in the show notes. Yuval, thanks very much for coming on. I really appreciate it.

Yuval Boger
Yuval

I very much enjoyed the conversation. Thanks very much for having me.

Konstantinos

That does it for this episode. Thanks to Yuval Boger for joining today to discuss Classiq and their new tool for development. Thank you for listening. If you enjoyed the show, please subscribe to Protiviti’s The Post-Quantum World and leave a review to help others find it. Be sure to follow me on Twitter and Instagram @KonstantHacker. You’ll find links there to what we’re doing in Quantum Computing Services at Protiviti. You can also find information on our quantum services at www.protiviti.com, or follow ProtivitiTech on Twitter and LinkedIn. Until next time, be kind, and stay quantum curious.

CATEGORY TOPIC:
SUBSCRIBE TO PODCASTS: