Podcast | Practical Quantum Computing Advantage for Businesses

Post-Quantum World series

Podcast | Practical Quantum Computing Advantage for Businesses

D-Wave has been making quantum computers for over a decade, and their annealers excel at optimization. If you look at the use cases the company has been helping customers with – saving time, money or both - it almost feels like quantum advantage is here. During this podcast, we discuss the power of annealers from D-Wave and how organizations can take advantage of the benefits today.

Guest Speaker: Alex Condello, Director-Algorithms, Performance and Tools at D-Wave Systems Inc.

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.

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Protiviti Podcast Transcript Transcript

Konstantinos Karagiannis
Konstantinos

D-Wave has been making quantum computers for over a decade, and its annealers excel at optimization. If you look at the use cases D-Wave has been helping customers with, it almost feels like quantum advantage is here. If you’re saving time or money or both, how can you complain?

Let’s live up to our namesake this episode and show why we’re living in 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 director of algorithms, performance and tools from a little tiny company you might have heard of called D-Wave. Alex Condello, welcome to the show. 

Alex Condello
Alex
Really excited to be here.
Konstantinos Karagiannis
Konstantinos
Thanks for coming. For those who don’t know — and I don’t know who that’d be — can you give us a quick overview of D-Wave?
Alex Condello
Alex

D-Wave is a Canadian quantum computing company. We’ve been around for, oh, about 20 years now, and we pride ourselves on being the practical quantum computing company. What that means is that we’re a startup, we’re stand-alone, we don’t have big funding backing, and so we have to be laser-focused on making our quantum computing products and our hybrid products available and useful to customers. To that end, we have been really focused on building a set of different applications and building a set of different tools and building a set of different hardware that is useful now to customers, and so that’s our main goal. 

Konstantinos Karagiannis
Konstantinos
The company has always been on my radar. That’s what we’re trying to do here: have things that people can do now — actually make use of this industry. Tell us a bit about what you do with algorithms and applications at D-Wave.
Alex Condello
Alex

I head up a research-and-product team here at D-Wave. We’re responsible for three main things: The first is our Ocean open source tools. These are a set of Python — and with C++ under the hood — tools that people can use to construct problems for the quantum computer and for our hybrid solvers. I’m also responsible for our hybrid-solver service. That is a set of both quantum and classical resources that make the best of both worlds together to give state-of-the-art results on different application problems. It’s also useful for folks who are interested in getting the power of quantum but aren’t necessarily quantum physicists or experts in this space. The hybrid tools allow them to interface with a much more abstracted solver. 

Then, finally, we also do benchmarking. What that means is, we measure the performance of the quantum computer and our hybrid algorithms on various practical problems as well as a set of synthetic instances that are useful for characterizing performance. We also are adjacent to some of the other teams in the company. For instance, we have a processor-development team, which is responsible for actually building the quantum computer, and then we have a hardware team that actually does the physical work, as well as other software teams that are responsible for our Leap platform, as well as other parts of our product offerings.

Konstantinos Karagiannis
Konstantinos

I want to dive in on the hybrid solver, but for a while now, I’ve been saying on this very show that I think the first quantum system to show advantage will probably be that one, that setup. I was interested in having you on especially because of that emergency-services optimization demo you did a few months ago. You said it’s not a true benchmark study, but at a glance, it does seem to show a lot of potential for meeting the criteria of advantage. I don’t know if you wanted to talk about that demo, and then we can dig in a little bit.

Alex Condello
Alex

I want to first talk about the word advantage and how we use it in the context of a hybrid algorithm, and especially in the context of a practical application that a customer or a person who is interested in using quantum might be interested in. At D-Wave, we generally are interested in what we call customer advantage, which is to say that our customer has seen value above their other potential solutions in our product — or in our hybrid solver, in this case. That’s a little bit different than a scientific definition of advantage, which would be, you can show that over all possible algorithms, you have some theoretical basis of an advantage.

The reason that we make that distinction isn’t because one is easier or harder than the other. It’s just that they’re different. We have a set of papers which we could direct folks to that talk about that more theoretical advantage, but when it comes to making the power of quantum computer available to the market or to customers or to commercial applications or research labs, really, what we’re interested in is, is it better than the thing they’re using now? Is it cheaper? Is it whatever?

