Realistic Expectations for Quantum Computer (Patreon)

[This is a transcript with references.]

Quantum computing will revolutionize the world. If you trust the headlines. Which you should not. But whatever the headlines say there’s no doubt that quantum computing is attracting a *lot of attention. Many countries are investing heavily into it. And it’s not just governments. Software giants like Google, IBM, and Microsoft are working on quantum computing, and many banks are investing in it too, including Goldman Sachs, JPMorgan, and Wells Fargo.

I’ve already done several videos about how quantum computing has been overhyped, but there are good reasons for this excitement. Underneath the hype, there’s real promise. So, in this video I want to talk about what we can realistically expect from quantum computers. What could we do with a quantum computer. How could they change our lives? That’s what we’ll talk about today.

First things first, what’s a quantum computer? A quantum computer performs calculations on quantum bits, qubits for short, rather than the normal bits that conventional computers run on. A classical bit can be in two states, usually denoted zero and one. If you have N bits you get two to the N possible states.

For the qubits of a quantum computer, we put the zero and one into weird-looking brackets. It’s not just to make them look more mysterious. It’s because if we use the laws of quantum mechanics, then we can do a new thing with them. If we have N qubits, there are still 2 to the N combinations of them. But we can do something else with them, we can bring them into superpositions. This means we can add them with arbitrary factors which are complex numbers. This sum of the qubits is an example of what we call a wave-function in quantum mechanics.

When I say “we can add” these qubit states, I don’t just mean mathematics. There are physical operations that you can perform on physical things. Like, pieces of metal and lasers and stuff. It’s physics.

This possibility of adding up quantum bits, the superpositions, and performing other operations on them, is what gives quantum computers an advantage. On a conventional computer those states just don’t exist, and you can’t compute with something that doesn’t exist, at least not in physics. If you compute with something that doesn’t exist, we call that politics.

On a quantum computer, you have all these new possibilities in superpositions. And that allows you do solve certain mathematical problems faster than on a conventional computer. If you’ve heard that quantum computers get their edge from entanglement, that’s also correct, because all entangled states are superpositions.

What you do with a quantum computer is then that you prepare some initial configuration. You perform a calculation by swapping around the entanglement between many qubits, and the final state encodes the result you want to have.

Yes, but. What happened to all the supposed weirdness of quantum mechanics? Don’t worry, it’s still there. The weird bit is that we don’t ever observe those superpositions. When we make a measurement, we only ever see one of those basis states. We say that the entire state “collapses” into this one state. This is why there’s so much discussion about the question of whether the wave-function is real. Because if you never observe the superposition, does it actually exist?

That’s a very interesting question if you like the experience of your brain slowly turning into mush, but luckily, we don’t need to know whether superpositions are real to use a quantum computer. We just need to know that the computation works *as if they were real, but that in the end you never get the entire superposition, you get one string of bits, that’s the basis that the state collapses into.

This already tells you one important thing. It tells you that you have all those additional options in the superpositions while you do your calculation. But once you measure the state, poof, they’re all gone except for one. This means, while a quantum computer can calculate with a huge number of states, it can’t output a lot of data.

Okay, so now let’s briefly look at what the hardware can do. In my previous videos when I’ve talked about qubits, I have always exclusively referred to physical qubits. That’s the ones you have in the computer. There are many different ways to make qubits. There are small superconducting circuits and trapped ions and defects in crystals and photons in a medium and so on.

But regardless of exactly what type of qubit you use, the quantum behaviour that allows to maintain the superpositions fades away very quickly. Depending on what type of qubits, they might last a few milliseconds up to a few seconds or so. You have to get your calculation done before that. In some cases, you’ll do the calculation repeatedly to get a probabilistic distribution.

That’s the physical qubits. However, in the literature, physicists often do calculations with what is called a logical qubit. Logical qubits are perfect qubits, they don’t have any errors. They’re idealizations like spherical cows, unmoveable objects, unstoppable forces, and images you see in cooking books. These things don’t exist in reality and neither do logical qubits. But if you want to know what it takes to make a calculation, it makes sense to quantify that in terms of logical qubits.

