Rene – Hi, welcome to QuBites, your bite-sized pieces of quantum computing. My name is Rene from Valorem Reply and today we're going to talk about the BMW quantum computing challenge again but this time a little bit more technical and with a focus on quantum machine learning circuits which is a super interesting topic. And I'm very honored to have a special expert guest today, Anuj Doshi. Hi Anuj and welcome to the show, how are you today?

Anuj - Hi! I'm really well, thank you for asking. How are you?

Rene - I'm doing fine as usual. Let's start with the typical introduction. So please tell us a little bit about yourself and your educational background like what have you studied like computer science, math, physics, that kind of stuff.

Anuj - So I did my undergraduate in mathematics and then I went on to do a master's in theoretical physics and I was always kind of interested in innovation and technology and so throughout my entire university career I was doing a lot of coding, and so coming into quantum computing it was the perfect harmony between my math skills, my physics skills and my computing skills. So, to be honest it was just the perfect field for me to get into and so after doing a module in quantum information theory back at uni, then just carried on learning and here we are doing quantum computing.

Rene – Awesome! Well, that's nice to hear. Let's dive into today's topic. In season four episode eight, we talked with your colleague, Marine Pigneur, who took part with you and other colleagues of Reply at the BMW quantum computing challenge, right. And a lot of things were learned already in the episode when I talked with Marine, and she explained the quantum machine learning really well and the hybrid approach and why that actually works. So, well because this was always a kind of a question right, why does this hybrid approach with a quantum layer inside of the neural network work so well? And so, I understood that really well. But at the time we were talking, the project was still ongoing and so maybe you can give our audience, first of all a refresh what was the project about, so that everyone is on the same page and then also what was the final result?

Anuj – So, the project was using quantum machine learning and like you said it's a hybrid architecture. So, there was a classical layer and then a quantum layer and we had to use this for image recognition in the quality assurance line. So, identifying defective doors or cracks and some of the parts and things so that way when they scan these parts as they come through we'll be able to pick up on the ones that are defective and take them out of the line. Overall the challenge was really enjoyable, you know. I was working with some really smart talented people and the outcome of that we didn't manage to win, but I think they're interested in having us back and they're really interested in the work that we did. So, I think at some point in the future there's talk of another conference. Maybe. So, fingers crossed.

Rene – Nice. But you should also say, I actually heard it from another colleague that you made it to the final round, right? So that is quite an achievement already and so yeah congrats on that! And like you said a lot of things came out of that also from the knowledge, right, like learning a lot and you know gaining a lot of new knowledge and experiences and all of it and I mean getting to the final list of such a challenge with that many participants and so on is definitely quite an achievement. So first of all, congrats to you and the whole team.

Anuj - Thank you, thank you.

Rene - Great stuff. So we already touched a little bit on the circuits in the intro. So let's talk a little bit more about the quantum machine learning circuits and tell us why is the design of these quantum circuits so important that you design them correctly and what have you found out during the challenge? What is your learning there?

