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0:00
If someone was to make a fully functioning quantum computer tomorrow, then at least at the moment, we wouldn't have all that much we could do with it. I left quantum Computing in 2020 after finishing an applied maths PhD in that field from Cambridge University. And the thing is, I'd loved being a researcher and I even got offered a few postdocs kind of informally when I was thinking about leaving, but I still decided to leave.
0:26
And the reason is because I became a little bit concerned that maybe quantum computers aren't gonna be as useful in the real world as we might have hoped. Well, it's been five years and a lot has happened in quantum computing. So I want to go back and see if my assessment from back then is really still looking like it's gonna be true. So yeah, on the hardware front, I think things are actually going really well. In 2020,
0:51
when I left, most quantum computing companies only had like. Dozens of qubits. I think the state of the art might have been like around 50, but now there are companies that have like 10 times that, and what's even more impressive is that most companies seem to be on track with what they said they would be able to do in 2025. I mean, I'm not an expert in that area, but it seems like despite all the incredible
1:16
challenges engineering wise, to make it happen. These companies are doing it, which is awesome. I have no idea when fully functioning quantum computers will be built, but some people say 10 years or 20 years, and I have no reason not to believe that. I think that we really are on track, but on the software front. I think things have been much more disappointing. To explain why I need to explain one of the most misunderstood things about
1:42
quantum computers. Quantum computers are not just general purpose super computers. It's not like every single thing that you do on a regular computer can be done faster on a quantum computer. Like you can't play games faster on a quantum computer. In fact, quantum computers are very specialized at doing very specific tasks, and I wanna explain a little bit about quantum computers so you can see why that is. I'm not gonna explain what a qubit is or anything like
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that because if you wanna see a full explanation of like exactly how a quantum computer works, then I have a video that you can watch where I built a small kind of useless quantum computer at home. And hopefully that explains it a little bit better. But right now what I wanna do is give you an overview of like how you should be thinking about what a quantum computer can do and what it
2:31
can't do. Let's say that this is a normal computer that does this algorithm. Every time you put in a bit string, if I put that into my computer, I type it in, then it will output some other bit string. There's some sort of computation that this program is doing to the bit string to make it something else. Well, what happens when you replace this computation with the quantum version of this computation? So let's say this is my amazing quantum computer. It acts
3:03
in a very similar way where if you put in this bit string, you'll get out another bit string. But the thing that you can do with quantum computers that you can't, with a classical computer is you can put in more than one input at a time. In fact, you can put in every possible bit string and the output, instead of being a single number will a combination of. All of the outputs for every single one of the inputs.
3:28
This seems miraculous, right? Like you can do an exponential amount of computation with the same amount of resources that a regular computer would take to just do one computation. This seems like there needs to be some sort of catch, and there is, you see, it is true that a quantum computer truly does do this whole amount of computation all at the same time. The problem is when you try and ask the quantum computer what the answer is,
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so with a regular computer, you might expect it just outputs this whole thing in a way that's readable. But with a quantum computer, you have to then go and measure this output. And when you measure it, what happens is it collapses to just one of these things randomly. So all the rest is completely gone, and you just have one number that comes out and it's just a random computation, and that is not useful. You see, even though technically a
4:26
quantum computer really does do a huge amount of parallel computation at once with the same cost that a regular computer would take to just do one computation, it's not possible to. Easily extract all that information. In fact, you can extract very little from the output, and if you do it in the naive way of just trying to look at the answer, you just get a random answer. So, how are quantum computers ever going to be useful then? It turns
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out for very particular types of computations that it is possible to extract just slightly more information from this whole huge list that lets you actually get out something very useful. This is my second sponsorship for the charity farm kind and they told me that last time loads of you donated, which is so awesome. Thank you so much. So almost no one thinks it's okay for chickens to live in horribly crammed cages like this for
5:22
their entire lives, where they can barely even move. But it's still really common. This report from June of 2025 by the USDA says that about 55% of all egg laying hens are in cages like these. The mission of Farm Kind is to prevent these kind of cruelties in the most effective way possible. They research which charities have actually made the biggest difference for animals. And then when you donate to Farm Kind, they split that money amongst these charities.
5:50
So for example, the Humane League, they run campaigns that have pressured the likes of McDonald's, Walmart, and Nestle to treating their hands better. The track record is so good that they can prevent a chicken from living her entire life in one of these terrible cages for just 85 cents. It often feels like we can't change the world, but for the individual animals that your donations will help.
6:15
It makes all of the difference. So if you wanna donate, the link is in the description and I would really appreciate it. Now, back to the video. Let me give you the classic example, Shaw's factoring algorithm. So the problem that Shaw's algorithm is trying to solve is called factoring. So say I give you this massive number. Then the factoring problem asks, what are the two numbers that you have to multiply
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to get that massive number? In other words, can you factorized this number? And it turns out this is really hard to do on a classical computer. Like, yes, you can do it by sort of just checking every single factor, but that will take you ages and ages. But in 1999, Peter Shaw showed that actually you can solve this problem quite quickly on a quantum computer. The first step of that algorithm does look like putting in a huge super position of all the inputs into a quantum computer
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and calculating the output. But the next step is not to just go and measure this, because as we already saw, doing that just collapses the state and is totally useless. So instead, Shaw's algorithm uses a very clever way of manipulating this state further. So you put this back into.