In reality, however, you need error correction. This means you need a lot of physical qubits to create one logical qubit. The relation between logical and physical qubits is kind of like the relation between actors in a Hollywood movie and all the people working on the set. You need a lot of supporting staff to get one error-free sequence of events showing people who wake up in the morning with flawless makeup.

The reason I have never mentioned this before is that I’d noticed the relevance of this distinction between logical and physical qubits had completely got lost in the popular science media and I didn’t want to add to the confusion. But I think that by now everyone’s got used to hearing about qubits.  

Estimates say that if we reach a few hundred to a few thousand *logical qubits, then quantum computers will be able to solve commercially interesting problems faster than conventional computers. How many *physical qubits that’ll take is difficult to say. Depends on what you want to calculate and what error you’re willing to tolerate. Some say a few hundred thousand qubits might be enough, others say it’ll be more like 10 million, but somewhere in that range it’ll probably get interesting.

At the moment, we’re far, far away from that. The current record for the number of physical qubits is 433 and is the IBM Osprey chip that they are planning to make available in the cloud soon. IBM also has a roadmap according to which they want to reach more than 1000 qubits later this year. They’ll almost certainly get this done. But it’s one thing to lump qubits together on a chip, it’s another thing entirely to get it to do something useful.

That’s why I’m very sceptical that quantum computing will have much of an impact in the next decades. It’s because I believe it’ll turn out to be incredibly difficult to control the errors and when the problem starts eating up too much money, companies will drop the ball.

But, well, I don’t myself work on quantum computing and never have, I’m just from next door, so to speak. And there are a lot of people in quantum computing who think it’ll be possible to get a grip on those errors. Quite possibly they’re right and I am wrong. I guess we’ll see. Until then, we can have some fun with speculations.

This is why I want to talk about what you could do with such quantum computers if you had sufficiently many qubits. The possible applications that have attracted most of the attention are (a) code cracking (b) quantum chemistry (c) finance and (d) logistics.

Let’s start with the application that historically got people interested in quantum computing. It’s code-cracking. And not just any code, but codes that have been extremely widely used, to encode national secrets and almost certainly also your personal data.

These codes work by using an algorithm that scrambles up data in a way that’s easy to do but very difficult to undo. The best-known example is taking two large prime numbers and multiplying them. This is easy enough. But once you have multiplied them, it’s very difficult to figure out what the prime factors were. So you use the two multiplied numbers to scramble up data, but to unscramble the data, you will need one of the prime factors.

This method is used by the algorithm known as RSA, after its inventors Rivest, Shamir, and Adleman. This encryption protocol can be broken, because we have algorithms to decompose numbers into their prime factors. You could for example just try to divide the large number by all possible primes and see which one works.

But the thing is that these algorithms take very, very long, to give you a result, even on the world’s presently most powerful computers. The standard RSA encryption today uses 2048 bits. Cracking such a key on a conventional computer would take trillions of years, about as long as my husband needs to decide which pizza he wants to order. But if you had a quantum computer with about 2000-3000 logical qubits, you could bring that computation down to a day, and with 4000-5000 you could do it in seconds.  

Luckily, there are cryptographic protocols that cannot be broken by quantum computers, or at least no one knows how. These are called quantum-safe protocols or sometimes post-quantum cryptography. It’s very likely that the switch to quantum safe protocols will be completed before quantum computers solve any interesting problem. Besides that, code-cracking is probably not the first application that quantum computers will be put to work on, because they require quite a lot of qubits.

That said, it isn’t only plausible but quite probable indeed, that spies or hackers have in the past obtained encrypted data but have not been able use it so far because they couldn’t crack the code. If quantum computers become powerful enough to break the codes that were used to encrypt this data, that could expose details of financial transactions or military secrets. Even if this data is a decade or two old it might be, well, inconvenient for some people if their secrets were spilled.

I may be somewhat cynical, just maybe, but I suspect that pretty much every nation is sitting on some stolen data from every other nation. And whoever is first to crack the codes will shift power balances in their favour. No one wants anybody else to be better off. And that, I suspect, is one of the reasons why governments from China to the EU to the US are investing heavily into quantum computing.