In the context of that vehicle-routing problem, a lot of the advantages come from the fact that we can return state-of-the-art results using our hybrid algorithm. That means that we’re competitive with many other different state-of-the-art algorithms and that we can do it in a way that is easy to understand and easy to formulate. We can start with your more abstract problem, this vehicle-routing emergency-preparedness problem where you’re trying to move, say, ambulances over streets in as efficient a way as possible to deliver resources or maybe pick up patients, taking into account things like rubble or weather conditions. 

The ability to formulate that problem easily for a hybrid algorithm that can then make use of both classical and quantum resources to give that state-of-the-art performance is the overall goal, and that’s something that we feel like we’ve accomplished. It is worth mentioning, though, that there are many use cases even within the problem classes that we’re interested in where classical is state-of-the-art. 

That is the nature of these sorts of solvers, and so, one of the many advantages to using these hybrid algorithms is that it’s robust to those cases. It can take problems that are classical state-of-the-art on, it can take problems that are quantum state-of-the-art on and it can take problems where you need both to get state-of-the-art results. By smoothing out that curve, you’re not setting up a situation where a customer needs to be a quantum computing expert to decide where to route their emergency-preparedness algorithm, because that’s not the thing they want to be thinking about at that moment. They want to be dispatching ambulances. They don’t want to be thinking about, “Is this a quantum problem or not?” It really smooths out that experience and makes it more practical for typical use cases.

Konstantinos Karagiannis
Konstantinos
Yes, and to take a step back, for those who didn’t get to see the demo, so you set up a bunch of parameters like, here we have this city, and something happened, and we need to get goods to people who need them and trucks, obviously, have to do the traveling-salesman problem then: They have to get through areas. They have to bypass flooding and downed wires and whatever. If I remember, it was, the quantum hybrid solution sent trucks around 20 kilometers total to do all the deliveries, but then the classical K-means, you did 27 kilometers. That was a pretty impressive savings of driving.
Alex Condello
Alex

Yes, exactly. It was for a similar amount of runtime, so in this case, we were able to show a performance benefit to using our hybrid algorithm against this other K-means clustering, which is a state-of-the-art classical algorithm for that problem. That was a very cool and exciting result for us that we were really excited to show off.

Konstantinos Karagiannis
Konstantinos

Because it was a similar runtime, we have a situation where they’re doing it in the same amount of time and we’re getting better results with the hybrid solver. What would it take, then, to truly make a benchmark? For example, a portfolio optimization, the thing that Sam from Multiverse did. There, they did orders of magnitude faster in the optimization, but they lost a little bit of accuracy — the Sharpe ratio would suffer. What would happen here that would make it not be like we’re jumping up and down on the rooftops, “We found the thing — we found the advantage”?

Alex Condello
Alex

There are a couple of things, and this is an infinite well, but I’ll try to keep it relatively straightforward. The first thing that you would need is to run it against many more classical algorithms. In fact, you would need to be able to say with some degree of certainty that not only did we beat this K-means clustering, which is a state-of-the-art algorithm in this space, but also that we’ve beaten all state-of-the-art algorithms in this space, and there are many, many of them.

This runs squarely into an issue of defining the problem. For a given set of locations — you walked through this, but just to spend one moment on it — the problem is, I have a central depot located, say, in the city, and I have a set of different destinations also located at real intersections in the city, and I have, say, five trucks. I would like to have those five trucks within all of those locations as efficiently as possible. For a given city with given locations and a given central depot and a given number of trucks, there’s an algorithm that’s the fastest possible algorithm, which is, I know I can study that answer for hours, and I do it once and then I solve that problem forever. 

For a very specific instance, there’s a constant time answer, which is, find the optimal answer offline and save that. You have to define the problem, like, what do we mean to say is this problem class? Is it that I can vary the number of trucks? Is it that I can vary the depot locations? Is it that I’m varying the speed limits on the various roads? 

Again, you have to be very precise if you want to make a statement about the performance of our problem on this problem class. You have to define that problem class, and then you have to do it over all possible algorithms that solve that problem class. It’s much more complicated and, frankly, expensive operation to run that sort of thing. That’s part of the reason that if you are interested in understanding advantage results for quantum computing, you want to look to more of the academic research, because there, you can rigorously define a problem class, and then you can rigorously define the space and algorithms that can solve that problem class. 