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Another quantum computer doing a whole lot more steps and you end up with. Some sort of quantum state here, where now it is possible to measure this state and actually get out a little bit of useful information, and that is just enough to find out how to factorized that huge number. But the point is you have to come up with some very clever manipulation at this part of the quantum computer, a particular algorithm that is going to take out just the useful
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bit of information so that at the end you can read out what that information is. Designing this algorithm is hard and it depends exactly what the problem you wanna solve is, and some problems like factoring have turned out to be amenable. So it turns out there are a bunch of problems like that where we have been able to come up with some very clever quantum algorithm that does let us extract the information we want and solve the problem. But for most hard problems that you might
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wanna solve with a quantum computer. We haven't yet found quantum algorithms. That might be because no one has yet found it, or it could be that there is no algorithm to find that quantum computers just can't solve that class of problem, and we never know which it is until someone eventually finds a quantum algorithm for that problem. So you can see why quantum algorithm design is quite tricky. You really never know which problems you're going to be able to solve with
9:01
a quantum computer or not. When Shaw's algorithm came out in 1994, there was a lot of enthusiasm that we would be able to find many more problems like factoring that quantum computers would be able to do so much better than classical computers. And yet, by the time I was leaving my PhD in 2020, I was pretty disappointed by the lack of progress. There were of course, other quantum algorithms like for example, phase estimation,
9:26
which is actually very related to Shor's factoring algorithm, and also another one called Hamiltonian simulation, which is quite different and allows you to simulate quantum objects. I. Now, five years later, I wanna go back and see if, well, there's any new algorithms, but also whether there have been new applications found for the existing algorithms. And the spoiler is, I think it's been a little bit disappointing,
9:53
but there have been some hopeful signs. Let's start with quantum machine learning. So we've all seen how incredibly good AI systems are, and I think there's this worry that sometimes gets brought up in the media that when we have full quantum computers, we're going to have these supercharged ais. In fact, when I was in the field, quantum machine learning was super popular and there seemed to be papers being churned out about it all the time.
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But I was very, very skeptical that any of those would amount to much, because I just don't think that quantum computers are very well suited to machine learning problems. Quantum computers often exploit structure and you know, machine learning algorithms are all about putting in. Tons of data and the data isn't particularly structured. It's like whatever examples, for example, from the internet. So I just don't think this is
10:48
playing to quantum computer's strength, and it seems like more and more people have gone off this quantum machine learning idea. So I don't think that's gonna be a big deal. But there is another area that gets heaps of hype that may be more justified. In fact, when I was in quantum computing, this was the area of quantum computing I was most excited for, and which I was ultimately most disappointed by. It's quantum chemistry.
11:17
Simulating molecules is a big deal, for example, in medicine where you wanna see how a particular drug is going to interact with, for example, proteins in your body. And so there was a lot of promise about quantum computers being able to speed up these very important, um, chemical simulations. At the time, that seemed justified to me because quantum computers are able to do something called ground state energy estimation,
11:47
and they seem to do it exponentially more quickly than a classical computer. But it turned out, there's actually an assumption in there that kind of makes the whole thing invalid. So let me explain. Say you had these two chemicals and you wanna know what's the chance that they're going to bond together and how hard is it gonna be to make them do that? One way to get a handle on that is to estimate the energy of both of these states.
12:15
So you can look at this state and you can look at its energy and you can look at this whole state and look at its energy. And if this energy is significantly lower than that one, then it's more likely to end up in this state. Estimating these ground state energies is super important, and there's a quantum algorithm called phase estimation that seems to do it super well. This is the gist of it. You put in a blank qubit that you're going to write the answer onto, and
12:45
you also put in this qubit, which is in the ground state. If you have this ground state and the blank qubit, you can just put them straight into your quantum computer That does phase estimation, and then the blank qubit ends up coming out of this computation with the ground state energy just ridden straight onto it, and you can read that out and find out what the energy was. So this seems perfect because this algorithm runs really fast, and so it seems like you
13:15
can find out the ground state energy of any molecules, which would be huge. But unfortunately the trick is this thing. So this is a state, a qubit state, which represents the ground state of the molecules. In other words, you need to already know. What the ground state of those molecules is to be able to run this algorithm. You can kind of see the problem, right? But at the time I thought that this would be
13:44
fine because there are ways to estimate what the ground state would look like more or less. And as long as there's a good overlap between your guess and the reality, then you end up with something that is good enough to find the energy. But there's no guarantee that your guests and the actual ground state will have all that much overlap. It was actually a couple of friends of mine who weren't in quantum computing,
14:07
but did know a whole lot about chemistry and biology that actually pointed this out to me. They made me see that there's actually no guarantee that this overlap is big, and so it's not clear at all that quantum computers can solve this ground state energy problem. And in fact, in 2022 there was a paper called. Is there evidence for exponential quantum advantage? And it was written by a whole lot of very respected scientists in the quantum
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computing field and also in chemistry. And so their conclusion was this. We conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for quantum chemistry. It may be prudent to assume exponential speedups are not generically available for this problem. So yeah, quantum computers aren't actually a silver bullet for solving
15:04
quantum chemistry problems, but there is a class of problems that's quite related that quantum computers are surprisingly good at, and that's quantum simulations. Quantum simulations are actually what inspired quantum computing. The idea is simple. Quantum systems are actually very hard to simulate in general if you try to, for example, simulate what a bunch of electrons are doing when they interact with each other. Quantum mechanically, you find that on a regular computer.
