From Q*bert to Qubits

I have this problem. I was using my computer the other day to work on a non trivial math problem, and it gave me an estimated time of completing that particular task as four hundred and seventy eight years, and I've got plans that day. I'm actually washing my hair. So I was hoping that maybe we could talk about classical computers, how they process information, and maybe why you're still washing your hair and your cyborg body and years years his cyborg body has hair. Yeah, it actually it

takes to wash only my body has hair. But yes, it's uh, it's you know, let's not I don't want to go too far into my personal details here, so we all understand classical computers are reading machine language, binary language, zeros and ones. Technically there's actually something electronic going on there, but we're specifically saying that you know, it interprets information

in sequences of zeros and ones that represent other things. Yeah, any piece of software running on your computer is actually a really long, I'm generally really long sequence of on and off switches of ones and zeros, right, and it's following specific rules. Yeah, and so there are two options as to work with. It has on and off their own one or one and zero whatever. On and off

would be one in zero um. And everything that it does has to be translated down to that level before the hardware can make use of it, right, because the hardware doesn't understand things like run Assassin's Creed four. It actually has to break it down into understands one zero

one one. Right. But if you tell it that run equals one zero zero zero one one one, right, Yeah, if you establish what the rules are, then it can it can interpret it through multiple levels of translating from whatever language you're using into machine language that that binary system. So these sort of this sort of approach is really

good for certain types of operations. For example, if you want something just really simple, like you want to multiply one number by another number, and you input then too the computer and it understands what the operation is understands how to multiply then, and by understand I mean it has the instructions to do so, not that it actually comprehends. Yeah, you can listen to our artificial intelligence episode and hear that whole argument again. But the the idea of being

that it does that very well. It can do that operation quickly, you get it. You know, if you use a calculator, you're going to get that information very quickly. That's first computer, more quickly than a human being, certainly than most most human beings. Yes. Yeah, your classic computer is very good at math, and it's very good at doing lots and lots of math problems way faster than

you can. But if it needs to do a whole series of those in order to get the one results you want, because the question you're asking is actually going to require many, many, many operations before you can get an answer, that's where the classical computers start to slow down. Even when we're talking about modern classical computers, which often have multi cores, right, you know, you'll hear about these

multi core processors. They can break down certain types of problems into parallel chunks, and each core of the processor can work on a chunk of that problem, which cuts down on the amount of time it takes to solve the overall question that you've asked. But even then it's you know, you're talking like like maybe sixteen cores. That's still nothing if you're talking about a truly difficult problem. And that's that's traditionally where we run into a barrier

with classical computers. There are certain types of non trivial problems that classical computers have trouble solving. And here's an example we've talked about before, the traveling salesman problem. You know, the idea that you've got a traveling salesman who needs to visit let's say ten cities, and your job is to try and find the most efficient route for that traveling salesman to go through to spend the least amount

of energy on this trip. And there are a lot of different potential wants to choose from, you know, choosing city A first and then going to city D and then going back to CITYB, or going straight through, and really you don't know what the right answer is until

you've compared all those options. And as you add cities to this this question, it becomes more and more difficult to answer, and a classical computer essentially what it has to do is go through and run every single possibility and then at the end of running all of them, compare all the results to other to come up with

your answer, which can take a long time. So that means that we need to look at maybe an alternative to classical computing if we want to be able to solve those types of problems in a more efficient, faster manner. But how do we get more efficient than than a bit? I mean, on or off seems like a pretty pretty simplified What if you could be both on and off at the same time? That's crazy talk. It is crazy talk, Jonathan. Yes, I have never seen a light switch that was both

off and on at the same time. No wonder you haven't seen it. If you had observed it, it it would either be off or on. Yeah, can't. You can't see it and see it that it's both off and on at the same time, then you've observed it. Well. The problem is because the light switch is actually a really

huge thing. Yeah, it's a macro level thing. It's on our scales, um, so it's position tends to be pretty stable, right, Yeah, But if we're looking at things on say a quantum ski ill that's sub atomic, tiny world where things just don't make sense an electronic Yeah, we're talking like tiny

