- Quantum computing has gained attention in recent years due to advancements in lab experiments and the potential for new capabilities.
- Companies are showing increased interest in collaborating on quantum research, marking a significant shift from previous years.
- The challenge lies in controlling qubits, which are unstable and prone to collapsing into regular bits.
- The Oxford Iron Trappers have achieved a high level of control with a 99.9% fidelity rate for two qubits.
- The ability to control multiple qubits is crucial for building a functioning quantum computer and conducting algorithms.
- The issue of error checking in quantum computing has been addressed through the use of multiple physical qubits to store one logical qubit.
- An algorithm is used to check for errors without directly observing the qubits, allowing for error detection and correction.

- The video discusses the concept of error correction in quantum computing.
- The main qubits store information and the extra qubits are used for checking errors.
- The measurement of the extra qubits is not guaranteed to be correct, so layers of protection are necessary.
- A threshold of precision is needed to control a quantum computer and remove errors faster than they occur.
- The gap between what is needed and what can be achieved has closed, with a threshold of around 99%.
- Topological codes, such as the Katayev surface code, offer a simpler architecture for building quantum computers.
- The codes allow qubits to be laid out in a grid, with each qubit only needing to communicate with nearby qubits.

- The use of topological codes in quantum computing eliminates the need for swapping qubits, reducing errors and simplifying operations.
- Network approaches to quantum computing allow for more connectivity between qubits, but also increase the risk of errors.
- The field of quantum computing is confusing due to the many different approaches and the commercial interests of companies involved.
- The lab in Oxford is working on various approaches to quantum computing, with the ion trap method being one of the most successful.
- The concept of Schrödinger's cat is used to explain the superposition of states in quantum theory, highlighting the weirdness of the microscopic world.

- Quantum computers are like Schrodinger cat experiments, with multiple components in multiple states simultaneously.
- To isolate atoms, a vacuum chamber is used to prevent interaction with the outside world.
- An ion trap chip is used to manipulate and hold the atoms without physical contact.
- The ion trap allows for long-lasting quantum superpositions, with decay times of up to 50 seconds.
- Decoherence time is a measure of how well the system is isolated, with longer times being better.
- For shorter calculations, the system can be measured and the answer obtained before decoherence becomes a problem.
- Techniques for error correction can also help mitigate the effects of decoherence for longer calculations.

- The paper's referee pointed out the omission of natural decoherence in the research
- Iron traps are a successful system for isolating quantum units and are considered the gold standard of qubits
- Superconducting qubits are another approach taken by Google, IBM, and Intel
- The challenge lies in scaling quantum computers and making them work consistently and robustly
- Quantum supremacy refers to the point at which classical computers cannot simulate the power of a quantum computer, typically around 50 qubits
- There is a significant gap between the usefulness of 50 qubits and the point at which quantum computers can perform tasks like breaking codes, which requires thousands to millions of qubits

- Quantum computing is still in the early stages and it may take more than a decade to have millions of well-behaved qubits.
- Quantum devices that are close to or just over the quantum supremacy threshold are expected to be released in the coming year, but they may not be immediately useful for practical applications like breaking codes.
- Quantum computers have the potential to break codes and improve areas like drug discovery by predicting the behavior of complex molecules and materials.
- The number of qubits needed for these tasks is still uncertain, but it may be possible to achieve them with fewer qubits and without the need for error correction.
- The current state of quantum computing is around 10 to 20 qubits, with the goal of reaching 50 qubits.
- Different approaches to scalability are being explored, such as linking small quantum computers together using optical links.
- The quality of the optical links is currently a challenge, but using the links multiple times can improve the overall communication quality.

