about Hamiltonian complexity. So, Sunday, she did her PhD in Berkeley on classical algorithms, and then we're very lucky that after she became a professor at UC Irvine, she switched to Quantum, and she has done great job in this field. And actually, also very importantly, she's very important for the community. Even she was like, I think in 2019, she received the TCMF Distinguished Service Award for her important role in making TCS more safe and inclusive. So, Sunday, the first years. All right, good. And I can see you a lot better if I stand here. Is this okay? Do you, okay, good. If I stand up there, the light shines in me and I can't see anybody's face, so I have no idea if you're understanding what I'm saying. So, let me just start by saying a little bit more about myself. As Alex mentioned, I started out in just sort of classical computer science theory. I was working on algorithms. And I worked on algorithms with sort of a computer systems focus, stuff like memory management and scheduling and resource allocation, but always from sort of a theory mathematical point of view. And about 15 years ago, I got bored and I needed to do something else. And the beauty of being in academia is that you don't have to ask anyone's permission to switch fields, you just do it. And so, I moved into the area of quantum computing, which was very different, very different mathematical tools and sort of it was a little tough to come up to speed, but it's been very rewarding and the field is just kind of taking off recently. So, I'm really glad I did it and it's been a fun adventure. But because I'm a computer science by training and I was never a graduate student in this field, when I'm talking a lot about physics, I'm a little bit on thin ice. So, I'm absorbing it and learning it. But I always approach it more from the mathematical computer science perspective. So, but we're gonna start with a little bit of physical motivation for the basic problem that we're gonna be talking about through the week. Let's see, turn this on. Okay, so a basic postulate of quantum mechanics is that any observable entity that you can measure, whether it's energy, momentum, corresponds to a Hermitian operator. Hermitian just means it's a matrix that has real eigenvalues, okay? And let's say we have an n-dimensional quantum system. If I measure that system, if I measure my quantity in the system, the outcome has to be one of a finite set of outcomes. So, assume for now, non-degeneracy, so all of the lambda eyes are distinct. If I have an n-dimensional system and I measure, say, energy, there are n-possible outcomes I could get from that measurement. And after I do that measurement, the system has to be consistent with what I just measured. So, after the measurement, the system has to be in a state that is an eigenstate of my measurement operator. And each outcome, each energy outcome corresponds to a particular ending state. So, if I measure that the energy was lambda one, I know for certain that my state is in the state v1. So, this gives rise to the Hermitian operator where the eigenvalues are the outcomes of the measurement and the resulting states are the eigenvectors of this operator. And if I view this thing as an operator, if I'm measuring some quantity a, I can see the operator as the unique linear operator whose eigenvalues are lambda i corresponding to eigenvectors v i. Now, if I'm measuring and my state just happens to be an eigenvector of this operator, then I know for sure what the outcome is gonna be. It has to be lambda i. But more often than not, it's just a generic quantum state. And I can express that state in this eigenbasis. And so, this is gonna be a superposition over all the possible eigenvectors of my matrix. And the probability, if my state is in the state v, the probability that I get some lambda i as the outcomes that say I'm measuring energy corresponds to the magnitude squared of the amplitude in this expression as I express v in this eigenbasis. And the expected outcome, of course, is just the probability, the sum of the probability of measuring a particular outcome times that outcome. And if you just work out the linear algebra, this is this inner product. So this is the probability. So this inner product is this amplitude alpha i. I'm looking at alpha i magnitude squared, that's expressed here. And so this is the probability of measuring lambda i, and this is the value of the measurement. And if I just sort of swap in this sum operator, so everything's linear, so I can take the fee, I can bring in this summation inside, I get basically the linear operator a. So if I look at this inner product, a fee, a fee, that's the expected outcome. So that's the average, let's say, a is the operator for energy, and I have some state that's fee, the average energy of the system is expressed by this inner product. And there it is in sort of matrix form. Now, the Hamiltonian, we're gonna be studying the operator corresponding to energy, which is called the Hamiltonian. And it plays an especially important role in quantum physics. And one of the areas where it's especially important is it governs the dynamics of a system. So according to Schrodinger's equation, this is the Hamiltonian operator H, the system evolves in time according to this equation. And we won't be looking at this too carefully, I'm just sort of giving a little background