That’s very nice for showing performance results, and we have papers that do that. It’s just that it’s a little bit hard to then link that rigorous definition directly to an application that’s easy to understand, like routing trucks in an emergency-preparedness situation. Bridging that gap is something that we spend a lot of time and effort on, and we’re working on all the time: Can we meet the bottom-up theoretical approach from the top down? I’m starting from a business-problem approach and have those two meet in the center, and then we can really jump up and down and say, “We’ve proven that — both theoretical and business forms of advantage.”

Konstantinos Karagiannis
Konstantinos
Yes, and it solves a different kind of business problem: If you do achieve advantage, it’s free press.
Alex Condello
Alex

Yes, exactly. One of the things that is true, though, is that we — for anybody who’s listening to this podcast who maybe has or is thinking about doing quantum startups and are getting involved in the space, it is true that most customers are a little bit disinterested in this question. They’re just interested in, “Did you save me money?” or “Did you get a better solution in time?” 

Really, part of the reason that we are so focused at D-Wave on customer advantage — answering that question — is that that’s the thing that keeps the lights on and keeps people buying time on our systems, because there is a simple question they’re trying to ask, which is, “Did you do it better than what I’m already doing? Yes? No?” That’s really the question we’re most focused on answering. While the science and the theory is really important to justify the work we’re doing and underpin all of it and direct us in the future, in some sense, it’s less important to the people that we care about, which are the customers and the users of our products.

Konstantinos Karagiannis
Konstantinos

That’s a great point, and a lot of times, when we’re doing proof of concepts for customers at Protiviti, it’s not just about necessarily, have we reached true advantage? Obviously, we haven’t, but can we show them some benefit now? Can they extrapolate a future benefit? Can they see clearly that once this overtakes classical, it’s going to be by orders of magnitude and improvement?

The types of work you’re doing now, I think this is going to be extrapolated to a different use in general, like shipping, logistics. I was just thinking, imagine UPS with a problem like this. You were talking about how you could, offline, chart the five deliveries with a hub, but with something like UPS, every single day, all your deliveries are different. You have to run this daily, at least, if not multiple times a day, depending on changing conditions. Have you started adapting this kind of approach for companies like that? 

Alex Condello
Alex

We have, and it’s worth mentioning that this multivehicle routing problem, this emergency-preparedness problem, is in a problem class that is really flexible. For instance, we’ve had a couple of customers. Denso has done factory automation — moving drones around factories. This is a multivehicle routing problem. Volkswagen somewhat famously did their bus-routing problem at a conference a few years ago and has similarly looked at paint-shop scheduling how different vehicles get painted and in what order. We’ve also worked with a couple of customers recently — which unfortunately I can’t talk about in great detail — looking at moving shipping containers around. How do you combine the routing of the trucks that deliver the shipping containers, say, with the packing of those shipping containers? 

One of the really interesting things about the types of abstraction that we use, the types of problems that we’re trying to solve with our hybrid solvers, is that you can start layering different problems on top of each other. At the heart of this multivehicle routing problem, as you mentioned, is this traveling-salesman problem, but you’re layering traveling-salesman problems on top of them, and then you’re layering information about the truck capacity or the fuel requirements on top of that. This ability to stack different optimization problems and take this global view of your overall problem class is really one of the powers of our hybrid solvers —it allows you to take this big picture, rather than solving these problems individually.

Konstantinos Karagiannis
Konstantinos

Right now, obviously, the world is having a serious problem with shipping. This is becoming its own pandemic side effect no one knew was going to happen. It sounds like you might be working on an approach to solving this problem, and obviously, any kind of gains we get here, who is really going to care about the academic papers that come out of it so much if we could save time and money and, especially, the holiday season, for example?

We’re going to talk in a moment about the new advancements that are coming out of D-Wave. Your work is about to change. There have been some announcements. The gate-based machine is one. We’ve talked about that. Advantage 2 is a way off, but right now, we’re supposed to be seeing advantages to improvements to Ocean and to the current platform, the 5,000-qubit Advantage system. I don’t know if you want to talk about how that’s already maybe impacting your work behind the scenes.

