We're going to be talking about representation learning for quantum systems. Go ahead. Thank you, Agnes. Well done on the pronunciation. Good morning everyone. How many of you were at the school? Because I'm hoping I've kept the talk a little bit more accessible, I hope. So please also feel free to interrupt and ask questions. And basic questions but for the for the experts if you want to ask more detailed questions please do that too. Representation learning for quantum systems what I want to talk about and let me start by checking if you're all awake. I'm giving you I'm very proud of this animation. I'm going to give you 10 seconds to solve this question starting now. I have to show this because of the animation. Anyone wants to take a guess or knows the answer? What did you do in your mind? No, I think if I didn't make a mistake the answer should be a little bit easier. So what did you do in your brain when I asked you this question? Yeah, so you transformed the Roman numerals to numbers, Arabic numbers exactly. And then the answer should have been this. Then, okay, so then I will, this is my mistake, but I wanted to deflect it. I just took this literally from this book. I did not make up this, sorry? 221, you're right. Yes. Okay, 221 divided by 9 was then probably the answer you had. Well done. Here's the importance of having representations, but also having correct representations. Here's another one that, this is not a question anymore. Here is an important practical representation. This is about how you represent lists in memory where if I asked you to insert the number 6 into a list in the bottom left here, if I give you a data structure, this is for computer scientists, but if I give you a data structure that is a so-called linked list where you can only ask for the next and the previous element in memory, then to find the number 6 you have to start somewhere and do order of N operations to find where to insert the 6. Whereas if I had given you this data structure in a binary tree where you can always ask larger or smaller left and right, you can do this in log N operations. This is the same data, it's the same task. I'm just listing these to highlight the importance of representations. I'm sure you're all aware of this, but I want to drive that point home. Here, very practically, data structure representation is important. For those of you who were at the school, here's an example that you have also seen. The same is true also for things that we do in physics in tensor networks. You have a representation of your wave function which is exponentially large, which is a problem if you want to go to large systems, but it turns out that at least for some types of systems, actually you can do this for all types of systems, you can always have this representation where you decompose this exponentially large number of elements, this tensor, into something that has fewer. Did you all see this in Miles' stock? Where D is this bond dimension, this is the dimension of these matrices? You can always do that. In the worst case, these matrices have to be again exponentially large, and then you don't win anything, but it's a good representation because for some states with not too much entanglement, this representation is also useful. It's not only different, but it's also useful in that sense. Then in general, it's a bit of a vague question perhaps, but finding a good representation then depends on what you want to do with it, and then we need to define what is a good representation. Many people have asked this question, but I think a useful one for me is if it's representation that I can use to solve a task. I'm not just asking how do I represent this data, but I want to do x, y, or z with this. How do I find a good representation for that? Making a subsequent task easier. There's many things you can say here. It's either easier to interpret. That's what I will focus on a little bit in the next example. Maybe it's less memory, tensor networks, for example. Maybe it has other properties like being more symmetric. Maybe also for tensor networks, it's easier to manipulate, and I can also have any or all of the above. I maybe want to have one that is less memory or more memory efficient and easier to manipulate both and have them all in the same part. Then this is a very standard thing that people nowadays do in semi-supervised learning, which is also relevant if you have data, for example, from experiments where some samples have labels, and many do not, because they're perhaps expensive. You have to have a human label the data, or maybe it's easy to generate a whole bunch of samples, and then some of them have class labels. Then what you do in such cases, or a thing to do in cases where you have this separation, few labeled samples, many unlabeled ones, is to take the unlabeled ones, learn a representation from that. Come back to this in a moment, and then with that representation, solve the supervised task, where you do have the labels. This allows you to do bootstrapping. You can then also extend that. Once you have learned it from that representation, you can assign labels to the unlabeled data set. It's a very interesting topic, semi-supervised learning. It's what it's called. There's also self-supervised learning in this setting. If this applies to you, if you have experimental data, this is worth trying. Now, I said representation, I said learning representation. So far, for example, if you think about tensor networks, it's a representation that we have come up with as humans, the same for the data structures. But for a lot of learning tasks when it comes to deep learning, the idea is that we would like to extract such a representation from the data. This is what representation learning is all about, and if you have been doing machine learning, you have all been doing representation learning, maybe just not very explicitly. So here's, I took this from this quote because I like it from the website that show here. The idea, therefore, is to learn a representation but make this now explicit by embedding it as a separate step in a learning routine. Here it says, is a representation learning, is a process in machine learning where algorithms extract meaningful patterns. We'll come to that in a second ago. Also, what meaningful means, from raw data to create representations that are easier to understand and process. Maybe interpret even. So that's what the next sentence says, actually, representations can be designed for interpretability if you care. They can reveal hidden features or they can use for transfer learning. They can use for many more things like single shot learning. If you're interested in doing that, again, if you have very costly data or very costly experiments that give you few data samples, that might be interesting. So the idea really is to have this learning of the representation as an explicit step. And one way of doing that is dimensionality reduction. Using, in this case, an autoencoder. Did you, does everyone who does not know what an autoencoder is? Nice. Okay, good. No one, or those of you who don't know, don't dare say it. An autoencoder is a very simple thing where some data goes in, you compress the data and you also decompress it and then you just compare the output with the input and you tweak the weights of this network so that the output resembles the input as close as possible. Just reconstruction, reconstruction loss. This narrowing and going back out is called an information bottleneck.  I'll use probably both. Typically, I call this latent space. And then the layer, the variables, the numbers in this layer are called latent variables. And so we can, we can then start playing around with this type of network where we have typically this inherent trade off, right? I could, if I make this network large enough in some sense or expressive enough, and I'm, there's also, there's all kinds of practical things that I'm sweeping under the rug here, right? I'm assuming that these neurons have some fixed precision. They're not infinitely, infinitely precise, because otherwise I could stuff everything as an important point. I could stuff everything into one neuron if I just, you know, take each sample of my input and code it into some set of numbers and have this single neuron just learn by heart all the samples by putting the representation as digits behind the comma, right? If you know about space filling curves, this is what it would be doing. But that requires that you have one number with infinite precision. And we don't have that. So when I talk about large enough, I just mean a large enough network, many, many neurons. I meant just showing a small example here. I can then try to make this information bottleneck a little bit smaller, constrain it, force it, force it to represent whatever I give as input in fewer and fewer numbers. Typically, there's a good middle point or all the way, all the way to, you know, maybe one single number in some cases, where nice properties could mean it's interpretable. I can use the same representation for several tasks interoperable. Different properties that you might think that you might call nice, which again depends on the on the task that you're considering. So here's a task that we considered. I give you a simple, very simple two qubit density matrix, which I generate according to some simple circuit.  So I give you the density matrix, you can extract one single number. And then after you've done that, I give you many samples to learn from. I will then ask you for that single number. And then based on that single number, you need to reconstruct as well as you can the density matrix that corresponded to that single number. Does anyone want to take a stab at what you would do for this particular case? Is the angle, what were you going to say? Quaternions, okay. Yeah. Also, that's not a bad representation for matrices. Anyone else who agrees with angle? I need many people. So in this case, that's exactly it. That's a little bit of a silly question. If I give you this matrix, if you get many of these matrices, of course, with fixed numbers, with alphas, some numbers, so these are literally floating point numbers, you could hopefully learn from that that there's this one generative factor, so it's called, which is the alpha, which is the angle alpha, right? So if you were to take many of such matrices, squeeze it through an autoencoder with one latent variable, we did that. And I don't have, I'm not going to show you that result here, but you, it does exactly that. It learns to just extract this angle, okay? That's not very interesting. So instead, we scramble that by scrambling with higher measure unitary operators. So that the numbers that you get in this matrix are now no longer recognizable as that angle. What do you think happens then on each of the individual ones? Yeah, so explicitly that's indeed, so we're not scrambling something that is still left in this representation. And if you figure out what that is, then you will have the answer. Yeah, for a given, for a given alpha, for a given angle for each shot, we will do different random unitaries. Yeah. Okay. So the answer to that is what I'm going to go through now. Of course, we had some expectations, we had some, maybe, you know, hopes or what would come out. The bottom line is we as humans are doing something useful already. That's, I can, I'll show you in a second. That's that's a good thing. So here's how, here's how that would work. The same model we had before, just to show you the whole pipeline. If we take this data set as input, the MNIST numbers, we would also