- The use of entanglement is crucial for achieving good quality connections between modules in a quantum computer.
- The goal is to create a machine made up of small quantum computer modules that are interconnected.
- The quality of the entanglement between modules can be boosted by sacrificing one entangled pair to improve the other.
- The speed of the modular quantum computer is currently limited by the rate of connection between modules.
- The plan is to build a large facility with interconnected modules to create a scalable quantum computer.
- The end user may not have a quantum computer in their phone, but they can access it through the cloud.
- The size of the modules can be miniaturized, and there are no fundamental impediments to building the envisioned quantum computer.
- The network approach is seen as a potentially faster way to achieve a quantum computer compared to other approaches.

- Quantum computing has gained attention due to advancements and potential capabilities.
- Companies are collaborating on quantum research, marking a significant shift.
- The challenge lies in controlling qubits, with the Oxford Iron Trappers achieving a high level of control.
- Error checking in quantum computing is addressed through the use of multiple physical qubits.
- Topological codes offer a simpler architecture for building quantum computers.
- Network approaches allow for more connectivity between qubits but also increase the risk of errors.
- The field of quantum computing is confusing due to different approaches and commercial interests.
- The lab in Oxford is working on various approaches, with the ion trap method being successful.
- Quantum computers are like Schrödinger cat experiments, with multiple components in multiple states.
- Techniques for error correction can help mitigate decoherence for longer calculations.
- Quantum supremacy refers to the point at which classical computers cannot simulate the power of a quantum computer.
- Quantum computers have the potential to break codes and improve areas like drug discovery.
- The current state of quantum computing is around 10 to 20 qubits, with the goal of reaching 50 qubits.
- Different approaches to scalability are being explored, such as linking small quantum computers together.
- The use of entanglement is crucial for achieving good quality connections between modules.
- The plan is to build a large facility with interconnected modules to create a scalable quantum computer.
- The end user may access quantum computers through the cloud.
- The network approach is seen as a potentially faster way to achieve a quantum computer.

- The modular approach to quantum computing allows for easy scaling with a relatively modest amount of investment.
- Demonstrating the ability of two modules to fully link together to form a single quantum computer is a goal for the next year.
- The transition from the lab to a commercial setting is a challenge in quantum computing.
- The hype surrounding quantum computing may lead to unrealistic expectations and over-investment.
- There are opportunities for individuals with various technical expertise to get involved in quantum computing.

- Modular quantum computing allows for scalable and cost-effective expansion.
- The goal is to demonstrate the linking of two modules into a single quantum computer.
- Transitioning from the lab to commercialization is a challenge in quantum computing.
- Hype may lead to unrealistic expectations and excessive investment.
- There are opportunities for individuals with different technical expertise to participate in quantum computing.

Simon Benjamin - http://www.materials.ox.ac.uk/peoplepages/benjamin.html - is a Professor of Quantum Technologies at Oxford. He is also the Principle Investigator for Oxford’s project on Quantum Optimisation and Machine Learning - http://quopal.com/

This episode is more technical than last week’s episode with John Preskill - https://blog.ycombinator.com/john-preskill-on-quantum-computing/. We start by covering some fundamentals then go into different approaches for constructing and scaling a quantum computer.

Read the transcript here - https://blog.ycombinator.com/simon-benjamin-on-quantum-computing-architectures

The YC podcast is hosted by Craig Cannon - https://twitter.com/craigcannon

Simon, why in the past few years has quantum computing gotten so much attention?

Well, quantum computing is something that academics have been working on now for decades.

But what's exciting is that it's all starting to work in the sense that what we now have in labs is getting to the regime where it can actually do stuff that we can't do by other means.

So it's, you know, it's got that feeling that it's all about to happen.

That said, you never know how far it is from where you are to when you've actually got a working machine until you've actually got the working machine.

But then also people outside the field, companies, people who look for disruptive changes in technology are obviously receptive to this and they're starting to get excited as well.

And I guess it's a kind of feedback loop.

But I can say that just in the last 3 years, we've had tons more interest from companies who come to us as academics and say, look, can we jointly work on something with you?

If we went up to companies even 5 years ago and said, how about investing in some research?