little particles. They exhibit behaviors that if if that same behavior were to suddenly exhibit itself on the on the on the macro scale, on our scale, we would all just think that we had been sucked into some sort of David Lynch weird al. Yeah, would make sense. No, nothing would make sense, because the quantum world and the

classical world are are very different in the way they behave. Well, yeah, our our intuitions are evolved to deal with you know, like trees and rocks and animals, nothings, superpositions and in further more, trees and rocks and animals that don't suddenly shift three miles to the right for no apparent reason. Okay, so what what are we talking about? How can something

be in two positions at once? It is called superposition, And asking me how is the wrong way to go about a joe, because I certainly could not tell you how I can tell you what's going on here. So super position is a concept within the field of quantum engineering, quantum mechanics, where a sub atomic particle is able to coexist in multiple states at the same time. And they don't mean states like the United States. I'm talking about

actual states of being. So, for example, with electron, we often talk about spin, Like let's say that it could either have a spin that's up or spin that's down, and that's going to determine its magnetic field as well. Right, the direction of its magnetic field is that will be determined by this electron spin. Now, on the quantum level, technically, an electron can be in superposition, meaning that can inhabit both an upspin and a downspin at the same time.

It has a probability of being in either one or the other at any given moment, were you to observe that electron and therefore lock it into that one one state or the exactly, So, if you were to observe the electron, the electron would then suddenly in have but just one of those two states, and that would be determined by the probability of which state it was most likely to be in. Sometimes it's going to be in

the less likely state. That's why they're probabilities. Right, it might be a chance that will be a spin down and a six chance of spin up and you observe it and it's spin down. That can still happen because as long as the probability exists, that's how things can sometimes shake out. Now, if you were to do that same sort of experiment over a really long run, then the probabilities would start to manifest themselves, assuming that everything

else was identical, which would never happen. But anyway, superposition is that crazy idea that a sub atomic particle can exist in both of these states at the same time, at least until you observe them, at which point, once you observe them, you would say that the system decoheres.

That's it's an idea where a quantum system is a very delicate thing and if you interfere with it in any way, if you try to interact with it in various ways, it will decohere and become a classical system where things behave more the way we would expect them to based upon our own experiences. In terms of thought experiments. This is kind of going back to if you've heard about it Stronger's cat, It's it's it's you know, poking the system and seeing, you know, trying to identify what

a particle is doing is going to make the cat either. Yeah. So the basic Strodinger's cat thought experiment is that you've got a box with uh, some sort of castor in it that is going to that could release a poisonous gas anytime after thirty minutes have passed. So you've got a cat inside this box with the cast of poisonous gas,

and you wait for thirty one minutes to pass. And at that at thirty one minutes, there's a fifty percent chance that the castors released the gas and a fifty percent chance that it hasn't, which means at that moment, before you open up the box and observe it technically from a quantum level, the cat is fifty percent alive and fifty dead. And then once you observe it it those those uh that quantum state deco here's and it

forms a classical state. Right. Of course, the idea of Schrodinger's cat was first introduced a sort of like a reductio out of serdum. The idea was like, this is so ridiculous, exactly, yeah, but it turns out like works. Quantum physicists were like, well that's tough, you know, Yeah, on the On the macro scale, of course, it's ridiculous. You know, you would never say that the cat is both alive and dead at the same time. It's either one or the other. And because you open up the

box doesn't change that at all. But on the quantum scale it certainly does matter. Okay, But so if if this is how does this relate to quantum computing? Are we giving the cat a bunch of buttons to push? The cats and quantum computing? Lauren, I don't know where you got your notes, but let's just without cats. I think is a really sad. I think computers are made entirely of cats. Internet is made of cats, not computers.