Alex Condello
Alex

Maybe just starting with the Advantage system, we just put out our performance update of the Advantage system, which we launched about a year ago. It’s really important to us at D-Wave that we’d constantly be iterating and taking customer feedback and making our products more useful. Even within a certain product generation like the Advantage product, it’s really important that we continue to improve that and drill down to the best possible version of that product. 

One year later, here we are with our performance update, and it came with a lot of important improvements to its ability to contribute to problems, even when you’re using the quantum computer directly. Most notably, it has better noise characteristics. It solves these low-level sampling problems better, and it also has more qubits and more connectivity in the sense that it has a better working graph, which allows us to access bigger and more complex problems than we were able to solve a year ago. Both of those have had an impact on our ability to use this quantum computer both directly and in the context of our hybrid algorithms. 

Actually, I’m really proud of myself for that segue, because that brings me into our new hybrid solver, which is our new constrained quadratic model solver that’s available in Leap right now. As I mentioned before — but it’s worth emphasizing, even though it sounds like you’ve talked about this before — our hybrid solvers are solvers that combine both classical and quantum resources. One of the benefits of doing that is that it allows you to solve more abstract problem classes than the quantum computer can solve directly. 

Our quantum computer solves a problem called an Ising problem, also known as a QUBO, also known as a binary quadratic model. That problem class is very flexible and very powerful, but frankly, most industrial-optimization engineers aren’t thinking about QUBOs. They’re thinking about constrained problems — problems like, “I want to route my trucks, but my trucks have a total mileage of 100 kilometers before they run out of gas” or “I need to do maintenance at least every three days.” These are hard requirements on the problem class that if you’re outside of that regime — if you return a route that a truck goes 101 kilometers — it’s not valid. It’s not useful to anybody. 

These sorts of hard constraints show up all the time in practical problems, and our new constrained quadratic model solver allows users to specify these hard constraints natively, which is to say that they can say them — well, at least, by computer science standards — in plain English, as opposed to before, where you had to do some convolutions in order to express your constraints in the formalism of the Ising problem. 

This has had an amazing, immediate impact on our customer engagements. I can tell you that all of our customers have been excited about this, and many of them are already making use of it, and it’s been a huge benefit both in terms of their ability to express the problems they want to solve and then, also, subsequently, in the performance that they’re getting on those problems. For instance, that multivehicle routing problem, you can actually get better performance on that problem than we were getting six months or nine months ago, by using this constrained quadratic model solver. 

The other cool new thing that’s coming in Ocean, we have released a road map for our new gate-model system and our updates to the Advantage product going forward, and that’s been really useful for us to be able to now engage with customers and show them this is where we’re heading, and you can start positioning the different approaches we’re taking to take that into account. That’s been a really useful thing for us to finally be able to announce to the world some of the cool stuff that we’re working on.

Konstantinos Karagiannis
Konstantinos

Road maps are great for that: You work with the customer, you’re like, “Look, these are your limitations today, but once you learn how to do it and your staff is ready and you’re ready, then tomorrow, you can flip the switch and do it even better.” I noticed that availability of hybrid solvers — I think if I’m correct, is that still only directly through you? You know how that there are the other companies like Microsoft, Amazon, they’re doing their cloud access. I think hybrid is just directly through you.

Alex Condello
Alex

That’s right. If you want to access one of our hybrid solvers, that’s direct through our Leap platform, I’ll put the plug in, as I should, which is that you can sign up for free right now and get access to both the quantum computer and our hybrid solvers, so you can check it out anytime you want via our Leap platform.

Konstantinos Karagiannis
Konstantinos

Is that because of the benefits you were just describing to the constraints? It seems difficult to control it with, let’s say, going through something like Microsoft’s QDK.

Alex Condello
Alex

It’s a good question. We certainly have found that it’s a big draw to our platform. We like keeping them, because it brings people to us, and people have found that for a lot of users, the modeling part of their problem solving — let’s say I’m a midsized logistics company. I don’t have a specialized data science team, but I have problems. I have hard problems, and I want to use a quantum computer for that. We found that sometimes, for some of these customers, one of the things that we can provide to them is help in modeling their problem as something that can be solved on one of our hybrid solvers. And to that end, we have our launch program, which is our professional services program, which helps customers model their problems in a way that can get the benefit of the quantum computer or our hybrid solvers. 