They would say, well, we're aware of this, but it's over our horizon.

But now, we're almost having to fight them

Was there a certain basic research or maybe an experiment that made people realize, like, oh, this might be the time.

And so I'm a theorist, probably should put that up front.

They don't let me in the lab, except when they've tidied everything away, because my elbows tend to set them back a couple of weeks.

But in the lab, researchers have been trying to get better and better control of quantum systems.

So, you're probably familiar with the word qubit, which is quantum bit, which is of course the building block of quantum technology instead of bits.

But unlike bits, which are wonderfully stable, and with the right technology will just sit in the 0 or 1 for a long period of time, even years, qubits are horribly unstable.

They're constantly trying to just become regular bits, which means they, the usual word is collapse to 1 option or the other.

You know, they, we talk about a quantum superposition, a state that 0 and 1 at the same time, and we can talk a bit more about what that means, but the point is it's fragile.

Qubits don't in a sense want to be in 0 and 1 at the same time, or rather, their environment doesn't want them to.

Also, when we try and control them, it's very difficult to control them precisely.

So it's all about how good is your control of the quantum world.

And I can't resist at this point just mentioning we're here in Oxford.

The Oxford Iron Trappers, we might talk more about what that is, have the joint world record for the highest level of control of any quantum system of any kind.

And the really tough thing is to say how well can you control 2 qubits.

If you think about it, if you want to make a computer, It's not enough to just control individual entities, because if they don't talk to each other, you can't have a process, an algorithm.

All you've got is some kind of recording system, right?

So if you could go and set the state of a bunch of individual qubits, and then later come back and have a look at them, you've got a memory.

But if you can make 1 qubit control another qubit, you've got an operation, an element of an algorithm.

That's the hardest thing almost always, because it's the most fancy thing.

Now, we use the word fidelity, which means how well are you doing in terms of getting your control.

And the Oxford guys, their record is 99.9, a little bit, percent fidelity.

So that's the fidelity that it takes to do 1 specific operation.

I always use my fingers because I think of them as little arrows.

I tell this guy to flip only if this guy is, let's say, in state 1, but not if it's in state 0.

Okay, so that's a story about 2 qubits, which should just happen.

Ideally, you tell them to do that, they do it, exactly like you told them to, and you move on.

In practice, they won't do exactly what you told them to, because these things are very hard to control.

So 99.9% is the chances, essentially, that they will do what they're told, and if not, then they'll do something random.

99.9% seems like a good score in any context.

But compared to conventional technologies where that number might be something like 1-10-15, it's insanely good in conventional technologies.

That's why your software doesn't just crash over time on your laptop.

So whilst that number sounds good, it's actually still very challenging.

Imagine you're building an algorithm, you're gonna have to have a lot of these operations, right?

A lot of times, 1 qubit will talk to another qubit in the course of doing some calculation.

If 1 in a thousand times, it just goes wrong and yields nonsense, then if you've got more than a thousand or so operations and you will have, then something's going to go wrong.

You know, you're going to get an error in your quantum program, and unless you've been very smart about how you design it, that's just gonna make the answer come out nonsense.

So that's the kind of problem we've faced for all these years, and when I say we, I mean the actual guys in the lab, right?

I've just been at the whiteboard saying, come on guys, why isn't it working yet?

So to briefly tangent on this, How long have you been theorizing about quantum computers?

Well, the field has been theorizing in detail about quantum computers since the early or mid 80s.

Right, so it was David Deutsch and then getting started.

Right, and then in the 90s, we, so initially people thought this problem of control was going to be perhaps a deal breaker.

The thing is, you see, if you're running a quantum algorithm, okay, so if you're running a conventional algorithm, you can at any time check the state of your machine.

Because I'm going to have a look at my ones and zeros, see if they look about right.

If you do that with a quantum computer, because of this idea of superposition being in many states at once, if it's not yet ready to give you the readout answer, but you just want to check to see if it looks like it's on track or if it's gone wrong, you're going to destroy the state of the computer, you know, prematurely.