about the importance of Hamiltonians and why we care about them. But if I start out my system in some state psi at time zero, it evolves according to this equation, and it ends up, say, at time T in some other state, I can express this final state in terms of the measurement operator. It's E to the IHT psi of zero times the applied to the starting state. And a lot of really interesting work, I don't know if there's been a course on this during the school, but there's been a lot of interesting work in quantum computing in translating this time evolution into the circuit format. So how do, if I wanna compute this on a quantum computer, how would I convert this time evolution into a circuit and actually compute how a system evolves over time? That's not our concern today, but it's considered to be one of the most promising applications of full-scale quantum computers when we can build them someday. The Hamiltonian operator is also important because it tells us what the system equilibriates to at higher temperatures. So if I take my glass of cold water on a hot day like today and put it outside, it'll eventually reach some type of thermal equilibrium. Same true of quantum systems. If I take a small quantum system and connect it to a large bath and evolve the thing over time, it eventually will equilibrate to something. And the thing that it equilibriates to is called the Gibbs state. And this is generally a postulate of statistical mechanics. It's not really a proven fact, but at a given temperature, so beta is a parameter that scales inversely with temperature, the system will thermalize to what we call the Gibbs state and it's a mixed state where I'm taking, these are the energy eigenvectors again, and it's a probability distribution over those energy eigenvectors and it's inversely proportional to the energy. So and Z here is just sort of a normalizing factor so that these probabilities sum up to one. And another important sort of big topic in quantum computing research is sort of how to construct these states. Given a Hamiltonian and a temperature, how would I actually build the Gibbs state? I mentioned that this is sort of just a general, unproven but highly believed postulate in statistical mechanics, but it's actually been worked out quite nicely that in certain, for certain quantum systems under certain conditions, this is actually provably true and this is a nice reference for that. Okay, so now what we're gonna be focusing on is what happens when I take this Gibbs state and I drive this beta towards infinity. So beta's inversely proportional to temperature, so essentially what I'm doing is driving the temperature down to zero. And if I look at this Gibbs state, what happens when beta goes to infinity is, assuming that there's a unique ground state, is that this converges to the lowest energy state of my system. So if I look at Hermitian operator as a big matrix, it's gonna be the eigenvector corresponding to the smallest eigenvalue of that matrix. So the name of the game here is given a Hamiltonian for a quantum system, compute the ground energy, or more often in physics, the energy itself is sort of a proxy for what we wanna compute. You're actually interested in some properties of the ground state in some way, but we sort of get at it from a complexity point of view by saying how hard is it to actually compute the energy? Probably if you can do one, you can do the other, although that's not necessarily always the case. So this will be sort of the focus of what we're gonna do is the Hamiltonian itself is part of the input to the problem, and what we're trying to do is compute in the lowest possible energy state what is that energy, okay? So let me give a couple of simple examples. Here's the hydrogen atom, okay? Very simple quantum system, atom, electron, and the state of my system is the position of the electron relative to the proton, and here it's expressed in polar coordinates, okay? Here's the Hamiltonian that describes this quantum system. It's, we're not gonna get too into it right now, I just wanna sort of flash it up there sort of as a motivating example. We have a kinetic energy term, we have the potential energy between the electron and the proton in the middle, and given this equation we wanna know, say what's the smallest energy state, but in general here are the eigenstates of this operator. This probably looks familiar to you if you've ever taken high school chemistry. So it's kind of curious, this looks like a completely continuous system, but if I measure the energy and I look at the state afterwards, I'm gonna get one of these discrete options. So it's one of the sort of beautiful things about quantum mechanics, you start with what looks like a completely continuous system and we get sort of these discretized states. In general we're not gonna be looking at continuous systems, we're gonna be looking at sort of finite systems with finite dimensional particles. So in general the systems that will concern us here will be sort of a system of a finite number of interacting particles, and generally I'll use little n to denote the number of particles. Each of the individual particles has a finite dimensional Hilbert space, so express it in say a standard basis, there are d different states that this individual particle can take on, and collectively for the whole system, the dimension of the whole