compress that and then decompress it. You would get some representation in this middle space. In this case, it would be a two dimensional one that I'm showing here. And we have colored here, the different classes, the different numbers in the data set with different colors. So you can see in this case, if you didn't have those colors, this result is not particularly useful because it doesn't cluster, but it is intuitive because now if you do imagine if you didn't have the numbers like we do here, you can see some relations that, I mean, it's a little bit small perhaps here, but that some numbers that look alike are close together in these, in this space. And I just want to show you this so that you have an idea of what we're doing. So now what we're going to do is replace this data set of numbers with those density matrices. And then see what this later space will look like. Generate many of those scrambled as a function also of this alpha. So what comes out of this circuit would be a pure state. We turn it into a density matrix with alpha because later we will want to also include mixed states. And then embed this into a latent space of two dimensions for this particular representation. And what comes out is such a structure, not always the same, but something that looks quite ordered and structured. I'm showing you here also already some colors. But even without these colors, it's a very it's a compact shape. It seems to have some symmetry, right? Maybe two lines going through. So already if you do the simple auto encoder on such a simple data set, you get some structure. Is the is the pipeline clear? Yeah, great. So there's structure, but we don't have a handle on this. We would like to have a way of tuning or playing around with how with this information bottleneck, apart from just asking, maybe one number, two numbers, three numbers, also for a given set of two numbers or one number, we would want to have a handle on on the representation that it learns. And so the way of doing that is by what we did so far is go I'll come back later to what state of the art is now is to do a variational auto encoder. Have you seen variational auto encoders? Also a lot of nothing great. So in a variational auto encoder for each latent variable that I I think of doubling them. I now don't predict that latent variable, but I interpret this prediction as predicting the mean and standard deviation of some normal distribution. Okay, so for each input that goes in, I compress it with some encoder network and I interpret that middle layer as means and standard deviations of normal distributions. Okay, I'm just showing you one here. If I had two latent variables, two of the sets I'm showing you here, or in the previous slides, I would so for two, I would have four, I would have four numbers here, right? Two means and two sigmas. And I didn't tell you this, didn't show you this before, but in words that's exactly what I did here. Density matrix goes in. Some gets compressed down to some numbers and gets decompressed and some other density matrix comes out or something that we interpret again as a density matrix. And we're just doing the mean squared error between those two element wise. Minimizing that means that it tries to reconstruct as well as it can what goes in with what comes out, right? But because we have now this middle layer, this variational altering encoder, we also have this extra loss term which I will call now a regularization term. And what it does, forget about the beta for now, what it does is it tries to keep this middle layer, this distribution as close as it can to a normal, to a standard Gaussian distribution. So mean zero and standard deviation one. I'm not going to go into why this makes sense or how this leads to more interpretable or actually disentangled latent representations. This is a very standard thing that you do with variational alter encoders. And there's an extension of that which is this beta variational alter encoder. And this is the thing that we are going to tune. So this is going to put relevance on how strong do we want to have this representation be regularized. Again if beta is zero, we're back to an alter encoder. And if it's one or larger than one or larger than zero, we are trying to enforce some statistical independence. I'm not explaining this, but this is what it does. Some statistical independence on the different latent variables. So it tries to say if this latent variable changes property X in my data set, then the other one, if I have two latent variables, I had better try to change something different than whatever the first latent variable is changing. Go for it. That's right. So the question was indeed, if you have more latent variables, then what I'm trying to do with them is to have them all separately. Each of the latent variables of those pairs be uncorrelated standard distributions. Yeah, more questions. Sorry, yeah, in the back first. Yeah, so this is exactly. So your question is if the number of input layers is the number of elements in the density matrix, that's what we did. Yes. So I think what Manin talked about, for example, would be a different representation where from these density matrices you first measure two body reduced density matrices and then use those as input. This, what we do here, indeed, obviously will not scale to large qubit systems because you are feeding in the whole density matrix. But you can also do a representation learning of that first and feed that as input. There's many ways that we can try to reduce that. But for here, we're going to focus on this interpretability and not so much on scaling this to very large qubit systems. Yeah. Does that answer your question? Another question, yeah. If they are overparameterized. Yeah. What happens? So you're asking what happens if you have more latent variables than you have generative factors. Yeah. Ideally, what will happen is that they all become redundant. They also are being copies of each other and you see that, you detect that. In the worst case, if you don't regularize properly, they're going to learn, depending on your activation functions, but they might learn all some non-linear weird combinations of that input of the generative factor. And then that's a bad situation because you have difficulty keeping them all apart. Yeah. Anything else? Keep the questions coming. That's great. So, recap plus a small demonstration there. Density matrices scramble, density matrices go in. We, in this case, give the latent space, we give it an eight-dimensional latent space. And then we start tuning data. So, we train on the same data set several different models with different datas and then check. So, on the x axis here are the latent variables, actually the means, the mused latent variables, and the color, and y is actually the beta, the color code says, for each of those latent variables, how much did it contribute to this Kullbach-Leibler loss? And we've sorted them from left to right in higher-intensity. So, you see that for this data set with the scrambled row, it almost never, it's very faint, but it always never uses more than three latent variables. And more interestingly, there is a range in beta space, let's call it, which I see, okay, there's a range in beta space where it finds a one-dimension representation, which is what I asked you before, find me, represent these data, the density matrices with just one number, okay. So, let's take a look at one of them. Here 0.75, I think, was the right thing, the beta space, beta has shifted. And then we look at, so we're still plotting, it has eight latent variables, we're still plotting number one and number two, just to get a visualization. And clearly something happened, and that was also the right interpretation of this plot, namely something happened, okay. There's clearly some structure here that we can still exploit. So, let's investigate that a little bit more. Now, let's take that one latent number, number, the first one we called that 0, and plot it against what we have the data, so we know for each sample what the alpha was. Remember, this was a very small, but this was the circuit with alpha, and we see these two lines. So, there's, you know, there's clearly a symmetry that we did not get removed from the system, but that's okay. Does anyone, this is a question for the information theorist, does anyone recognize what such a curve as a function of this, you know, alpha would be? Yeah? So, what alpha does, so the answer that Benoit gave was entropy. What alpha does, of course, if alpha is 0, I never explained the circuit properly, apologies. If alpha is 0, I never do a rotation, and I just have two non-entangled qubits. If alpha is so that I do exactly a bit flip on the second one, then this circuit is exactly the circuit that generates a bell state, so I have a maximally entangled state. So, between here and pi, I go from a non-entangled state to a maximally entangled state. And then a measure for two qubits specifically that we already knew is, for example, the concurrence, which concurrence is not, you know, it's not easy to calculate per se. You have to first compute this matrix R, for which you have to do the square root of the density matrix. Sorry, I just realized you don't see my cursor on this screen. I've been pointing at all kinds of things. The density matrix R, which you first have to do a transformation with sigma y, take square roots, and then of this R, you compute the eigenvalues, and then it's this function, the max of this, with the largest eigenvalue minus the other ones. And there is also this, yeah, go for it. So, first we, okay, I'll come to that in a second. For your concurrence, actually it turns out it's the same thing as negativity for two qubits. Thank you. This is, I cannot help, this is the joke that a science teacher once told me that, how do you distinguish experimentalists from theorists? Is you give them a laser pointer? Exactly. You give them a laser pointer and the theorist does this to see if it works, and the experimentalist does that. I am more of a theorist, but I've learned not to do this anymore. So it's not easy to compute, but this curve, so we, how we found this is looking at, you know, we expected, because we are scrambling only locally, we expect that things like non-local information between two qubits, so things like entanglement entropy, would be preserved. So we intuitively already knew that we should be looking for entanglement properties. And then, you know, there's not that many that you compute for two qubits, and so here this is, this is the one that we knew to look for. Other questions? Okay. And so this curve, it's not exactly the same. You see there is some linear shift in the latent variable. This thing starts at zero symmetric, and so you have to, there's linear transformation that you have to do on that, but it's a monotone in both cases. So if you now, if we now take, you know, the value for a given representation for here, the value of the concurrence as a color, then, then this, oops, then, then, you know, you again see that there is some structures, the same color that I showed you in the very first plot where you have, with the autoencoder, you also see that, you know, moving towards larger z zero, you get more concurrence and at z zero in the middle, I don't have any labels here, it is also so. So this representation clearly is entanglement information. So if I told you, if this was something else, I would have been perhaps even more excited because it means that what we have been using as representation for two qubits as a single number should maybe not