The act of looking for errors, naively it would seem that it's going to actually destroy the state of the machine, right?

So How can I keep on track if I'm not allowed to see?

It's a bit like trying to navigate with a blindfold and you've been told a bunch of landmarks but you can't see them, right?

You're not allowed until you get to the end.

So people thought, including some really substantial thinkers like Ralph Lander, thought that that might be a deal breaker.

The fact that you can't check for errors, but they are going to be happening, would mean that for anything except the simplest toy calculation, you can't really get where you're going to.

And in the 90s was when people, including Andy Steen who's here, but also Peter Shaw, who's famous for 1 of the big algorithms, figured out the solution to this.

Which it sounds almost like a philosophical paradox, right?

I want to be able to check and fix errors as I run a process, complicated long process, but if I look for errors, if I ask the information whether it's in a good state, I will destroy it.

So the answer is, what you do is, you use several qubits, even a large number of them, to store 1, what we call logical qubit.

This is the same thing that, well, it's a grander version of the same thing that happens in conventional technology.

There, if You know you're going to store a lot of information and there may be some errors because you're storing vast amounts.

You may use an error correcting or an error detecting code, which means you dedicate some of your bits to being watchdogs on the others.

Now the quantum version of that is much tougher to work out, but it's the same basic idea.

So we use a bunch of physical qubits, which might be individual atoms or superconducting loops, many different exciting hardware options.

But whatever they are, you use a bunch of them to store 1 logical qubit.

And you do it in such a way that if 1 of those physical qubits goes wrong, you will be able to fix that 1 guy by using the information that's stored in the others, essentially.

So you've spread out your burden of representing the qubit over a bunch of guys and collectively They're more robust than they would be individually, but you're still not allowed to just look at them directly So the real trick was to say well look we'll have another bunch of qubits.

And then we do a little, we stop the main calculation, if you want to think of it this way.

And then we bring in these extra guys and we have a little special calculation really, a special computation which is just to look for errors.

So a computation takes place between the new guys who are just in a reference state and the guys you actually want to check.

And what you basically do is a calculation where the question, is there an error or not, is now stored on the extra guys.

They don't know what the main information is.

Now, you can actually have a look at the extra guys.

If they say there was an error, they'll also tell you which guy was the problem.

And you can fix that guy without looking at him.

Or it may be that when you measure those extra guys they basically say, okay, I don't know what the information stored on the main qubits is because I'm not supposed to know that, but I can tell you that qubit number 3 has been flipped.

I don't even know what state qubit number 3 is, but he has, or

Sorry, this sounds a bit technical, but it's a huge breakthrough in the field.

And just to pause you very quickly, so The

information you're passing through, these are qubits as well?

Right, so what you have is, you have your main guys who are storing some information.

They're going to be part of the checking process.

And then we just talk between them, doing a little calculation, little computation between them, using these 2 qubit gates that I was talking about.

So again, errors might happen even during that process.

So we have to be very, we have to think of all possible bad things that could happen and make sure that none of them are a deal breaker.

But basically this trick of not looking for errors where they are, but looking to 1 side, because you've basically done a separate little calculation that now in the what we call ancillar qubits, It tells you just 1 thing, the 1 thing you do legitimately need to know, which is, is there an error?

So that was a very simple idea, but very, very important.

But measuring the ancillary qubits, how do you know that measurement is correct?

So it's like, who guards the guards, right?

I mean, if there was 1 thing that you could trust absolutely, that would be fantastic for us and we'd be able to simplify all our designs and solutions.

But we must assume that everything is untrustworthy.

So measurement of a single qubit might be a bit more reliable than say the 2 qubit gate, but they all have a number on them that says how dodgy they are.

And yet what you need to do is come up with an approach where there's enough protection that even if, say, the measure...