system is d to the n. So this is sort of our basic sandbox here, and now if I look at, we're interested in what I call local Hamiltonians, and it's motivated by the fact that I don't really think of particles that are far apart as interacting very strongly. So this notion is captured by what we call local Hamiltonians, meaning that I'm gonna have, if I just look at say these three particles, I can express the energy interaction between these particles, they're close to each other in space. And if I just look at these three particles, let's say for the time being I have two dimensional particles, so this is a spin, up spin down, I can think of it as a qubit for example. The Hamiltonian for this little three qubit system is an eight by eight matrix, two to the three by two to the three, okay? Simple enough, I can easily express that. But now, and if I look at, it's really these three little particles that are part of a larger system, okay? And so I really have to take this little matrix and express it as an operator on a large system. And how do I do that? I basically tensor it with the identity on everything else. So for this particular term, I'm just describing the energy between these three particles, and it's tensored with the identity with everything else. And if I look at this in matrix form, now I cheated here a little bit, just to make my matrix pretty, is that I'm looking at now H is interacting on the lower three bits as opposed to the higher three bits because the matrix looks nice block diagonal in this way. So if I look at this tensor product, what I really have is I have many copies of my little H, and the little H is this eight by eight matrix for every possible configuration or standard basis for the rest of the particles. So that's just basically the tensoring with the identity. And because I chose my operator to act on the three lowest order bits, I get this nice diagonal, block diagonal structure here. And if we look at a term that acts on another three set of particles, it'll just be sort of a permutation of this structure. Okay, so what I really have now is I have a sum of these things. I have the term describing how each set, potentially each set of three particles interacts with each other, and the total energy is just the sum of all of these things. Okay, so when I refer to a local Hamiltonian, it's a sum of terms. Each term is sort of a constant size little matrix that's telling me the interaction between say generally k qubits. In the previous example, k was equal to three. And I can have d-dimensional particles. The Hilbert space, as I mentioned before, said it's a huge matrix, but I have a very succinct representation of this now. If I restrict myself to local Hamiltonians, how many terms can I have if I'm saying that each term can act on at most k particles, I have n choose k terms. And each of those terms can be expressed efficiently as a d to the k by d to the k matrix, okay? So I have this super efficient representation, but what I'm interested in is the ground energy now of the system, the overall state that minimizes the total energy. Now, if I were to take this succinct representation and express it in this huge matrix form, d to the n by d to the n, all I'd be doing is computing the smallest eigenvalue of a matrix. So we know that computing the smallest eigenvalue of a matrix can be done efficiently, but efficiently in the size of the matrix. And in this case, the matrix is huge. So we're interested in algorithms that are efficient as a function of the size of the system, the number of particles. And d to the n is now exponential in the size of the system. So it is a simple operator if I could blow up this whole matrix, but in general, we're not gonna be able to do that because it's just too large to do. So we're interested in what is the ground state of the system. Now, there's a precision issue here is that I can't expect anyone to compute this energy too precisely. So I give myself a little wiggle room in the form of this delta. So when we express this, and computer scientists, by the way, love decision problems, it's sort of easier to get at from a complexity point of view. So when Alexei Kutayev first formulated this problem, he formulated it as a decision problem so that we can sort of study it through the lens of computational complexity. And that's sort of the basic idea of what we're gonna be doing here is given the input is this Hamiltonian in its succinct form and two real numbers, E and delta. And all I have to do is answer a yes, no question. Is the ground energy of the system less than E or is it greater than E plus delta? And typically we're thinking of this sort of threshold or precision as one over polynomial in the size of the system. Okay, so you can imagine different varieties of this local Hamiltonian problem. So the term locality is a little bit unfortunate and if we could rewind the clock, we might name things a little differently. So locality implies some spatial geometry, things being close to each other. In the mathematical sense, when we talk about local Hamiltonians, we're really only saying that each term operates on at most K particles. And it's not necessarily the case that there's an embedding of those particles in say three space where every term operates on particles that are close to each other. So it's really just saying, all it's saying is that