have been entanglement information. Maybe maybe this compression method, this quote-unquote AI, would have come up with some other number that we should have been looking at. Here at least it confirms that things like concurrence or negativity, which is the same for two qubits, works. And what I'm not showing you here is that this thing works also for density matrices for mixed states, which is the nice thing about concurrence. For the expert, concurrence works for two qubit mixed states, same as negativity, but there are cases for which negativity no longer works if you go to more than two qubits, three also works, but if you go to q-dits for example, then in those cases we don't have, I see someone maybe disagrees, the other way around, did I say the other way around? Okay. Yeah, concurrence is only for two qubits, that's correct, sorry, I missed that negativity works for others, but if I'm not mistaken, also if I go to larger systems, maybe more q-dits or q-bits coupled to q-bits, does negativity still work? There is a strong question, so ideally we would try, of course the next thing that we would do is we didn't do that yet, is try it and see what happens, what set of numbers, because if you have more qubits you can make more bipartitionings, would this method come up with as for representations? Just to show you already flashed it before, of course it's interesting to also now look at what happens at other points, can you, could we have seen this just from looking at those and the answer is yes, so here you see the representation, it comes up with, if you have three latent variables we're just showing two here, interesting, you know, if you have the colors, if you didn't have the colors this would not be any informative at all, but there is this point at 0.75 where you have these two latent variables and you have this very clear one-dimensional representation, again also separated from in color scale. We did try some things just to see if this two qubit thing works for subsystems of three qubits, this is just as a check, so we also know how to make three qubit entangled states, in this case, W-like entanglement for those not going into detail here, this is a W state and you can also parametrize those with some angle so that for a zero you again have three separable qubits and if you increase alpha you get more and more like a fully mixed maximally entangled state, sorry. And then with three qubits, like I said, you can now start thinking about the bottom two, let's call them A, B, C, how are B and C, what is the entanglement between group B and C with the first and all the other subsets and for that, of course, in this case maybe this should have been called negativity, but this also again works, so there you see the correlation of this latent variable we didn't take out, so these absolute values to take out that symmetry that you saw in both directions and they're nicely very linearly correlated again with concurrence here. Okay, so yeah, so yeah, yeah, they're asking can I tell you a bit more about this linear correlation, so I think go back to the two qubit case where now we talk about concurrence then if you make the same plot of this latent variable and plot it against concurrence if there is a linear relation between the two then they're clearly linearly correlated, so one is a linear rescaling of the other, right, so this is how we checked is is that latent variable indeed doing something like concurrence and if it's linear then yes, so I think you should turn this question around and it's, this is a confirmation that whatever Z is doing is linearly related to the concurrence, right, if this was not, if this was not a linear relation then Z was not concurrence, it would have been something else, does that make sense? I can, yeah, yeah, yeah, yeah, that's right, I cannot I cannot prove that it's exactly computing concurrence but whatever it's computing is linearly correlated with that, but you're right, it could, I don't, yeah you're right, it could, it's a coincidence perhaps but the interpretation is that concurrence therefore is probably that the number you should be computing as a human too to do this representation yeah, yeah, yeah, so this, yeah it is true, so that's why, I mean that's why we have eight here so for this four by four you would, or you would need eight if you want to fully capture the whole density matrix indeed and if I turned beta off entirely so to go to zero and without, and including the scrambling you're right you would need eight latent variables and you, you could then have one latent variable where like learning the elements of density matrix, right so this would be, I think this is what you mean and then you can see exactly that here what happens for example in these cases where you have a little bit more it, I think if I'm not mistaken but I should also look at Felix, where is Felix up there he did all that you will find that it starts learning exactly this redundant information so I think you're right if you remove this, if you remove the data and you're really just forcing it to do a perfect reconstruction then you get this result but as soon as you include data it, you introduce this bottleneck and you, you see that it starts finding other combinations does that answer your question oh that it learns those features yeah maybe there, yeah yeah I don't think we ever truly looked at all of these and see if for example those would map to other preserved information maybe we did not check we can, I'm happy to try yeah because then I would want to go to a few other very quick, quick statements or quick things so what, what for representation learning has emerged as as a useful thing to do nowadays a state of the art is to do contrastive learning contrastive learning doesn't have to be for representation learning per se but it turns out it gives you good representations useful ones to do other things with and so for contrastive learning the idea really which is capturing the same information the same statement as with the variational autoencoder is that you are trying to take inputs you're trying to map all of the inputs into a latent space but now I try a different way to make sure that if the inputs are similar they end up close in the latent space and they end up far away if they're dissimilar in that latent space and here contrastive learning does that explicitly so instead of saying I want to do that by trying to have uncorrelated gaussians here I'm really saying I'll explain this in a second I was really saying in that latent space I introduce some distance measure and I'm trying to then maximize the distance between dissimilar samples and minimize them between similar inputs and then of course I need to have a way of saying which inputs are similar or dissimilar and you do that by picking an example of your data set which we call the anchor and then compared to that I pick two other samples one I could pick from the same distribution that I you know called a positive sample one that I know is similar could be this picture but with noise it could be one that I know is supposed to be another type of dog and I also pick one that is dissimilar maybe because I'd pick I just take it from a different distribution or because it's a different animal right I use the same encoder to bring them into a latent space so each of these pictures is now represented as a feature vector this latent vector one for the positive sample for the anchor and for the negative sample and then I try to to make the maybe I should have flipped these but it depends on if this is a distance or not but I try to make the anchor and the negative sample as far apart as I can and the anchor and the positive sample as close as I can right this turns out to work really well and so what we're trying now is to do this exactly on these systems on circuits now not with two qubits but with six qubits or maybe more or less for these measurement induced phase transitions and I think maybe you've seen a little bit about that in previous talks but the intuitive idea I think here is very simple if I have a circuit where I don't do any measurements I likely at the end get some some state that has that is entangled has some measure of entanglement probably if I do this with random random unitaries random hard measures I get to some volume law entangled state and intuitively if I now start measuring everywhere in particular at the output then I get the product state and so I I get lower entanglement and somewhere in the middle between not measuring at all or measuring always there happens to be a transition between when the average circuit with measurements is area law or volume law if you're not familiar with that don't worry about it just saying how does the how does the entanglement scale with the number of qubits so we do this we do the same thing we pick a density matrix the negative one is with measurements and the other one is the same circuit but scrambled and encode that and very sorry very preliminary but also intuitive result is immediately what you find is it it starts distinguishing those two classes what I didn't tell you is that the measurements or happened with some probability that I'm not showing you here just because it's preliminary and intuitive hopefully but immediately the representation that you find in one dimension already gives you those that are very entangled versus those are area law entangled and I hope this is also intuitive there is then a way of doing explainability on these looking at individual pixels but what you see what you see here is a density matrix of six qubits and the dominant features that it looks at for determining is it area law or for volume law and I think you know I hope no one it's a it's a simple but important result but I hope no one disagrees that for volume law you probably have to look at many more entries then time in my time is up I think the last thing I wanted to quickly show you is because I cannot help not I have to talk a little bit about quantum games this is quantum games so I think my favorite playground for thinking about representation learning is in quantum control problems quantum error correction you all know hopefully this card call problem in reinforcement learning where you have a stick and you try to balance it right you can you can make a quantum version of that and then have a reinforcement learning agent try to control that system not going to explain exactly how that works with all the weak measurements and the control but here too you can think about how does an agent how does a reinforcement learning agent given for example the wave function or weak measurements what is the representation it uses for for doing that same thing with quantum error correction which can be on the surface code a Torah code or color code can be interpreted as a as a single player game that you can also play with a reinforcement learning agent and again there's a neural network in the brain of this agent and you can ask what is the representation there there's also a few other games that I would encourage you to check out um there are less you know those those are more entertainment type of games but still making an AI for chess is already a difficult problem we all know alpha zero now or mu zero even there's an extension of quantum of chess in which you have some set of quantum rules there's a whole there is some something called quantum game theory combinatorial quantum game theory so you can you can add you can embed this with a lot of mathematical rigor but the AI for storage games had better also find a representation for these states of