Uh no, no, no, we're going to We're going to back off the cats and the Internet and the quantum computing for just a second. There's one other there's one other concept of quantum that we have to cover, which is entanglement. Yeah. This is the idea of where you have multiple sub atomic particles that are entangled in some quantum way. So remember when I was talking about the

spin of the electron being either up or down. If you have two entangled electrons, those electrons are going to be kind of opposite but mirror images of one another, and that if you know the behavior of one, you know what the behavior of the other one was at that moment when you observed the first one. Knowing that from that moment forward, you can't really predict anything, but being that if if two electrons are entangled and one is spinning up, the other one would be spinning down.

For that, for that particular set of features, that's not just limited to spin. There are other things we have to take into consideration, but that goes well beyond just the basic idea of entanglement. Entanglements very important with this when it gets to quantum computing, the concepts of superposition, entanglement, and coherence are all really really important. So you asked, you know about quantum computing. That's that's the where we're

getting at. The idea of quantum computing is being able to harness these features of the quantum world in a way that can do compute computational work for us and UH. And the the base unit of that. You know, if you were to say the base unit of a computer is the bit, either a zero or a one. The base unit for a quantum computer is the cubit, which I had to be reminded, is not a little orange

guy who bounces around the pyramid. Okay, so instead of a silicon microprocessors, say, you would have computational activities being done by something like a photon or an electron or preferably lots of them. We need at least two. But um, although I guess I know you need at least two. So what the cubits are? Uh? Interesting in that if a bit a bit can only be a zero or a one, it's one or the other. It gives you

a single value. Yes, cubits are both zeros and ones at the same time superposition uh, and technically all values in between, although that's not really that important. So the interesting thing about cubits is that the the relationship between cubits and computing power is exponential. You take two to the power of however many number of cubits you have, and that is the equivalent of your quantum computer's power, meaning that with with you know, two um cubit's you

have four potential values. There. Uh. You have to look at the things as like, uh, two zeros zero, one one zero or one one um and they're all the same things, and there are all of those at the same time, right, But if you were to add another cupid in there, then you're talking about two to the third power. So you're talking about eight pieces of information from three cubits, which is different from the way it would be if it were just bits. And as you

add cubits it becomes exponentially more powerful. By definition, you're talking about actual exponent here the inn in that two to the nth power. So the interesting thing here is that all of these different cubits could uh and inhabit these two values of zero and one at the same time.

If you have enough of them, then you could, in theory, run a very complex problem through a quantum computer and it could solve for all aspects of that problem simultaneously in parallel because it's essentially doing all of those calculations at once because all of the cubits are all possible values. So it's kind of uh great for very specific types of difficult problems. Okay, so this sounds like, though, um, it's not going to be a replacement for the kinds

of computers we use now, not at all. Because while it's great for certain complex problems like the traveling salesman problem where it could solve for all of those different variations simultaneously. It's not necessarily going to be any faster, and in fact, might even be slower than a classical computer for your basic computing functions that that regular schmos

like like myself, like like I do. If it's not gonna show YouTube super faster, you're not going to be able to run the latest video game even faster, like I love the idea of running a video game on a quantum computer and all possible outcomes of the video gameplayouts simultaneously, like I was both good and evil and

everything in between. But that's that's not exactly what would happen. Okay, So you're saying that a machine like this might have really incredible powers in some kind of specialized way, very specialized, like cryptography breaking. If if we had a working quantum computer of sufficient power, cryptography as it exists now would be meaningless. And the reason for that is that basically the way cryptography tends to work is take two really

large prime numbers, like really really large. We're talking digits that are hundreds of digits long, like it's it's an enormous number, and then you find another enormous prime number, and you multiply the two of them together and you get that product, and then your your encryption is based upon a party that's authorized having one of those two large prime numbers, and as long as it's one of the two right to correct numbers, they can get access

to that uh, that particular information or site or whatever. I'm oversimplifying for the purpose of this podcast. Now, publicly, all you can see is the product. So you see this huge product. I mean, it's a no enormous number. I remember, it's the product of two big prime numbers. And if you don't have the information already, trying to figure out which two prime numbers made this even bigger