So you might falsely conclude that there was an error, and there wasn't 1, because the measurement went wrong, right?

Then you're fixing an error that didn't happen.

So you basically need to construct the overall story so that that event is so rare that you can run your whole calculation, and it probably won't have happened.

So there's ways of checking the measurements as well.

Which makes sense why error correction and the minuteness of the error, the likelihood, keeping it low is the most important part.

So I mentioned this number 99.9, which I said we're very proud of.

It's actually a very important number because when you work through these schemes for protecting information Because anything can go wrong you tend to what you find is something called I use another technical word now a threshold and that means that If you're doing things better than a certain number, you will be able to use the protection to get rid of the errors, the physical errors, as they occur.

You'll stay on top of the problem, and you'll be able to run a long calculation with nothing going wrong at the logical level.

But suppose that every time you tried to do something, make a measurement, make a two-qubit gate, something like that, you had a, let's say, a 30% chance of just wrecking it.

That would be hopeless because you'd, it's like trying to fix a broken watch wearing boxing gloves or something, right?

You're, You're going to cause more damage than, you know, so in a slightly more formal language, you might say it's like entropy.

Can we remove disorder more efficiently than we're putting it in, given that the process of trying to remove it itself is a little bit noisy and damaging.

So you have to make a net benefit, right?

You have to take out more trouble that you're putting in, then you can stay in control.

And added to this is you're running actual code.

So the code might be erroring out as well.

There's also a whole other question, which is how reliable is the algorithm itself.

But all of this is just, is the machine even doing what I'm telling it to do, right?

So you have this number which the theorists can derive, and I've spent quite a lot of time deriving it for particular approaches, which is essentially how good do the lab guys have to get before they could now, with enough funding and whatever, build a big quantum computer and know that it will stay on track?

Because they're now so good at doing the operations that as errors happen, they can take them out of the machine faster than they're happening.

And now the threshold when these results were first discovered in the 90s was about 10 parts per million, so 99.9999 was the kind of level of precision that you would have to have in order to control your quantum computer and take the bad things out faster than you're putting them in.

So or almost regardless of them enough to be able to run very large algorithms and be able to do the things that we dream of for the big for the big machine.

It's always the case that if you have enough qubits and you have.

So basically what happens is the more you have, you have to slightly dedicate more and more of them to the checking process.

But it's not too bad in the sense that if you double size of the machine, you might only need to slightly increase the number of guys who are checking.

So this number, this threshold, in the 90s, it was very demanding.

So in the 90s, we had the theorists saying, good news, we can tell you how to build a quantum computer and It will work, and it won't go off track, despite the worries from, let's say, the 80s that it would have to go off track.

You know, that problem has been solved, said Andy Steen and Peter Shaw, and many other people who were excited by that.

Bad news, the level of control you need to achieve in the lab to use these ideas is still very demanding.

It's modest by comparison to how classical, I'm sorry, classical computers being everything that's not a quantum computer.

It's modest by comparison to them, but compared to what you guys are achieving, let's say in 1990, in the lab, it's horribly challenging.

In the lab, maybe 2 cubic gates might have been around the 90% fidelity mark at that time.

And yet the theorists were saying, I need you to be 99.9999, you know, and that's a gap.

And that was a real time for optimism versus pessimism.

Because how long will it take a technology to get a hundred or a thousand times better in its precision?

Really, there were optimists, and I was, at that time, I was like getting into, I was just getting interested in the in the late 90s, in this area and hearing about it.

And so of course I was a super optimist at that time as a student,

to be like, ah, everything's just happening, right?

So, I was like, I'll probably have it in a couple of years.

And then there were pessimists who would said this gap between what we need to be able to build, the theorists say, and what we can build is so wide, it's probably physically impossible.

You could say that and no 1 would be able to prove you wrong.

Now, To come back at last to your original question, why are people excited now?

It's because that gap has completely closed.

The theorists, as a community, have been doing better.