the system and it's interesting for me at least to think about what would the what would that representation be so any further questions please feel free to find me here or reach out thank you for your attention thanks a lot for this great talk are there any more questions for the contrastive learning yeah what's kind of so I know there's the self-supervised contrastive learning where we augment the data by cropping or adding noise or rotating in order to not have labels yeah so my question is how like how little can we have of similar data because like there's a limit on how much we can augment the data before we kind of like crop out all the information or like transform it way too wrong and the other question is if it's maybe like the hundreds variation of the same data point is it possible for example to train a hundred autoencoder on density matrix and then we have hundred different embeddings maybe the autoencoders have different kernels or different just by randomly you know learning different embeddings and then now we can use these embeddings for contrastive learning yeah okay so okay two questions the first one I I think the first one really probably depends on the exact problem if I understood correctly like how many how low can you go in terms of number of samples for the for data points I don't think I have a good rule of thumb for this I think there's probably a little bit trial and error is that do I understand that correctly is it yeah I've like I've seen papers with like few tens to hundreds and I've seen papers with like hundred thousand different for each data point so I was like it's way too different yeah so I think I think a good approach that if you if you can get more data get more data I think one thing we clearly see is more is better even for these small systems but I I like for this particular case I don't remember exactly about 10 is not enough a million is probably more than you need but somewhere in between is a good point where you find stable representations so that was that was one for the second question there is there is more I think to add because a lot of it also for us for example here depends on the specific loss function so I I didn't spend the time on this but we we did the I'll keep it short we did the mean squared error element wise on the density matrices now there's more off-diagnose than there are diagonals so in this mean squared error we are already emphasizing that it should be looking at the day off-diagnose more just from the loss function for reconstruction so with that choice we're already biasing it a little bit towards looking at off-diagnose right and so which we what we're trying what we're also trying to investigate now is what happens if we already do different input representations so I'll change the representation that we give it instead of the density matrix do what marine did the two body density matrices or some other set of POVM measurements right and I think this is what you're getting to a little bit is that then if you because that already means we have a different representation that we're feeding it feeding this this autoencoder right and so I think there's definitely an interesting idea to train many different autoencoders and use those as inputs to to the representation learning scheme yeah thank you there any more questions you can also shout and I can repeat it but uh yeah yeah but if in our case for the in the contrastive learning the negative samples were those with measurements no no I think no we're just trying to we're trying to we just say some samples like is it similar to the anchor or not and the anchor did not have the measurements and the other one did have the measurements and then we're not telling it explicitly that you know it's volume lower area law even though very likely with measurements you get to the area law but but yeah there there's no yeah I mean it's a yeah it's a very simple step I think still but if this didn't work then something was wrong are there any more questions that note I also wanted to ask so so regarding the question just now yeah um if you want to learn something that goes beyond entanglement if you're thinking about that so so is there maybe a way that you would say okay anchor and positive sample you already destroy entanglement in a specific way and maybe then you learn something else that is stored in the circuit I'm not sure I fully understand you're you're asking if if it might learn something that is not related to area lower volume law exactly and if you maybe have to modify the setup such that you're already between the anchor and the positive sample destroy the entanglement such that it does not learn that yeah yeah I think I mean we're just starting that so that excellent suggestion that's yeah we'll try we'll talk more yeah that's good yeah well then let's think over it again


Hey everyone, Dylan Schumacher, Citadel Defense. I am hosting the modern samurai project in May for a pistol course. So he's going to come down, he's going to teach a one-day appendix class and then a two-day red dot class. So it's Friday, Saturday, Sunday. The dates on that are the last weekend of May. So May 27th, 28th, and 29th. And we're going to be doing that at Almond's Gun Shop, which is just south of the Twin Cities area. So if you live in the Midwest and you want to come on out for a couple days of pistol class, I'm going to be there because I'm hosting obviously. So I'm excited to learn and hopefully learn how to shoot my pistol better and faster and more accurately and all that good stuff.  We'd love to have you. I probably expect the class to sell out because all of that guy's classes sell out. I do not know Scott at all. I've never met him personally at all, but was able to reach out and was able to host this class. So excited to have it out, excited to shoot it. And if you're interested, hope to see you there. Do brave deeds and endure.


us on behalf of the energy program here as well as the Sumitro Chair for Southeast Asia Studies. I'd like to welcome you to this, which is the inaugural session of the U.S.-Australia Speaker Series. This is a series we're really pleased to present. It will focus on a whole host of issues that are really important to the deep and abiding and growing relationship between U.S. and Australia, including issues of investment, trade, security and other issues. Throughout the series, we hope to focus on a wide range of perspectives coming from the private sector, the government, civil society, and we know that there's a great interest in this topic throughout Washington in addition to our viewers around the world, so we're really excited and pleased to be able to kick off this series. This speaker series is made possible through a partnership between CSIS and BHP Billiton. As many of you know, one of the world's largest global resource companies. We're very pleased and privileged today to have Andrew McKenzie, the CEO of BHP Billiton here to talk about some of his views on a series and kick off this series in a proper fashion. Andrew, thanks so much for being here. I'm going to hand it over to Frank Ferrestro, who is the Senior Vice President here and Slussinger Chair for Energy and Geopolitics at CSIS. Thanks, sir. I think I'm okay. Thank you. Okay. Let me add my welcome to Sarah's as a Senior VP here. It's our pleasure to welcome Andrew. I had the pleasure of actually seeing Andrew down in Houston during Sarah Week and found both his remarks insightful, but he's also the perfect person to kick off this US-Australia speaker series because he not only has the company, and I think the Wall Street Journal has described BHP Billiton as the mining titan, but they're actually more than that. On a personal level, the stuff that he has done in terms of organizing this, it's really a more diversified conglomerate now. They do oil, natural gas, coal, uranium, metals and materials that are supplied for both infrastructure and for renewable energy. As a mining company, they may be on the forefront of doing work on CCS for climate change. So this whole notion, especially in this town, when we look for energy companies that have the full portfolio and certainly look at energy from every aspect, I would say that BHP Billiton certainly equals that description. They are all of the above company. Andrew himself, and it's a pleasure to have him here as our keynote speaker, but Andrew is a geologist and a geochemist, so near and dear to my heart. He hosts his PhD in chemistry from the University of Bristol. He's published over 50 research papers as a scientist, which is unusual for a CEO. As a businessman, he joined BP's research division in 1983. He moved his way up into finance and capital markets and later into petrochemicals. In 2004, Dr. Mackenzie joined Rio Tinto as chief executive of the Industrial Minerals Group. In 2007, he joined BHP as chief executive of nonferrous. And in May of last year, he was selected as the CEO of BHP Billiton. He speaks five languages, and in his spare time, he currently serves as the chair of the B20. And we're going to ask a little bit about that, and one of the reasons he's in Washington is yesterday he co-chaired the second meeting of the Business 20 Roundtable. We've asked Andrew to offer some preparatory marks to start us off, and then we're going to settle in for a more relaxed Q&A. And then we want to open it up to questions from the audience, and that's why we're all glad you've come. So ladies and gentlemen, please join me in welcoming Andrew Billiton. Andrew Mackenzie. Welcome. Thank you, Frank. Yeah, as Frank said, I did give a speech earlier in the week, and I'm going to cover some of the similar themes at which I covered in a perhaps more detailed way with energy specialists down at CERA. But Washington plays a key role. It shapes global policy and influences the world's economic development. So I'm absolutely delighted to be here to launch this US-Australian speaker series with CIS, which we consider a preeminent thought leader on geopolitical trends important to both nations, I would say, important to the world. As Frank said, we are the world's largest diversified resources company. Our portfolio, as he covered, is special. It spans just to repeat steel-making materials, metals generally, energy, and potash for fertilizing. We're the only company that supplies all of oil, gas, coal, and uranium, as well as the metals that are critical for energy infrastructure and renewables. I like to think that makes us semi-objective in some of our choices about how the energy portfolio will evolve, because many, of course, have called for all of the above approach to energy. In fact, that was something that I think President Obama mentioned in one of his more recent speeches. And our uniquely diversified portfolio delivers this. It gives us a powerful perspective on the influence of geology, technology, and trade on supply, and how demand changes when countries develop as their people secure better housing, better transport, and better food. And today there's no better example of this than China. When Deng Xiaoping launched his market-based reforms over 30 years ago now, he and envisaged the industrialized and urbanized society that we see today in China. And certainly myself personally and many members of our team are regular visitors to China as our most important customer. Takes about 30% of our revenue. And this has caused investment-driven growth in demand for iron ore and metallurgical coal, which is required for steel, and that's the steel that they needed to build factories, apartment blocks, and infrastructure. And then