number is really hard to do. In a way a classical computer would do it, is it would start by dividing by prime numbers and then run through all of the prime numbers that possibly could be. So, if you're talking, if you pick a large enough prime number, that alone is going to guarantee that any computer working on trying to force this cryptography, this brute force stile attack is going to take longer than it would be you know,

feasible to run. So you would you know, most people would not ever bother to try, because to do so successfully would take forever. But if you had a quantum computer that could solve for all potential prime numbers at the same time, you could crack that roll relatively quickly. In fact, yeah, it could. It can make the most advanced encryption tools useless. It could also usher in a new era of quantum cryptography, which would be even more difficult to crack. But you know, it's it's one of

those things already where that's just one application. Obviously, there are lots of other applications for quantum computing. Yeah, that was one of the early applications. Actually, in the in the early nineties, Peter Shore of Bell Labs developed a quantum algorithm that that was a method of of entangling cubits and using superposition to um to find prime factors of an integer. Although that's not to say that that we can run that on all of our fancy current

quantum computers. It was really like a proof of concepts saying that once we are able to do this, it's going to change our world, and it's good to know about it now rather than three months after the world's fastest quantum computer is made, and then we all realize all of our stuff is public. It's better to know it now, so we can say, huh, that's a problem.

How do we fix this? So I mean, but yeah, it's a great example, and a lot of work has been done on quantum computers since just that that that algorithm was really for a hypothetical quantum computer. But now we've got people who have actually built at least preliminary quantum computers. Yeah, what's out there? I think I think the fanciest one that we've got was built in two thousand and seven. It's it's called the d Wave and

it's a sixteen cubit quantum computer. I know they were working on one that would have been five and twenty eight cubits, which would have been phenomenal, and that that would have been unveiled within the last year or two, But I honestly don't know if they ever uh successfully

demonstrated that one. But the fact that we've had people demonstrate this at all is pretty phenomenal because keep in mind, you have to be really careful with the way you operate one of these things, because just by observing it, by by trying to interpret the results you could cause decoherence, and then you end up with a very primitive classical computer that can't do much of anything, Like can you imagine going from a sixteen cubit computer to a sixteen

bit computer? Would not be great? Right, And they've been working on these kinds of problems for UM since the since the sixties and seventies and eighties when all of this was sort of starting to come together, and it required a lot of work in UM and first of all, bringing reversible logic gates into the computing world, which which allows you if you have a one way gate, then you're going to experience a lot of data and therefore

heat loss in your computer system. UM having a reversible gate lets you UM basically not burn out your processor every time you turn it on. Essentially, UM and and quantum electrodynamics, which is just starting to hum look at how electrons and photons interact with each other, so that we can start creating these little quantum pieces of of electrical information, right right, yeah, I mean, how do you harness this stuff? It's it's really tricky. Are you have

to be able to create entangled particles? That's already kind of tricky there's certain minty materials that are being used right now in an experimental way that that are potentially a source of entangled photons. That's pretty exciting stuff. You have to figure out how to create a system that these can work in that is not going to allow

it to go into decoherence. You have to figure out how to program for it so again that you can take advantage of it using it for the right sort of problems, and you have to figure out how to get the solution out of it again without disturbing the system, which is pretty tricky stuff. And even then, you're talking about probabilistic results, right, you mean you're getting results that

are assigned certain probabilities of being correct versus incorrect. And sometimes the probabilities you get are so high that you

might as well say it's a certainty. I mean, you can't really say that statistically speaking, there's always some room for uncertainty, but you know from human experience and be like, well, you know, times out of a hundred it's right, but there's still a chance that could be wrong and not all and of course some results may end up being like we're sure this is the right answer, So it's a it's a very uh specific, kind of niche oriented version of computing. It's not something you're not gonna go

and get your uh your your your laptop. That's gonna have you know, the cotum version of the last model you owned, right, sure, and it is it is. Yeah, like you said, just slow going. I mean it wasn't until two thousand and one that there was a successful demonstration of shorts algorithm, and that was with a seven cubit computer that found the factors off. Yeah, they have factors of It's still it's still something. I mean, hey, no, no, no,