Keeping that full stack in-house has been really useful, because it allows us to bring our expertise in solving to meet with the customers’ expertise in their problem, because their problems aren’t in D-Wave. It’s really important to us that we engage with customers because we want to be practical, but we’re not experts in solving your logistics problem or your paint-shop scheduling problem or your protein-folding problem. We’re experts in solving. We’re not experts in the problem. Working closely with customers has been really fruitful both for us and for the customers.

Konstantinos Karagiannis
Konstantinos

When you have future customers, they can take advantage of what you’ve already done. It’s like, “Oh, we already solved this problem before,” and then you can just apply it quickly to them. There’s still that kind of sharing.

Alex Condello
Alex

To that end, we have a growing library of examples on, say, GitHub that when we do problems and when we are able to talk about them in any detail, we can open source them so people can use them as starting points for their next problems. It’s been really powerful to see that ecosystem grow. It’s amazing to see customers starting to submit variations of these problems that are useful to them and seeing that connective tissue grow between these different problem classes and go further and further up the abstraction tree and further and further toward the practical problems that different businesses want to solve.

Konstantinos Karagiannis
Konstantinos

Is there anything you could share about the gate-based machine, anything interesting to summarize the goal of it?

Alex Condello
Alex

Yes. We at D-Wave think that annealing is still incredibly important, and, in fact, the community at large seems to be saying these days that if you want to be doing optimization problems that gate-based isn’t necessarily the way to go. We feel that annealing is, and our track record is showing that fairly clearly. It’s really important to us that we continue to develop our annealing-based quantum platforms. 

However, there are a set of problems that are more native to gate-based, and that goes both ways. The future of computing is quite heterogeneous. You’re going to see CPUs and GPUs, and then you’re going to see annealing QPUs and gate QPUs and who knows what else by then — vector-processing units, tensor-processing units, all these different things. Each of these different hardware implementations has a place. For us, it made sense to leverage our deep knowledge of superconducting quantum computing fabrication to access another domain and access even more of these problems that you can use quantum computing for, and so adding gate model in addition to our annealing stack really made sense for us. 

I’m just really excited to have even more flexibility at our fingertips when it comes to these hybrid solvers because, as I mentioned before, one of the powers of hybrid is that you can smooth out that performance curve. You can use the right tool for the right job, and having another tool in our tool belt, these gate-model systems, it’s just even more powerful, and that’s something that’s going to be exciting over the next couple of years. We’re already thinking about, how do we start bringing that to bear for customers in Ocean and in our Leap platform? 

Konstantinos Karagiannis
Konstantinos

Yes. I imagine it’s like a customer comes to you and then they have a problem. I don’t think one day they’re really going to care which machine gives them the answer as long as it’s cheaper and faster.

Alex Condello
Alex

Yes, exactly. In the same way that I don’t care what Netflix is doing under the hood in terms of, are they running on this CPU or that GPU or whatever? It’s all abstracted from me. This is a fun and exciting time to be involved in quantum computing, because it’s still a place where you can really understand the full stack, but that stack is getting more and more abstracted as time goes on. We have some customers who want to access the quantum computer directly. We have other customers who are interested in — they don’t want to know the details. They don’t want to know the sausage. It’s fun to be stretched out over that full stack, and it’s a fun time in the industry.

Konstantinos Karagiannis
Konstantinos

Yes. When people ask me about annealers, I basically say they’re going to be like ASICs. They’re always going to be around because they’re really good at something.

No matter what else happens, how do you think that Advantage 2 is going to impact what you’re doing, the types of improvements you’re going to see within two years?

Alex Condello
Alex

As I mentioned before, the annealing-based quantum computers are, as far as I’m concerned, that’s the place to go in terms of optimization problems in quantum computing. Advantage 2 continuing on that path is really critical for us to be able to continue to develop our hybrid solvers. Some things that I’m looking forward to, specifically, in the context of the Advantage 2 update is that we are making it larger, but, almost more importantly, we’re making it more connected. What that means is that our qubits connect to other qubits in the processor, and that’s really important for solving complex optimization problems. 