coal and natural gas, increasingly important as they generate electricity and consume more energy as they move towards a consumer society. And for us, very importantly, copper, which really has one use primarily and that's to transport electricity. So in the process, certainly in the past 20 years as Deng Xiaoping's reforms got going, this has lifted more than 650 million people in China alone out of poverty. And that's more than the population of Latin America, and most of you can do the math and know that's double the population here in the US. Globally, what's happened in the last 20 years is more than a billion people have been lifted out of poverty, but clearly two-thirds of them in China alone, which is extraordinary progress and progress that we at BHP Building have been really privileged to support. Because the commodities that we supply and questionably are critical as building blocks for modern societies. Energy is crucial though, at all stages of economic development. And as developed economies like this one become more efficient, their demand is plateauing, in some cases even reversing. So the real area of growth in energy demand, and therefore for which supply is being increased, is in emerging economies. So people gain access to electricity and living standards improve as countries modernize. It's kind of interesting to reflect that more than 100 years, way back in the past, since Edison built the first power station, a fifth of the world's population still lacked access to modern reliable energy. We had a lot of talk about switching between coal and gas and renewables and so on. But we still have over 700 million people in the world relying on burning wood, or charcoal or coal to, wood or charcoal to keep their homes. And a lot of their time is actually just spent collecting that. But thankfully this is changing. So in the next 20 years we expect 1.7 billion people to gain access to electricity for the very first time. A large percentage of the population in China now and probably many of the other developing East Asian economies are already connected to the grid. And this is unquestionably heralded in the development of their industry. It's created a rise in incomes and further increased the demand for energy. As more people can buy consumer goods such as cars and fridges. The growth of the resources industry is fundamentally tied to the alleviation of poverty, abject poverty, as well as to the further successful development of emerging economies. So demand for energy is likely to increase. We think by 30% in the next 20 years, my co-speaker when I was done at CERA, John Watson from Chevron said it was 40%. So it's a big deal and two thirds of this new demand is going to come from Asia in about half from China and India. But the fastest growth will be in Africa. And the way these regions meet their energy needs will significantly influence the commodity demand amounts and pattern, as well as the health and stability of the global economy. In practice, every nation will choose a different mix. And it's very important not to generalize, for example, the experiences here in the US, because each nation has to balance affordability, security of supply, and public preferences to fill their demand. And by the way, you see similar variations even between US states. So in the next few decades, we believe, however, that fossil fuels will remain central to the energy mix. Their affordability and the scale of existing infrastructure make them extremely hard to replace. So while renewables may be a rapidly growing source of energy, which we absolutely encourage as we strive to reduce carbon, we will only really be able to rely on them when a large scale and cost effective storage of energy is truly available. Nuclear, it does provide a low carbon base load. And as you've heard it as a uranium producer, we are keen to encourage that as well. But post Fukushima, it does face strong public resistance in many countries, which is likely to slow or even reverse its growth for some time, maybe not forever, because many countries still have quite ambitious nuclear programs on their books, just kind of waiting to see how public opinion evolves. So as we look to 2030, we anticipate that 70%, only down from 80% of the world's energy will come from oil, gas, and coal. Gas, of course, is expected to see the strongest growth through its wider use in power and transportation. But I would say, as I said, Sarah, that I don't believe the shale gas revolution that you've seen here is unlikely to go global quickly. Despite what many have claimed, we're unlikely to see gas replace coal elsewhere, anything like at the scale and pace that you've seen here in the US. Costs and security of supply that mean most places will favor the use of their local resources to meet their energy requirements. And the fastest growing Asian economies have much easier access to large coal reserves than they have to cheap gas. Cost of generating electricity today from gas is more than double, often a lot more than that, than the cost of generating it from coal. And so coal will remain the region's primary source of affordable energy for some time, and the basis of its energy security. Every form of energy relies on the resources that we extract from the earth, and whether that's oil, gas, coal, uranium, or indeed the fertilizers that you need to promote the growth of biofuels and biomass, or even the copper, a very important business for us that's used in wind and hydro turbines or to connect solar panels. A renewable future is extremely good for that business, since it uses about seven times as much copper on average relative to the traditional fossil fuel industries. That's where our, if you like, our objectiveness comes, I think, in from. So, but however, as our understanding of the earth crust improves, and it does, I'll talk in a moment about some of the big advances in my own base science of geology, we are getting better at securing the resources for the future and can remain extremely optimistic about that. Of course, in some commodities we do face more complex geology, fuel decline, or even lower grades. But history shows we do substitute, we do innovate, and we do improve efficiency and overcome and meet those challenges. So take our experience in oil and gas. The era of easy oil came to the end in the 70s, you know, partly exaggerated by the Arab actions at that time, but fortunately that was the time when an understanding of plate tectonics emerged. And for those of you who followed that science, that's what actually got me hooked on geology as a school student and why I chose to study it at university. I actually had the privilege later on in my research career in working with one of the, if you like, the co-identifiers, I don't do the you, of plate tectonics in some of my research, which was very nice. But carrying on, in the 80s, advances in drilling allowed us to move into deeper water. And in the 80s and 90s, 3D seismic technology, which always gets the credit, but also geochemistry, significantly improved exploration success. And over the last decade, everybody's heard how the combination of pre-existing skills and horizontal drilling, and just as an aside, the first big long horizontal well was drilled at Witchfarn in the south coast of England while I was looking after technology at BP. And I remember those days in 1995 when we were trying to drill two miles horizontally under Pool Harbor so we could protect an area of natural beauty. Well, that combined with hydraulic fracturing that's been around since the 40s has actually enabled the shale gas revolution to occur. The energy historian and chair, if you like, of Sarah and actually a good friend of mine, Dan Yergin has noted that there have been at least five occasions when the world thought it would run out of oil. But in practice, continuous innovation has meant that world oil reserves have continued to keep pace with demand. And they've grown by around 30 billion barrels a year. So what's true for oil and gas, and that story often gets rehearsed, is actually true for almost every other commodity that we're in. So come back to copper, power lines, wind farms, and the devices that increasingly turn waste heap more efficiently into energy rely on copper. Copper is also an energy efficiency story. It's the best conducting metal you have. The quicker you can get your energy in the form of electrons in a copper wire, the more efficient you will be. So it's critical. But despite average copper grades falling from 4% to 1%, over the last 100 years, production has increased 16 fold. So as I like to say on many occasions, energy security is a matter of governance, not geology. What's above ground usually matters a lot more than what's below. And that's why right now, close to 90% of investment in resources, old and new, is still made in more developed countries, which have more of the correct governance to allow those developments and investments to occur. So at BHP Billiton, we firmly believe that open market society and free trade in goods and services and ideas create the right conditions for development. Shareholders, host nations, and consumers all benefit from the competition it follows. Between countries for investment and between companies for the privilege to invest. And if this occurs in more places, supply will become more diversified, and the pace of innovation will quicken and quicken. As it is today, as we connect more and more, the big brain of mankind, of 7 billion and increasing people working together, hopefully trading goods, services, and ideas. Asia's continued development does depend, as you can imagine from my remarks, on its access to affordable energy and resources with half of the world's population in the region and global growth depending on its progress, much as its stake. And the debate here in the US regarding energy exports, which is all over the newspapers again today, I believe is very important. I kind of don't want to count my chickens, but my sense is that even before some of the new spice added by what's happening in Ukraine, the argument has more or less been one, that exports of gas is the right thing to do. But still, I hear some have argued and continue to argue that the US should not export gas, and that exports will lead to much higher prices for domestic consumers. Curiously to us, they use the difference between Australian and US gas prices, in some case, to substantiate their claims. Well, I can tell you as a very large consumer of gas, the largest consumer of gas in Western Australia, through all of our operations here, as well as being a major gas producer, perhaps what's not known is that we are a very major oil and gas company worldwide. You know, we're the biggest foreign investor, a very large investor on any scale in US shale, and we have a huge operation in the Gulf of Mexico, but we also have big exposures to LNG in Australia. Well, that kind of perspective means that we know the price difference due to the, is not down to exports. It's simply due to the higher costs of offshore production in Australia compared to shale costs in the United States, not exports. So I would put it to you, an extremely open market and one that we stand very strongly alongside our government with has enabled the development of Australia's reserves. It's made it one of the world's leading gas exporters and bolster their own economy. Exports I put to you can benefit both the US and its partners, and US customers will continue to enjoy, however, much lower gas prices in the nations that choose to import their gas. And the country will