each term acts on K qubits or q-bits, we don't necessarily know that they're close together. Okay, so it's slightly more general than what we think of as locality. We can vary the particle dimension. A lot of times we'll be looking at qubit systems, but you can imagine any finite dimensional particle. And finally, we will be looking at sort of geometric versions of this problem. So where the particles really are laid out in some sensible space. A lot of times what we look at are sort of lattices, two-dimensional lattices, one-dimensional lattice, three-dimensional lattice, where the particles are sitting on the vertices of the lattice and the terms are now two local. Each term is telling me the energy interaction between two neighboring particles on the grid. So this is a common format that we'll sort of encounter along the way. And generally these Hamiltonians, I should say, aren't capturing everything about a quantum system. A lot of times we think of the Hamiltonian as what's given in this problem. It's a project in and of itself and physics to sort of come up with sensible, useful Hamiltonians. And they're approximating something about the system. They're a simplification of the real picture. But hopefully capturing some important physical property that we're interested in studying. Okay, so when I present this to computer scientists, I always sort of have a couple slides on an example. And I chose this example. It's an example of a paper from condensed matter physics in which they are studying exactly this problem from a numerical point of view. I chose this particular paper because Steve White is my colleague at UCI and I could go to the next building and he could explain it to me. So that's why this, out of the thousands and thousands of papers in numerical condensed matter physics studying ground states of Hamiltonians, why I picked this one. So in this particular case, they're looking at this beautiful Kagome lattice. It's not a cubic lattice anymore. It's this nice particular structure. And the model, which is telling me the energy interaction between each pair of particles that are connected by an edge in this beautiful lattice is what's called the Heisenberg antiferomatic, ferromagnet. And antiferromagnet means that basically the particles want to be anti-aligned. So if I look at this, there's a energy penalty. Positive is bad, negative is good. So there's an energy penalty to having two of my spins either both up next to each other or both down. There's a reward for having them anti-aligned. And then there's this kind of hopping term that indicates the fact that these spins can flip back and forth. And essentially it means that my ground state is gonna be a true quantum state. And notice that I have, in this lattice, I have cycles that are of odd length, which means that I can't perfectly satisfy this need to be anti-aligned. So in general, it's gonna be a frustrated system. And what they were studying in this paper is they wanted to know not just the ground energy, but they wanted to know something about the structure of the ground state. So they were asking, what does the ground state of this model look like? So one possibility is that it's a valence bond crystal where you have these, where the neighboring spins pair up and are entangled with each other, but there's not entanglement between the pairs. So that's one option. The other option is that it's what physicists call a spin liquid, which isn't a super well-defined concept. But the idea of a spin liquid is that if I measure one of these particles, it looks completely disordered. So all the symmetry is broken, sort of like a liquid. And spin liquids are a little bit mysterious, you know, quantum matter that physicists are interested in studying and understanding their properties. And it's believed that sort of underneath the hood, a spin liquid actually does have quite a bit of structure. It looks disordered like it does here, but it might be the superposition of a bunch of different sort of valence bond states. So this is what they were studying. I think the upshot here was that it actually has been liquid properties. And they did this completely numerically. So this is on, you know, a system of like a few hundred qubits and they did it numerically to sort of figure this out. Steve, by the way, is the sort of developed one of the most successful heuristic algorithms for finding ground states called DMRG. And it's an inherently 1D algorithm. It works, it's sort of designed for 1D systems, but they've managed to adapt it to these 2D systems by having the 1D system kind of snake around the 2D system. So that's how that worked. And I use this quote from their paper, a key problem in searching for spin liquids and 2D models is there are no exact or nearly exact analytical or computational methods to solve infinite 2D quantum lattice systems. So this is a hard problem. We're gonna see it's a hard problem sort of from a formal complexity perspective, but it's also just a really hard problem in terms of the numerics. 