I mean that's impressive. I mean I think that the very first one added one in one and everyone was so excited. I mean I mean understandably so. But nonetheless, and you know, and there's there's a few different ways that you can work on this coherence problem. I think

that that is the largest issue that we're talking about. Um, yeah, that's that's I mean, none of these are trivial, but I would say that's the hardest or from what I understand, keeping in mind, I'm not a quantum physicist, right because I mean you can either I mean, you can like trap ions and super cool them until they're in a quantum state so that you can work with them, or um you can use liquid to to kind of wrangle cubits so that you can spread a single cube it

across a few different molecules, which will decrease your your rate of coherence. Right, But all of this is you know, I mean, we're talking about very tricky particle physics. Yeah. And while we're talking about you know, kind of humble beginnings, keep in mind that other things that we depend upon today very heavily had very humble beginnings. For example, the Internet. You know, if you remember back when the Arpanet was first being put into into action, you know, that was

a predecessor to the Internet. Some people call it kind of like the grandfather to the Internet, but it was it was a network of networks, was the idea, and it was this um. The one of the earliest messages sent, actually the first message set UH ended up crashing midway through the message. It was a one word message. So you know, you've got, you know, something where you point

to that and like look at that. If we had just assumed that everything that followed that that failure was also going to be a failure, we would not have the Internet right now. So while we talk about these kind of tiny exam balls, you know, when you're thinking about proving a concept to be viable, that's huge, right, even if it seems relatively tiny and you're talking about, oh, you found the factors of fifteen. Wow, that's something that I learned in third grade. But you know, for something

that until that point was hypothetical, that's amazing. So yeah, I mean, these quantum computers have a lot of interesting potential, not just in decryption or even the traveling salesman problem. Joe, you had, you saw something, right, Yeah, they might be able to help us actually study some things in the real world that are really difficult to study with the computers we have today, or might be really expensive, say

to simulate physically. I've got a press release from last year from the n I s T Information Technology Lab UM, and what this talks about is that quantum computers might be able to simulate particle collisions. So the kind of work that we have to do now with like the particle accelerator, like the large Hadron collider and something it's miles across and die amateur, Yeah, it could could actually

be simulated just in software. And of course, like with a regular computer, it's really hard to do this because digital you know, the computers we have today can't determine all these quantum states. There's just like too much information

to keep track of um. But this press release talks about a team that came up with an algorithm that could basically run on any quantum computer, regardless of what it's quantum hardware was um, and it would simulate all of the different ways that two different types of particles could collide and interact. Interesting. Yeah, see, this is kind

of fascinating stuff. The idea that we can uh add in all these known factors that we are aware of and create a simulation that could potentially create stuff we aren't aware of. It's kind of to me, that's that that's almost like magic at that at that stage where you're like, all right, I know what this does, and I know what this does, I don't know necessarily all the things that can happen when the two collide, and you create a simulation that can actually show you that.

To me, it boggles my mind. You know, it's just such a phenomenal thing. And yeah, again, the quantum computer would be a use in that situation, but not so much if you want to play mind Sweeper. Well though, we're not saying necessarily that a quantum computer could never run a game or a video player or something like that. We're just saying like, there's really no reason you'd need one when a classical computer can do the same thing

for a long time. Because, I mean, while while your power of your quantum computer does, uh does expand exponentially with the number of cubits you add, you still would have to add a lot for it to really uh for for classical applications, for it to be better than a classical computer. Now quantum applications, it would just leave everyone else in the Yeah, but you would you would need you know, a whole gallon of quantum, right, Yeah,

you gotta get that. Gotta go over to the quantum refueling station and fill up your quantum tank and bring it back just to just to play like like Super Mario Brothers. Oh yeah, I don't know about you, guys, but I'm ready to go and play some video games. So I'm gonna wrap this up. Guys. If you enjoy our show, please go check f w thinking dot com. That's our home web page where We've got all the blog posts and videos and podcasts, cool stuff that you

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