gain a lot more jobs at home. Frankly, the transportation costs and financing constraints and global competition will limit the volume of US exports. However, these exports will help US allies diversify their supply and, particularly important at this time, send a strong signal to the world on the importance of open markets and geopolitical stability. I believe, we believe very strongly that successful transition of the world's most populous nations into vibrant consumer economies both relies on and is crucial to geopolitical stability. US leadership therefore can encourage the development of a global market that supports this process improves the resilience of supply and advances free trade policy around the world. And over the long term, open markets will also help countries reduce their emissions, and very importantly, next part of my talk, adapt to climate change. Diversifying the supply of resources and making technology more widely available will make it easier to switch fuels and become more efficient, but more action is needed. We have to acknowledge, particularly as producers of large amounts of fossil fuels, that unless we control emissions, the most likely energy mix that I've pointed to will have negative consequences for the broader environment. There's a lot of disputes about it, and many of those disputes center on how accurate the forward forecasts of temperature changes or conditions in the oceans. Those predictions are incredibly fraught. We've just spent a lot of time running reservoir models. The range of these sorts of things or climate models, as we know, just looking six days forward at a weather forecast, are tough. And using discrepancies around these sort of things that I find is not entirely helpful to the debate of what's really going on with the climate. As a geologist, I like to go back to the geological record and look what's going on there. And I'm not gonna bore you with all the scientific details, but I am 100% convinced, when you look at it, that substantial variation in CO2 and other greenhouse gases does result in temperature changes, which has potential and generally not good implications for life on earth. Warming of the climate is real. This epidot sort of warming is unquestionably down to human influence and physical impacts are now unavoidable. But the solutions that we must choose must address both the issues of energy poverty, I've already spoken to you about, and climate change. You can't solve one without the other. Almost certainly if you do that, then either objective is destined to fail because the world will continue to rely on fossil fuels over the longer term. Their continued growth in supply is vital and is critical to drive the economic growth I've spoken about and probably even more important, the huge environmental benefit which will come from huge reductions in abject poverty. But also, we need it to increase all our living standards. As an industry, we have to work with government and other shareholders to pursue long-term solutions to reduce emissions that actually have a lasting impact. As Jim Yong Kim, president of the World Bank said recently, we have to focus on the good that we can do now. We should be confident about the future. And in relation to this, while resources security offers so much opportunity for many, there still is out there the risk that corruption, real and perceived can stifle this kind of opportunity. So for us too, revenue transparency is important. BHP Billiton was a founding member of the extractive, still is by the way, extractive industries transparency initiative. And we are pleased that transparency and international recently recognized our efforts and ranked us third in transparency across companies around the world. Transparency, we would say unquestionably, is good for business. It's good for shareholders. It's good for communities and the communities in which we operate. So with innovation, good governance and open markets, we can supply the resources the world needs, deliver returns to our owners, address energy poverty and improve the world's ability to solve complex global issues like climate change. Clearly, I feel the circle can be squared, resource security for the planet and its people compatible with environmental responsibility is achievable. And that's a prize worth having. Thank you. Excellent, Andrew. Not surprisingly, thank you so much for a content rich presentation. There's a number of avenues we can go down. And for the day traders in the room, I think they walk away with copper futures as a primary takeaway. I want to start with your role as CEO. So you've been in the CEO role now for a little less than a year. You're credited with focusing the company back on the four kind of core areas, but still needing to maintain a global strategy. And you've got a long history of bringing projects in like on time and under budget, which is so critical. How do you select with the diversity, with the changing landscape going on in the world and rising costs, how do you select where you want to put your assets and the finances to back them up? Well, you talk about the four pillars that we concentrate on. I mean, our company, it was an old adage from management advice back in the 80s that you should stick to your knitting. And in our case, our knitting is petroleum engineering, mining engineering and geology. And we need to find things where those skills will give us the maximum return to our shareholder. We've been very conscious that the patterns of demand are shifting. The bulk of our profitability in the recent past has come from making things that get turned into steel by others, but we see that shifting, particularly driven by China, as it kind of starts to slow its infrastructure building phase and moves so far so good into something based more on consumption. And that's why I spent more of my talking on energy because as we go forward, the bulk of our investments are likely to be concentrated on increasing our ability to supply energy, particularly to Asia. But very long-term, we do think that a hopefully stabilizing world population will want to eat better and will want to run its agriculture better and be more efficient. And that will lead us to use opportunities on our skillset to work on fertilizers and things like potash. But I have to say, you address the day traders, I address our investors, they know full well that although we create the options, the selection of projects that go forward are exclusively based on a competition based on returns and the net present value that we can add to create the highest level portfolio that we can. And some of the things you've done that you referred to, the focus on the four pillars, has already led, in my view, to big savings and costs. We've announced that we've cut our unit cost by $5.5 billion in a two-year period as a result of that focus and a big increase in capital efficiency. So even though we're cutting our capital by about 25%, by promoting higher returns, we believe that we can actually add as much volume or value from, let's say, about $16 or $15 billion of capital that previously took over 20. Excellent. So one of the primary reasons that we put together this speaker series is to be able to draw the fact that Australia and the US have different perspectives on the world. And Ernie tells us all the time that from the Washington perspective, we actually really need to look at regionally what's going on. From the window that you see on China from Australia, how do you view developing Asia? What's changed over the last five years? Where's it going? I mean, part of it, just to very quickly add, is that they are moving towards a consumption-driven economy. And the sense that I have is that there's strong alignment from top to bottom in the country to do that. I'm very fortunate to serve on a group of 13 CEOs, foreign CEOs who advise Li Keqiang, the prime minister of China, and the way he lays things out. And the way that things happen is actually quite inspiring, to be honest. But what's perhaps more encouraging to us is that when we talk to the CEOs of state-owned enterprises who are major customers in the steel mills and the copper mills of China, or at high level, in my case, or at lower level, we find real strong alignment on this message. And they are now trying to use things like credit controls and so on to increase the efficiency of their industry. And they are desperately concerned about the environment and how they can restructure and improve the environment around things. And it's gonna be tough, and it's gonna be hard. But I think we have to be a little bit mindful of some of the lessons of history. I mean, I didn't take the job in the end, but I remember flying in for a job interview in 1979 in LA. And I can tell you, flying into LA in 79 is no different than being in Beijing today. Beijing today, exactly. Well, you've opened the door on the climate change argument.  But I love the fact that from a mining perspective and a geological perspective, you look at things like whether it's carbon capture and sequestration, or developing new resources to get a more sustainable future. But in your own mind, what are the responsibilities of companies to both make a profit, but also help the next generation?  And that doesn't matter whether you live in China or you live in West Virginia. In both places, they choose 95% of their generation to be made of coal. So it's very important that we understand that local resources will be critical. I don't think the oil and, sorry, the energy industry has been well-served by trying to demonize one version of fossil fuel energy versus the others. You know, and so whilst I do see in time the trend will be moving more towards gas, if we're gonna do everything I said long-term, it's gonna require a lot of coal. But the good news or challenging news is, as I say, with so much electricity and power dependent on fossil fuels, there's an even greater obligation on the industry to do something directly about what they might do. And there's two areas. I mean, one of them is clearly dealing with the emissions in our own operations. And we've reduced our intensity by 16%. We've invested $430 million in that process over the last five years. But I think, and that's a very full-sale 100% accountability, non-negotiable. Then we move into the 90% of the emissions that to some extent we affect by providing fossil fuels. And therefore it's a much more shared responsibility. But where we have the skills, we should be lending them more clearly. And therefore I think it's important, given that the big challenge, in the same way that there's a huge challenge to store electricity, to make renewables more viable, there's a huge challenge as to how you would have bulk storage of carbon, if we're going to make carbon capture and storage work. There's lots of good ideas there, and they're based in my core science geology. I was chief reservoir engineer at BP. And we just should lend our thinking about that. Because if we can actually make real progress there and create large-scale opportunities to capture carbon underneath major power stations, it might mean that fossil fuels not only can alleviate poverty and do things in an environmentally responsible way. Because I know the resources are there for another 100 or 200 years, they could be much longer in terms of their use of a fuel source. And we should work as one industry to do that. Because even you have to take a bit more carbon out for a unit of energy out of coal burning than you do gas. They're all producing carbon. And if we get a solution, it makes gas even