2D seems to be a sweet spot where a lot of interesting physics happens and it's also hard computationally. So that's why 2D systems tends to be the focus of a lot of study. So we're looking at now this problem from a complexity point of view. So what's the complexity of this problem? And it's actually a quantum version of a problem that we know and love in computer science, which is we have a set of local constraints and we wanna find some global state that minimizes the overall cost. So computer scientists like this problem has a great appeal for us because it's a quantum version of something that we study all the time that's our sort of bread and butter. So let's look at what I'll call a classical Hamiltonian, which is a special case of the quantum version that I just talked about. I think of, I will refer to the standard basis as sort of expressing states that are strings where a string of N characters where each character can be zero through D minus one. Okay, so if it's a system of qubits, the standard basis state is just N bit strings, okay? And if I express my Hamiltonian in this basis and it happens to be diagonal, that's what I will think of as a classical system. So now I don't have quantum constraints anymore. I'm just basically saying, for each, I have my overall cost or Hamiltonian is a sum of terms and now each term is diagonal in the standard basis. So what that means is it's just a simple classical function for if I look at each HJ operates on some subset of the K variables and for a particular setting of those variables, it has a fixed cost, okay? So this is a completely classical problem. N finite dimensional variables and I'm telling you a little function for a subset of K variables if I set those variables to a particular value what the cost is. And I have a sum of these terms and I'm looking for a standard basis state that minimizes the overall cost. And I know that if my Hamiltonian happens to be diagonal in this form, then the solution, the overall solution is also gonna be a standard basis state, okay? So this is basically weighted constraint satisfaction which is sort of a standard format of optimization in computer science. It's a standard optimization problem. And even more famously, we have the Boolean satisfiability problem which is a special case of this in which the variables are Boolean valued, zero or one and my constraints are what we call clauses which is a disjunction of three literal. So it's either a variable or the negation of a variable. So if the input would be a set of these clauses and I wanna know is there a global assignment to these Boolean variables so that they're all satisfied so that the conjunction is equal to one. And local Hamiltonian, this is a special, yet a more special case of local Hamiltonian where I can express a clause. It's not only diagonal, it's all zeros with only one one along the diagonal. So if I look at X or not Y or Z, there's only one setting in which this clause is violated and I can express this in ket notation in the following way and so if I express this Boolean satisfiability as a local Hamiltonian, I'm asking does my Hamiltonian of this very special form have a zero energy ground state and that is true if and only if the set of clauses is satisfiable. Okay, so complexity, famous result in computer science that Boolean satisfiability is NP complete. The class NP is the set of problems in a nutshell that can where a solution can be efficiently verified. It may be hard to find the solution but there's an efficient algorithm to verify it. So if I think of this as a language, if X is in the language, the answer is yes. If X isn't, the answer is no. So if X is in the language, there's some efficient algorithm and there's a witness that will cause my algorithm to accept it and if X isn't in the language, no matter what witness you give my verifier algorithm, it will reject and that's clearly an NP because the witness is just the satisfying assignment.  So the input is a string that encodes an instance of SAT and the witness is the assignment itself. I think of a polynomial time algorithm as basically a family of classical circuits. So I have the input is X here, the witness is Y and once I've specified X and Y, it's just a completely deterministic circuit that says one or zero. A little caveat is that we want our circuit families to be uniform, meaning that the circuit itself can't encode an answer to a hard problem. So if I tell you the size of the input, you have to be able to spit out this circuit efficiently. Okay, so now we're gonna move and I need to change our terminology a little bit. We're not looking at languages anymore in which every input has an answer. We're looking at what we call promise problems. So remember when I told you we have to decide if the energy of a Hamiltonian is below E or greater than E plus delta. Well, what happens if the energy actually lies in that no man's land in between? Then all bets are off. I don't have to actually answer that correctly. So we call this a promise problem. So in decision problems, the answer is yes or no. X is in the language or it's not. In promise problems, we're partitioning the input strings into three sets. Yes strings, no strings and invalid strings. So let's look at a classical version of now a probabilistic version of NP since our quantum verifier is gonna be probabilistic in nature. It makes sense to step first to the classical probabilistic verifier. So MA is the class of Merlin Arthur.  