Most customer problems, even the ones that are natively able to be solved on a quantum computer, they have complex relationships among the variables in that problem, and the complexity of one problem doesn’t look the same as the complexity of another problem. Our focus on making a more connected and more dense processor is going to help us solve these more complex customer problems. While Pegasus, our Advantage processor, was a really big step up from our 2000Q processor, we’re looking for the Advantage 2 processor to be another major step up in that direction, which makes it all the more powerful both as a direct processor and in the context of hybrid algorithms.

Konstantinos Karagiannis
Konstantinos
I want to make sure everyone understood that landscape and where we’re going. Before I let you go, the last big question I have for you is, do you have any other POCs that you’re working on that you like to give us a glimpse into, something that might be a future video or exciting moment? 
Alex Condello
Alex

We recently had our Qubits conference, and there were a lot of different customers who presented many of their different use cases. Frankly, customers are so good at talking about their problems in a way that I just never ever could. Some of the ones that I think are really interesting and exciting that we’re working on right now — you actually mentioned the financial-portfolio optimization with Multiverse and BBVA earlier. I think that’s really cool work, looking at bringing the power of quantum to the financial sector and optimizing a portfolio subject to a certain amount of risk. It’s a really interesting problem and, in fact, a problem that potentially can get benefit from our new hybrid CQM solver.

Also, I think some of our work with Menten AI, who had been looking at doing quantum peptide therapeutics for COVID-19, that’s a really cool study. Again, it’s fun to take this optimization approach and apply it to a field that isn’t traditionally thought of as optimization in the same way that,, say vehicle routing and all that stuff is. Then finally, Groovenauts and Mitsubishi have been working on sustainable cities and waste-collection optimization, which is, again, one of these more traditional optimization problems: You can imagine trucks routing, waste management or routing waste through different collection facilities. 

It’s been really fun to approach all these different disparate areas of financial optimization or pharmaceutical optimization or more traditional industrial optimization and to bring our approach to all these different areas. Again, I encourage folks to check out our set of examples on GitHub and in Leap, and I encourage folks to go check out some of the talks from our Qubits conference, which happened a few weeks ago, to really a get a sense of the amazing stuff that we’re working on and the amazing stuff that our customers are working on using our systems.

Konstantinos Karagiannis
Konstantinos

Yes. I’ve got to say, this show is called The Post-Quantum World, and D-Wave is one of the companies that really makes me believe we are living in it. Thanks for coming on — appreciate it.

Alex Condello
Alex

Yes. It’s been a pleasure. Thanks so much.

Konstantinos Karagiannis
Konstantinos

Now, it’s time for Coherence, the quantum executive summary, where I take a moment to highlight some of the business impacts we discussed today, in case things got too nerdy at times. Let’s recap: 

D-Wave’s hybrid solver combines the power of classical computing and quantum annealing to provide what the company calls customer advantage. This is not to be confused with quantum advantage, which is the goal of benchmark studies or lab research. The industry does want to prove a use case where quantum computing is superior to every classical option, sure, but D-Wave is helping companies come up with uses for quantum computing that provide a measurable improvement over the classical ways currently used to solve business problems. Cutting costs, speeding up processes or improving results are all examples of wins.

A recent use case showed that it’s possible to reduce the number of miles driven by delivery trucks in scenarios with changing variables. This type of optimization can have a significant impact on shipping and logistics. We’ve already seen speed-ups and other types of optimization such as portfolio optimization. The hardware and software D-Wave uses have both undergone recent improvements with a road map for further advances within the next two years. This includes the first edition of a universal gate-based quantum computer, which will expand the types of problems D-Wave can tackle. As the software gets better and customer examples continue to be published and shared, D-Wave users may find they need to know less about quantum to get started.

That does it for this episode. Thanks to Alex Condello for joining today to discuss his work on the ethics of quantum computing, and 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 us. 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 DM me questions or suggestions for what you’d like to hear on the show. For more information on our quantum services, check out Protiviti.com, or follow Protiviti Tech on Twitter and LinkedIn. Until next time, be kind, and stay quantum curious.

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