better. So I will draw you back into the policy debate since we are in Washington now. So this whole notion of being able to use multiple fuels and not pick the flavor of the day so that we discount coal or put it aside. My first thought was that going to see Secretary Moniz or Senator Manchin would be high on the list of things to do when you talk about coal. And when you look at poverty around the world and whether it's for cooking or basic energy that the role of coal needs to stay but needs to be improved, how do you sell that policy message to policymakers like don't move so like we have from nuclear, don't move away from that and then neglect it, lose the capability to try to bring that fuel back? Well, I think you start from the basis that we accept the mainstream science and we want to do something about the creation of energy that makes its impact, if you like, less negative towards the general environment. And then you say, but there is no one solution. You need a raft of measures. It's great that we have a number of choices of fuels that we can select from as we see which makes the more progress in squaring the circle of poverty, alleviation and environmental responsibility. But then in addition to that, you obviously need a range of technologies. I've spoken about the ones that I think the resources industry can make the best contribution to but there's others where other industries have to contribute and then you need to think about a range of policy measures and those policy measures, again, there isn't one solution and it's particularly hard to think of one solution when we're not going to get a global solution quickly. And part of it can be a little bit of government funding, R&D or whatever, and we have some direct action in Australia. Part of it can be regulation but I think it's hard to avoid the sound form of appropriate carbon pricing policy or carbon pricing mechanism is in there because that then will drive the incentives to make the right choices of fuels and to make the right choices of technology and to cause them to be developed in a way that would make me much more excited about progress and I'd wrap all around of that free trade and in good services and ideas that creates the flow of possibility and means it will move forward more quickly as well as growing quicker economically. Excellent. So we want to give the opportunity for you all to ask questions too. I have two more that I need to have addressed immediately and what is the resource, the super cycle and you talked a little bit about this in Houston. Can you explain what's going on and how we view the world differently now? Yeah, the super cycle was a once-off and it was a once-off caused by the massive acceleration of China as a result of Deng Xiaoping's reforms. It didn't really take off in terms of demand until the late 90s and then really accelerated through the 90s. The resources industry was not well prepared for it. The mining industry was a bit better prepared because it saw the steel demand coming through and so it moved a little quicker. But right until about 2003, 2004 all companies were still forecasting $20 oil. That's how caught out they were and we were probably not much better than the mining side in our price forecast. That happened because you saw particularly in steel. The steel growth in China through that phase was at some points more than 20% per annum and the industry, because China didn't actually have enough of its own domestic production had not fully built the infrastructure and developed the mines and the additional oil fields to cope with that demand. So the next thing that happened is that everybody ran around trying to build things very quickly, often quite inefficiently. Money was definitely wasted. Not all companies perform well, despite very high prices on behalf of their shareholders. But now we're in a different phase. China is moving through to more stable growth. It's moving to more of a consumption phase. It's going to grow around 6%, 7%, 8% for a while and the metals intensity of that growth is going to be much lower. It's going to be more energy based. We've built all the infrastructure now and so it's capable of being expanded rather than in big chunks but in small increments. And so we can look to, with reasonable optimism, that supply will be able to be adjusted to demand without these kind of dislocations. And as a consequence, we're looking at a period of probably flat to falling prices. So companies like us have to become more efficient while we're not going to hold on to our margins. We've been so far successful despite flat to falling prices, our return on capital is rising. And I think that's an agenda the whole industry will share as we go forward. I don't think when you look beyond China, there's another China waiting to happen. I'm a bit more optimistic than some about other Asia and so on and sometimes we're very hard on India which is still a long way behind. It's just not gonna happen the way that China happened and so it's lower prices, more on efficiency. But I think in doing that, people will perhaps become a little bit more sanguine about the resources picture because the high prices and their fall off created a little bit of a strange response. So our investors were worried about super abundance and the fact that they weren't making enough money and everybody else worried about everything running out. Whereas in fact, now we're more in the middle and we have a sense that there is enough resources to go around and we can actually use it to make good choices. Now it's timing and deliverability. I can't let you escape without talking about the B20, the business 20, which is one of the reasons that you're in Washington. So talk about your role in the business 20. Yeah, well, I mean, those of you who know about G20, I mean, there's a B20, actually there's an alphabet, soup 20, but I have C20, L20, F20 and so on. I've lost touch but I knew about B20 and B20 have chosen as their way of putting their input to the G20 deliberations. They've chosen sort of four themes that they're gonna run global task forces of business leaders all chaired by Australian CEOs. And I've been given the privilege of looking after trade just so you're interested. The other three are finance of course, because it's such a subject of G20 but also infrastructure and human capital. You've seen the announcement from the finance ministers which talked about trying to get more than an additional 2% of annual growth above what is a currently forecast. And the reason they come to that is everyone is very worried about zero job growth. And indeed, the things I've talked about about the progress and productivity we have in our company is perfectly possible we can get the growth that is forecast without actually adding much to employment. So to get employment, you have to add a lot more. Part of it is upskilling certain jobs and compensating for the digitization and automation of lower skilled jobs. We think trade can make a big difference. Its track record is strong. There has been good progress since 2008 and the moratorium on if you like tariff restrictions and protectionism seems to have held but the volume and the growth in world trade has slowed over the recent past. Maybe not in the emerging economies as much as the developed economies. So I'm more a bit more optimistic that better things are happening. But we believe if we have a few measures there is a possibility by liberalizing trade as we say of adding another Germany to the world which is another 50 to 100 million jobs and possibly as much as $5 trillion of aggregate GDP. And we've picked on three things that we want to work on. It's really attacking non-tariff barriers to trade which is how hard it is to get through customs and so on and so forth. One, and I said this in my speech, spending a lot more time and see what it takes to create a lot more trade and services. It's more than 50% of world GDP but it's only about 10 to 20%. We don't have great data on global trade. And the third area is while we like some of the multilateral or bilateral agreements that are happening, clearly keen to see the TPP happen and the T-TIP happen as well. Our new government in Australia is doing a lot of bilaterals. They're on the whole boot but the problem is if you've already got a trading relationship with somebody who has then pulled into one of those agreements and you're not in it, it can actually create complexity. And so we'd like to see some way in which we can come down to some simple rules that make sure that those bilateral multilateral agreements ultimately coalesce and will raise the standards and the possibility of something like WTO. But G20 is not WTO. It's not got any great executive power. So what we have to do is to take some of those things and break them down to individual actions that each country in G20 can commit to, even just one in a matrix of three by 20 that they say they're gonna do something about before Turkey and so that we can see measurable progress. Excellent. Okay, so for questions from the audience, we actually have a few rules, ground rules here. One is that you identify yourself and your affiliation, probably wait for a microphone since the group is a little bit larger and then to the extent you can, pose your question in the form of a question and that would be really helpful. So we're gonna start over here and I'll work my way back. Thank you. Jeff Hopkins with the Center for Climate and Energy Solutions. Given your, I guess, entry into all areas of energy, I was wondering, kind of a technological question, do you have an opinion on carbon capture and storage combined with enhanced oil recovery? Any thoughts on that? Yeah, I mean, I think it's a great way of proving it because basically you get the oil credits to pay for some of the development of the costs of the storage. But there is no way that you're gonna get the volume of storage through using EOR. And equally, I don't think you're gonna find a practical way of storing if you depend on conventional oil and gas reservoirs, even if they're only filled with water. You have to find a way that any old rock underneath a power station can actually be a significant sink for CO2. And there are a lot of ideas around that. It's how CO2 is very corrosive. It's the problem of pumping it, but it also means it actually etches the rock and so it actually can create additional space. It can create ways that you can precipitate it as carbonate and that's where we think, we've pledged quite a bit of money to get that research going. It's not really going, but ultimately it's great to prove things through EOR, but the long run solution has to work under a Chinese power station. Sir. Andrew, thanks very much. Fantastic comments. One of the things I wanted to bring it back to was obviously one of the things we're trying to do here is talk a little bit about the importance of the US-Australia relationship as well and you gave some really helpful perspective on the issue of LNG exports and sort of Australia's perspective. I just wondered if you could talk a little bit more about what you see as being shared values or shared perspective from the two countries that is sort of an interesting thing for you as BHP hugely important company in Australia, a huge investor here in the United States, global reach, what are some of those shared values that we could be talking about? Yeah.  