Arthur's the verifier, but Merlin's the all powerful, knows the answer to the solution. So a promise problem is an MA. If there's now a randomized algorithm that it's gonna be a verifier, if X is a yes instance, then there's a witness that causes my probabilistic algorithm to accept with probably at least two thirds. If it's a no instance that no matter what witness I give it, it's gonna accept with probably at most one third and invalid there are no guarantees. Okay, so I'm off the hook there. And I can think of a randomized algorithm as again a deterministic circuit that takes in now the input, the witness, and a set of random strings. Once I determine those random bits, the circuit itself is just completely deterministic. And so now when we talk about the probabilities, we're talking about the probability where ours chosen uniformly at random from the set of inputs. Why one third and two thirds? Also actually I'll get to that in a second. So the quantum version of this is quantum Merlin Arthur, which is QMA. And now it's exactly like MA, except my quantum witness is a quantum state and my verifier is now a quantum algorithm. So if X is yes, there's a quantum algorithm and a quantum witness that causes the quantum circuit to accept with probably at least two thirds, no probability of accepting is at most one thirds and again invalid, no guarantees. And so this is the picture that I have. X is expressed in the standard basis, it's just a string. The quantum witness is input into the circuit and then I measure at the end for the answer, whether I accept or not. Now for the amplification part, one third and two thirds are quite arbitrary. I can think of it generally as completeness and soundness, so if it's a yes instance, I wanna accept with high probability, I'm gonna express that as C, the completeness parameter, if X is no, then I wanna make sure that I don't accept with probably more than S. We had two thirds and one third here before and it turns out that we can boost probabilities quite easily by just repetition. So as long as C and S are separated by one over a polynomial, I can repeat this procedure over and over again and boost the probability of acceptance to one minus exponentially small or exponentially small. So if I have a separation there, I can repeat this M times and the threshold for acceptance is the midpoint between the two and using Chernoff's inequality, you can actually show that if you repeat this enough times, polynomial and N with high probability, you're driving these probabilities down exponentially small, the exponential, the probability of error. Same with the quantum situation, we can talk about the completeness and soundness and again, we can drive this down exponentially small. There's a little bit of a subtlety here and it has to do with the fact that if we're doing this repetition, it's possible that there's some weird entanglement between the distinct witnesses that you're given. So for completeness, this is Merlin trying to be honest and trying to convince Arthur that it really is a yes instance. He can always give Arthur M sort of completely separate unentangled copies of the witness and then each run of the verifier is a separate probability, they're all independent and then you can take the majority. For soundness, there's a little bit of subtlety. I mean, it's possible that Merlin gives me some big entangled quantum state, but it's actually, it works out okay because even if this is entangled, if I think of my verifier as operating on say the first M qubits, if it's entangled with the rest of the states, it's just a mixed state in that case, which means it's a probably distribution over pure states and if it's true that for any pure state that accepts with probably most S, it's certainly true for a convex combination of those and so that can even if you condition on the outcome of the previous runs. I am not gonna get into this in too much detail but there's a really neat trick due to Merlin and Watris. In this, in what I described before, I actually have to give you more witness bits. There's actually a way to boost the probabilities with only one copy of the witness and it's this cool trick, it's called a trick but it sort of makes it seem small but it's actually a beautiful result that's been used in many other places and so we can define a version of QMA where I'm telling you exactly how many witness bits I'm giving you and it turns out that I can use the same number of Q bits in my witness and still drive those probabilities down to one and zero and so the idea, so let me just sort of give you an idea is that you think of the verifiers having to measure at the end and measurement is not reversible but there's in this particular context, there's a way to measure and back up and measure and back up and do that repeatedly and this sort of backing it, you can't always back up but in this context you can and this backing up trick has been used in a bunch of different places in quantum learning color algorithms, in cryptography, in all kinds of different contexts so this is a nice technique that's been used in multiple different places but it was originally introduced to show that you can get this probability amplification without amplifying the number of Q bits in your witness. Okay, so here are complexity classes, NP sits inside MA, a classical verifier is a special case of a probabilistic one, probabilistic is a special case of a quantum one and this sits inside, PP is the class, it's like MA but I don't have the margin of error, it's a randomized, the verifier accepts with probably less than a half