What would be the consequences for people like you and I? Well, we’d all get tied up in the political consequences. There’s also a minor risk someone will find out you bought some really fancy underwear in 2005 and will demand an explanation. Other than that, factorising large numbers probably won’t have much of a direct impact on your life. However, there are other applications that have more far-reaching consequences.

The most obvious application of a quantum computer is to let it do quantum mechanics. I know that sounds lame but it’s commercially interesting because quantum mechanics is what determines the optical, electrical, and also chemical properties of materials. Indeed, it ultimately even determines biological properties. Yes, it’s all physics and, yes, this is why everyone hates physicists.

The interactions of atoms that hold them together to form materials or molecules are determined by the Schrödinger equation, the key equation of quantum mechanics. And we can write that equation down for all those atoms. But solving it for more than a few atoms is basically impossible on a conventional computer. It just takes too long.

This is what a quantum computer can do. You feed the properties of the molecule into the quantum computer, and it tells you the energy levels of the electrons, which in return tells you how the molecule interacts with light or more generally electromagnetic radiation, how stable it is, and how it reacts with other substances.

Physicists have done simple example calculations for this on real quantum computers. These are calculations you can also do on conventional computers, but they do show that the algorithm works as intended.

If you could calculate these properties without actually having to try and synthesize the molecules, this could dramatically speed up the development of new materials and possibly also aid with drug development. You could use it to look for new superconductors, or substances that are good for new batteries, or test whether a substance is toxic to cells. Of course it’s really just a ploy of physicists to take over chemistry and biology.

Okay, from chemistry and biology, let’s move on to finance. This seems like an unlikely connection, but the two topics are not so different. If you want to know what properties a molecule will have you have to find an optimal solution for the electrons that hold the atoms together. In finance, you often want an optimal solution too. Not one that’s optimal for electrons, but one that optimizes your profits given some acceptable risk, for example.

This is why quantum computers have multiple applications in finance. They could be used, for example to find out what combination of stocks, assets, bonds and so on you should invest to. Such a collection is called a portfolio, and going about it smartly is naturally something that bankers are very interested in. The trouble is once again, that doing this calculation takes very long on a conventional computer, basically because there are many different possible ways to put together your portfolio.

Another thing you can do on a quantum computer is try to predict the value of financial instruments like options. The way that this currently works is that you collect some data on the behaviour of the values of these options, and then you use a stochastic model to predict what is likely going to happen in the future. A quantum computer could allow you to do this much faster. And the better you can estimate what’s going to happen, the smarter you can trade. For this case, too, the algorithms are known, reasonably well understood, and have been tested for small examples on existing quantum computers.

Like with the code breaking a lot of what’s driving the interest by banks is the fear of falling behind. So long as everyone’s codes are equally slow, all is fine. But if one suddenly pulls ahead, the rest’s going to lose out. And no one wants to be the loser.

So there are good reasons why banks are interested in quantum computing. What does this mean for you and I? Well, the more efficiently the financial system works, the less money goes to waste in bad investments, and at least theoretically we should all benefit from this. In reality it means you’ll see other people getting rich. And you’ll see physicists taking over finance, too.

Optimization problems are also important for many logistical applications. An often-named example is the traveling salesman problem. Bob the salesman needs to deliver fancy underwear to 100 different cities, and he doesn’t want to waste time. Which is the shortest route that connects all places? The question is easy to pose but very difficult to answer because the number of possible connections goes with the factorial of the number of places. That’s the thing when you put an exclamation mark behind the number. It doesn’t mean you have to shout the number, it means you have to multiply all integers up to this number. The result gets very large very quickly.

In general, one doesn’t try to solve the traveling salesman problem exactly but one uses approximate solutions. The largest known solution on a conventional computer was for about 85000 places and it dates to 2006 because everyone involved was so exhausted, they didn’t ever want to do it again.

Now you might say, well, this isn’t exactly a very practical problem. I mean, no company sends one driver to deliver underwear all over the country, that’d be insane. And that’s correct, but the traveling salesman problem is one of a class of similar problems that do have a lot of applications.