Anuj – Yeah, so when I first started with the challenge, we were kind of using a circuit literature which was kind of well-defined. It was a standard general circuit which I think is denoted by hea. So it's just the way that the circuit's kind of designed and the reason we use the circuit is because it's just generally quite good. In the literature, there's no like mathematical like this is the perfect circuit design whereas I think something like NLP where we use machine learning to process natural language and it's a complete quantum circuit. I think Alessandra touched on this in the early episode where you can actually encode the grammatical structures inside of these kind of quantum circuits. The problem is, with you got this hybrid architecture is, it goes through its classical layer and it almost jumbles up all of the useful information. So, when we're designing the circuits, it's hard to get like a real understanding of the structure of the data that you're getting in because it's kind of been through an entire classical network. So, when we design circuits in the literature, there are two kind of really important things. One is expressibility which is this is defined to be the circuit's ability to generate states that are well representative in the hilbert space. So just it for simply put it's kind of how many different ways can the circuit represent the data. So, if there's like high expressibility, will be like more interesting function. So, like if you have like different data points and you've got to curve fit it using a Taylor series up to except to the seven or using just up to the x squared so the lower expressibility, the more generalizable the less detailed. So, there's this kind of trade-off between how expressible you want your circuit to be. The second is entanglement and we try to measure how much potential each state has to be entangled with one another and the key reason for this is in all the literature having higher levels of entanglement means far better, like machine learning circuits. So, increasing entanglement is always good. However then, there's another problem. When we have higher entanglement, it normally means we need longer depth of circuit. Now the longer depth we have with our devices that we have today, the more noisy it becomes and so you know we have to almost put a limit on our entanglement as well. So there's a lot of different problems here that we've got to try and optimize around. And yes we use like maybe a few different circuits specifically and so my job during challenge was I was experimenting with a lot of different circuits, a lot of different number of qubits and all these other things to kind of see what would happen. And so with this qubits that we found we realized that there was kind of so with the circuits that we used, there were a couple of other problems that kind of came up, one is the expressibility saturation problem. So as we add more complexity and more expressibility it and as we do the machine learning it kind of reaches a natural limit, which is almost independent completely of the previous like the actual expressibility or the entanglement. So there's like another value that we had to look at because we needed that to be as high as possible but you couldn't really find it out until you ran the circuit. The other problem that we ran into was the barren plateau problem and I think Marine touched in this briefly because she said we only needed six qubits. The problem is when we have more qubits, and we do the gradient descent function it almost turns into zero instantly. So, it doesn't learn anything and when we have enough keyboards, the function just becomes like oh we don't know where to go. So, we're just going to stay where we are. So that's another kind of problem with the conventional fixed circuits.

Rene - And so what you mentioned is like these fixed circuits probably are not that good or the right solution for the problem on this part or they seem to be problematic basically right? And so, what are some of the alternative approaches you could choose or that you explored?

Anuj - Yeah so going away from the fixed circuits or the circuits in literature, it's still like an open problem, there's not a perfect answer. And it's one of the most interesting problems in my opinion in the quantum machine learning space. However, one of the most interesting ones that I found was the variable Anzatt's algorithm. Now the way this works is you have you start off with a certain circuit and the idea is to kind of try and travel across your hyperspace of all the circuits and try to move in the direction almost like another super gradient descent on your entire circuit architecture to find the best circuit. So, the way that that works is you take one step where you try and add a certain gate or a certain entanglement or a certain feature. And then it compares both of those circuits and if it decides that it's improved to your model. If it decides, it's improved via expressibility attachment or just the general cost function, it will adopt that change. Then what's really interesting about this one is that then does the simplicity step, so it will then try to remove a random part of the circuit so kind of like with convolution neural networks when we remove a certain neural neuron, we remove certain gates and so this allows it to, what I was talking about earlier with the circuit depth, allows it to retain a small circuit depth. We're still optimizing all the other factors and they have shown that this does actually help. We can get similarly optimized solutions but with lower circuit depth which means lower noise and yeah more interesting solutions.

Rene - So you're basically using a circuit to optimize itself dynamically during or optimize the whole thing dynamically. Right?

Anuj – Yeah, it's almost like using machine learning to figure out the best circuit.

Rene - It's almost like you know auto ml right, auto machine learning, where they're exploring like different machine learning algorithms and basically try to pick the best one for your current problem based on the data you give and all that stuff. So, it could be well it's not of course that's the same thing but similar, something like this?

Anuj - Yeah, it's very similar I would say, like you are trying to figure out the best machine learning algorithm. So, in a classical sense, instead of using, say the sigmoid function, if you want to use a whole bunch of different activation functions, you're essentially testing across that space. That's essentially what you're doing here.

Rene - Super cool. Well, that is really impressive and like you said this is like state-of-the-art research. This is an unsolved problem that Anuj and friends are basically tackling at the moment. Looking forward to learn more and yeah, we could talk for many more hours about these things and super fascinating because again this is bleeding edge stuff folks! But we're already at the end of the show. Thank you so much Anuj for joining us today and sharing your insights. That was very much appreciated it was really good.

Anuj - Thank you! It's been a pleasure.

Rene - Thanks everyone for joining us for yet another episodes of QuBites, your bite-sized pieces of quantum computing. Please watch our blog and follow our social media channels if you want to hear more about the upcoming episodes and of course you can find all the episodes from season 1 to 5 now on our website. Until then, take care and see you soon, bye-bye.