The oil and gas part of BHP will have got started because of joint ventures between us and Exxon now Exxon mobile in the bar straight. And so we've been strongly linked. I mean, there are obviously very important differences between the two countries. In many ways, the resource endowment of Australia is comparable, perhaps even better than the United States, but the United States has great resources as we know, but actually more than 10 times the population. So the bulk of the US resources will be used in the US, even if you agree to export everything, which I think you should by the way, because I'm obviously a free trader now. And that's the way that Australia handles things, but obviously with such a small population, the vast bulk of its resources are exported. But that export flow, whether it's gas to Japan or it's still making materials to China and Korea, it's absolutely critical for geopolitical stability in the circum-Pacific. And many of the allies of Australia and the US are dependent on those flow of commodities out of Australia, much less so than they are in the US, but that also will build manufacturing in those places. I think we have a lot to do together. Australia is a small nation. Sometimes it's talked about it, but not being a member of G20 because of its relatively small economy. But I think the resource, if you look at it as a resource economy, absolutely needs to be in G20 and needs to be a fundamental player in particularly in APEC, which to some extent was kicked off by an Australian Paul Keating. And I think we should continue to build on that. And obviously in so many walks of life, Australia, and the US have been shoulder to shoulder, both in peace and in war. A little wide here. Hi, thanks for the comments. Jeff Epping with Energy Cell, we'll see. In China, well, in the US, gas shales have obviously been very successful. China has a good endowment for gas shales. How do you see that playing out in the next couple of decades? Do you think they'll be successful? That'll be a significant portion of their energy market? I think I would just sign a big note of caution, as I said in my speech about the shale gas revolution, if you could call it then, here in the US going global quickly. And I make that point on a number of levels. I think this is new technology. The geological habitat of those hydrocarbons is not well understood. And until people have decent well tests, and they can show me, sorry, technical term here, the decline curves and the likely recovery from individual wells, I remain a little bit skeptical at just looking at an in-place estimate and applying an average recovery. So first of all, we need to get that. And I would say that to any nation who thinks they've got a shale gas endowment. Don't hype it, but do go and drill it and do proper tests, and then we can have a proper debate about the next thing is, the reason it's gone so well in the US is not just because it's an endowment and it's got access to technology, is that only for a very brief period at the back end of the last decade was there any question markers to whether the US would be sufficient in low-cost gas, self-sufficient. So it has a enormous industry based on gas, the distribution of it, chemical industry raising power from it, that is all up and firing. So as gas comes up, you can quickly back out coal and generate more gas. Most countries in the world haven't got that. You know, their history is using coal or they're less developed. So they don't have a distribution system. They don't have lots of gas for our power stations waiting to be filled up. And a gas-based industry. And of course they don't have, they haven't evolved the regulatory way of doing things and the laws that promote its development. And so I think when you talk about shale gas, particularly in terms of geopolitics, I would aim off quite a bit, even in China for quite a few years. And you have to think as well about the remaining power balance that exists within conventional gas. We are again, sorry, I'm not totally wanting to be a champion for coal, but the availability of conventional gas is quite restricted in the world and more restricted than the availability in oil. As many of you know here, if gas-pec existed, absent shale gas, it would be a much more concentrated set of countries than OPEC. Just staying on that topic because I think that's really important. So we've gone almost whipsawed from the peak oil phase and totally running out to in some ways hyperbole and wildly optimistic assessments of how much, how long, all over the world at the same time. So you agree that we ought to reign some of the enthusiasm in until we see some results, right? I do, I mean, I wouldn't give up hope. No, no, no, no. I mean, I am optimistic, I mean, sorry, but when you drop organic matter into the earth, it's thermodynamically it wants to exist in two forms, carbon and methane, coal and gas. So there's bags of it around and we know there's lots of coal that we can get after. I think extracting that more difficult gas, the tight gas requires a lot of things to happen and it won't always be low cost, in which case people will have to turn to coal. So I'm very optimistic about supply. I just think the sense that the US change, as I said, will happen quickly in a matter of 20 or 30 years, I think is on the optimistic side. Okay, great. Jan, we'll keep the microphone there and then move back. I'm Jan Meyers with Resources for the Future. You commented about the potential desirability of putting a price on carbon as a way to reduce broad emissions. Almost every economist in the world agrees that if we wanted to change the emissions of carbon, we should put a price on it. Your country did this for a while and as soon, I think, gonna move away from that. Could you give us any insights, speculations as to what's required for a country to be willing to adopt a carbon price? Yeah, I can. I mean, and we've actually supported the repeal of the carbon tax as it's called in Australia because it ultimately was a tax that was designed in a way that was actually very injurious of Australia's competitiveness. And I think you have to balance how that tax, I don't really like, how that price works with your own competitiveness and not simply penalize local industry without removing one molecule of CO2 going into the atmosphere. And the chances are that what would have happened there is the coal industry would have invested less and as a result of that, more coal would be developed elsewhere, possibly less efficient in many senses than the operations that would have existed in Australia. You've got to understand when you put something in on carbon, what does the impact of competitiveness and what other nations are doing. And I think for a resources rich nation to think it might prejudice, it's some of its most successful industries is a tough call. We have to keep talking as much as possible to get global but realistically, we're not going to get there easily and we have to keep thinking carbon price on its own is not going to get there. You need a raft of measures and each country will probably have to do different things, regulations, some subsidies of R&D, making sure the energy mix is there, making sure you're developing the technology. But I do think it's something we have to keep working on and ultimately an appropriate carbon pricing mechanism applied in many countries will, I'm sure, speed the progress to finding a proper solution that squares the circle between poverty alleviation and environmental responsibility. Okay, in a democratic manner, we're going to move to this side of the room. Little D Democrat, we're bipartisan, nonpartisan. We'll start in this side. Hi, Andrew, it's John Keough here from the Australian Financial Review. Thanks very much for a very good speech. I just wanted to ask, is what happening in Ukraine at the moment bolster the case for the US to lift their export ban for energy? And second, BHP seems to be expanding its presence and profile and trying to be more influential in the US. Could you just talk a little bit about the thinking behind the strategy on that? Okay, I'm probably not going to answer your questions directly. I think the case for US gas exports is already well made without adding additional cases for it. And I think in terms of the US, as I say, we are a very large investor in US shale. We're a big investor in the Gulf of Mexico outside of Australia. It's our biggest set of businesses. Number three is Chile. It seems appropriate that because of that, people like myself spend a bit of time here and a bit of time in other places to be part of the debates we're having today. Okay, I'm going to take two more questions all the way in the back. And then we'll come back to this side. Bill Holland with Plats. I heard a talk by Australia's largest petrochemical manufacturer and dynamite maker. The name of the company escapes me, I think I knew. Then you're probably ready for what's coming next. He's convinced that the United States should limit natural gas exports that his experiences in Australian companies destroyed his manufacturing advantage because domestic prices tripled. And to the point where their new plants are all opening in Louisiana, not Australia. How would you respond to that? I think you may have already said it's a cost difference, not an import-export thing, but could you put some more detail on it? He was very convinced that it was the wrong move. Well, I mean, look, an economy like Australia has to balance what's good for the whole economy rather than select individual industries for what I might call sort of select favoritism. And I leave that to the politicians to make those choices. You can't look at one industry in isolation from the vibrancy of the whole economy. Australia earns enormous amounts from exporting resources. You know, it is a fundamental industry for the country. I'm not saying it's enough to be diversified, but if it violates the principles of free trade and goes down the road of protectionism, it goes against everything I think that Australia has stood for in terms of resources. The issue in Australia with gas prices is that you need to stimulate the supply. There's plenty of gas around in Australia. And if we stimulate the supply, then some of the concerns that are being voiced there may be a bit easier to deal with. But ultimately, you're right. People are paying the market price for the gas and I don't think you should interfere with that. Okay. Do you have a question? So right-hand side about the middle. Could you raise your hand? Thank you. Sheldon Ray, I'm a portfolio manager at Morgan Stanley and BHP is a sizable position in my portfolio. It was full disclosure. I knew they were here. You mentioned Africa briefly. Over the next five years, how would you see your overall revenue in Asia versus the continent of Africa in Middle East developing? Revenue, so sales to Africa. I don't have the detailed figures in my head, but Africa is, there's a lot of things happening in Africa, there's a lot of growth, but the bulk of the growth is already in the consumer base rather than in a lot of construction and infrastructure. So I think it will become slightly more important, but it will be completely overshadowed by what we supply to Asia. So typically when we get folks of Andrew's caliber, part of the agreement is that we let them go in a timeframe so that they can get onto other business and we try to carve out a section where we can get them to come to CSIS only if we release them on time. He has agreed to take a few questions from the press and we'll do a kind of press scrum immediately following this, but if the rest of you will join me in thanking Andrew McKenzie for joining us today, terrific opportunity, nice job. Thank you so much. Thank you. Thank you.