They've been improving their codes and making the demands more permissive.

If you've got 90, if things work correctly in your quantum computer 99% of the time, that's the turning point.

You don't want to be at 99% because that's also can be seen as the point at which things become impossible.

But 99.9, which is what the guys here in Oxford can do, is 10 times better than the threshold.

So how do you move to 99% and above being accepted?

On the theory side, We have a family of approaches now called topological codes.

And these things, 1 could say a great deal about them, but practically what's important about them is the following, a very simple property, especially something called the Katayev surface code, which is at the moment the go-to solution for how we would build a quantum computer.

Why is it better than the codes we had in 1995?

It's better because the architecture of the computer can be very, very simple.

In fact, it can be as the name 2D surface code suggests.

You're allowed to lay out your qubits just in a grid, which is great news for experimentalists.

Actually, they'd rather lay them out in a line because that's if there's something easier than a grid, it's a line, right?

I mean, conventional technology is laid out if you zoom in on a chip onto a grid.

And when I say you can lay it out that way, what I mean is that each qubit only needs to talk to the immediately nearby guys, north, south, east, west.

The code does not require a qubit to be able to reach out and talk to a guy 3 blocks over.

The early codes would have required that.

They would have required qubits to be able to link to qubits all over the place.

Most of the ideas for quantum computing actually involve direct physical interactions in the physics, which is short range.

So if you have an idea where you can lay out your qubits in a grid, that's very...

That reflects what is straightforward in the physics for you to achieve.

On the other hand, if someone says to you, I want you to do something where this qubit needs to talk over here, and then it needs to go and talk over here.

If you've only got short-range links in the hardware, and you're actually saying, I need this guy to talk to this guy over here, what you're going to have to do, more or less, is swap, swap, swap, swap, swap, swap, swap, swap, swap, swap.

And now they're next to each other and they can talk.

But you did all those swaps, and those are making errors as well, right?

So the cost was in permuting around the information inside the machine.

But now along come the topological codes, and they say, no, it's fine.

Everybody can just sit there and just talk to the immediate next-door neighbors.

It takes away a great deal, most of the operations actually, because most of the operations would have been used for swap, swap, swap, swap, just boringly moving stuff around.

Now, by the way, we might perhaps, it's up to you, talk about network approaches to quantum computing, which is something I'm super keen on.

And they actually do have the ability to link any qubit to any other qubit, which is still super desirable, even though the topological codes have told us we don't absolutely need it.

What it what it means is that it's Tougher to figure out how your hardware is going to work But if you can figure that out and we think we have got it figured out then you can build a machine where the qubits are able to link all over the place.

And that is fantastic for, I mean, it's always better to have more connectivity.

It's always more powerful to have more connectivity.

Rather than just what we would call nearest neighbor, which means wherever you've put your qubits, they can only actually talk directly to their surroundings.

But still, the topological codes showed that that was enough, and that's an enormous simplification.

So that was responsible primarily for moving from the multiple nines to the 99% threshold.

And then in the lab, well, the different kinds of technology, and there are a lot of them, and this is 1 of the things that makes the field quite confusing for someone who just, just, someone who Googles.

You type in, how does a quantum computer work, and you get 20 different answers.

And it's worse than ever actually, just as an aside, because before, Like 5 years ago, if you type in, how does a quantum computer work, you get different academics like me talking about our favorite approach.

But academics don't really have hostility to the other approaches.

I mean, the ones I don't work on, I wish them good luck.

You know, I just want to see a quantum computer happen.

But now because we have a lot of companies engaged, they need to take a little bit more of a commercial attitude to it.

So if they're investing in a particular approach, and you ask them, how is a quantum computer gonna work?

They won't tell you about the rivals, they're gonna tell you all about their approach and why that is the solution for sure.

I mean, I'm not complaining in the sense that obviously they must do this, right?

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Simon Benjamin on Architectures for Quantum Computing