For example, there’s what’s called the Vehicle Routing Problem. If you have a fleet of vehicles and places you need to deliver things, and each vehicle can only carry so and so much and go so and so far, what’s the best way to do it? There might be different ways of quantifying what you mean by best. The cheapest, the fastest, the one with the least carbon emissions. This isn’t just interesting for shipping companies but also for public transport.

Another closely related example is the Facility Location Problem. Suppose you want to set up your shipping company and you know where you want to deliver your stuff. Where do you set up your warehouses? Again, the issue is that there are a lot of options to consider and that problem is very difficult to solve on a conventional computer. A quantum computer can much speed up this process.

But even on a quantum computer one usually doesn’t try to solve these problems exactly, but one uses a combination of different methods that use both conventional computers and quantum computers. Typically you chop the problem up in pieces, and stuff some of those pieces into the quantum computer. At least that’s the plan. It’s called a hybrid quantum classical algorithm.

How will this impact your life? Your fancy underwear will be delivered faster! More seriously, making transportation more efficient is going to be good for the environment and by all chances will also make some things cheaper. Of course it’s just a ploy for physicists to take over transportation, too.

Those were all good examples, but there’s a bad example I keep reading about that I want to briefly mention. Quite a few sources have claimed recently that you can use quantum computers to help address climate change and even make weather forecasts better.

Now, quantum computing can help address climate change in the sense that the applications we just talked about could be useful to that end. For example, better energy storage. Or materials that are good at absorbing carbon dioxide. Or more efficient routes for trucks saving carbon emissions and so on. Green underwear, maybe?

But quantum computers aren’t any good for running climate or weather models. This is because the equations you need to solve for those cases are non-linear. And quantum computers can only solve linear problems. There are some ways that people have found to rewrite non-linear problems into linear ones and put those on a quantum computer. But for those cases, no speed-up has been demonstrated. Besides, there’s the problem that quantum computers aren’t good at outputting large amounts of data. So if someone tells you quantum computers are going to solve climate change or do the weather forecast, they’re making things up.

In summary. Quantum computers aren’t going to give you better graphics on your phone or make the internet faster or something like that. The way that they’ll most likely be used is that companies put some of their big computing problems onto a quantum computer and you’ll never notice.

I believe that quantum chemistry is likely to be one of the first applications of quantum computers. That’s because atoms and molecules are quite simple and well-understood systems compared to societies and stocks. For molecules or materials, it’ll also be easier to find out whether the results are actually correct and useful. *If we ever get quantum computers with sufficiently many logical qubits to function efficiently. Which I still think is a very big if

There are a lot of papers about quantum computing, but they have one thing in common. They’re all set in latex. Those equations you see in my videos. Yeah, they’re also set in latex. Working with latex used to be somewhat of a pain, but my life has got so much better since I use overleaf.

Overleaf is a platform for collaborating on latex documents. It’s owned by Digital Science who have been sponsoring this video. I now use overleaf for basically all my papers. You create a new project with a click, you invite your collaborators. You can see who is working on the document. You don’t have to send around files and collect changes. You can restore earlier versions if need be. Don’t know what to do with latex commands? Use the rich text editor. Overleaf also does away with the whole pain of getting somebody else’s latex to compile on your computer because one or the other package is missing and won’t install and so on. And in the end, you download the whole thing in one neatly packed folder and submit it to a journal or upload to the arxiv.

Overleaf also has a whole library of templates. Writing your thesis? Report due? Need a CV? Just pick one. I started using overleaf to work with others, but now I also use it for single projects because I’m lazy and it’s just so much easier. If you are regularly using latex and aren’t using overleaf, I think you’re crazy. Give it a try and I think you’ll see what I mean. Just go to overleaf dot com, set up an account and try it out.

Overleaf also has a whole library of templates. Writing your thesis? Report due? Need a CV? Just pick one. I started using overleaf to work with others, but now I also use it for single projects because I’m lazy and it’s just so much easier. If you’re regularly using latex and aren’t using overleaf, I think you’re crazy. Give it a try and I think you’ll see what I mean. Just go to overleaf dot com slash sabine, set up an account and try it out yourself.

Thanks for watching, see you next week.