15:31
This is really, really hard to do. The number of possible states inside of the super position become exponential, and so it's hard even on a classical computer to write down all of these states. And so quantum simulation has always been a difficult problem. But for a quantum computer, it's actually quite easy. So what quantum computers can do is they can simulate the way that electrons evolve
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by having their qubits sort of interact with each other in a similar way. And by doing that analog, they can give us a pretty good picture of what the original electrons would've done, and this turns out to be very useful. So here are some examples of what we might do with quantum simulations. So you might have heard of these things called superconductors. Superconductors are these kind of magical
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materials that have no electrical resistance. That means that when you use them in a circuit, they don't lose energy. But the problem with superconductors is that the ones that we know of have to be cooled down quite a lot to actually work. So one thing people dream of is coming up with high temperature superconductors. So we just have to figure out the exact materials to use to make the superconductor so that it has
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zero resistance even at room temperature. So. And quantum computers might help with that because it's really hard to simulate these kind of materials before you actually make them. Because of those problems I was talking about earlier. It's hard to figure out what the electrons are all doing, and so the easiest way to do it at the moment is just to make all of these materials and then test them in the lab.
17:09
But that's really difficult when there's so many different materials that you can make and test. So the idea is that, you know, once we eventually have a quantum computer. We would be able to basically just computer simulate what all of these different materials are gonna do and then just pick out the most promising candidates to use in the lab. And I think that that's a very exciting application. There are similar problems like this, like for example, solar cells. You might know
17:36
that at the moment our solar cells are like somewhere around, I think 20 to 25% efficient, which is pretty good. Like they can take 25% of the energy that falls on them and convert that into electricity. But that is actually near the limit of what's possible with silicon. The hope is that we'll be able to find different types of solar cells that have better efficiencies, and people have already started working on these and have examples of them,
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but hopefully once we have quantum computers, we'll be able to simulate way more materials and find something with really high efficiency because computing the efficiency that a particular material is going to have before you actually make it in the lab and test it is again very hard. There's many other examples like that, like for example, nitrogen fixation. We wanna figure out how we can do that much more efficiently than the current harbor brush process. And there's also
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applications inside of science. So for example, you might have heard that quantum computers can be used to simulate some models of black holes, and that may be somewhat useful for, you know, people who are studying this to understand what kind of behavior those sort of black holes would have. So yeah, I think that there are actually a lot of applications in this area that are very promising. So that is great. This isn't a new algorithm. Hamiltonian simulation
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is a fairly old algorithm. Where are the new algorithms? Well, amazingly and very unexpectedly in the last five years, there has been at least one new algorithm, so. In 2023, a group of researchers proved that a particular problem with a random oracle could be solved on a quantum computer exponentially faster than could be solved on a classical one. That is really cool as a theoretical result. But this random Oracle bit means that it can't actually be made in practice still.
19:34
I am actually really hopeful about that because usually when there are algorithms of this sort where they're sort of relative to some oracle, often people come up with a way to take that idea and put it into a practical algorithm. Like I think Shaw's algorithm even came out of sort of Oracle like results like that. So that's proof that there really are other quantum algorithms out there, and I think it's really exciting. If you work in quantum computing,
20:00
you might have worried that like most of my videos sounded quite negative and I'm really sorry about that. I actually don't wanna come down too hard on quantum computing. I just think that there has been a bit of a misallocation where a lot of work has, of course, gone into the hardware because it's a very hard problem and a lot of work has gone into, for example, quantum error correction, but it just seems like quantum
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algorithms have been neglected. If a quantum computer appeared tomorrow, we need things that we're going to use that quantum computer for. So we need to be searching for good quantum algorithms, but at least when I was in the field. It wasn't very popular to work on quantum algorithms, and that's because it had a reputation for being really hard, which makes sense because so few algorithms have been found, and even when new algorithms are found,
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often there's a mistake with them or people show that actually classical computers can do that too. And so it's quite a hard field to be working in, but I think it's one of the most important. So, yeah, I'm hopeful about quantum computers, but I think that there is a lot of work left to be done.
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