or greater than a half but there's no sort of, there's no promise problem there and then this sits all inside polynomial space, Boolean satisfiably is complete for NP and local Hamiltonian is complete for MA, we will go through this result in great detail over the next lecture and then the counter parts of these are the versions without witnesses so this is just polynomial time classical computation, this is quantum computation and this is randomized classical computation and those sit inside each of those classes so this is sort of the complexity picture that we have. So let me just really be now precisely defined the local Hamiltonian problem, we're given a set of positive semi-definite matrices operating on KQ bits, dimension D, I'm gonna assume here that the norm of each is bounded by one and they're positive semi-definite meaning that the eigenvalues are greater than or equal to zero and each matrix indicates the set of KQ bits that it operates on as well, if that has to be part of the input, I'm also given two real numbers, this is my energy threshold and delta my margin and I wanna know is the smallest eigenvalue of the sum of all these terms the most E or at least delta, now I did sort of specify the problem a little bit more here in that I'm asking for the eigenvalues of my terms to be non-negative, I'm asking you to the norm to be bounded by one, that's not a big deal, if you gave me an instance that didn't have those properties I could sort of scale it so that it does so I can shift the eigenvalues by alpha which will sort of cause, which will give me this positive semi-definite property so I can shift everything up so that all the eigenvalues are at least zero and then I can scale it so that the norms are bounded by one, so that's not a huge assumption here but it's a convenient one to assume as we go forward. So for local Hamiltonian, we talked about the fact that it sits inside NP the witness is just a satisfying assignment, for local Hamiltonian, a natural witness would be the actual ground state, if I wanna prove to you that the energy's at most E I give you the ground state and then you can measure the energy. So the witness it's the ground state itself and I'm guaranteed that it's some margin so I'm guaranteed that I'm giving you a state where the energy's at most E or every state has energy at least E plus delta and so now I need to be able to devise my quantum verifier so this I'm just arguing this containment here, I need to describe a quantum verifier where I have some measurement that tells me something about the energy or the outcome of the measurement is at least proportional to the energy and how would I do that? Well, I'm gonna pick a random term and I'm gonna measure the energy, okay? So here's the term itself and now I want some measurement that's gonna tell me what this lambda is on average and I can devise a unitary operator that operates on those k qubits and has an extra auxiliary qubit, zero and unitary operator will map the jth eigenvalue keep that state unchanged but it'll rotate this qubit according to the energy of that particular eigenstate. So this is why I wanted my eigenvalues to be between zero and one so that it's a sensible probability. So now if I measure that last qubit, the expected value I get is exactly the expected energy of that term. So if I have some general state and I express that state in the eigenbasis for that particular term that I've chosen to measure, here it is, I have, this is my amplitude of being in that energy eigenstate for that term and I measure each eigenstate is gonna rotate that qubit by a certain amount and then if I measure that qubit, in this particular case, I'm gonna get one with probably lambda and zero with probably one minus lambda and if I'm averaging over all the possible, this is a superposition of different energy, eigenstates for that particular term. Probably measuring one is the probability that I'm in this particular eigenstate times the value and that's exactly the average energy for that particular term, okay? So I pick a random term, I've now devised a way to sample, to measure a bit and the probability of outcome is exactly the energy of that term. Now I can do this if I'm averaging over all possible terms, the probability of measuring one is now averaged over all the possible terms that I could have chosen. So it is the, if I pick HA, then the probability of measuring one is exactly the average energy according to this particular term. But now I'm averaging over all the terms so the expected outcome is the expected energy of my whole Hamiltonian divided by r, the number of terms. So I'm just averaging over the number of terms. So that's gonna be either, the probability is gonna be either e over r by my promise or at least e plus delta over r. And so now I just need to measure that over and over again so I can sort of with high probability determine which one I have and the margin is important here. If I'm flipping a random coin and I wanna know the probability that comes up heads, I need to have that little bit of margin of promise there. Okay, so let's just talk a little bit about hardness. What I'm gonna do in the remaining 10 minutes is step through, maybe it's review for many of you, sort of what that proof looks like that Boolean-Satisfilia is NP-hard in the classical case. And next lecture we're gonna walk through the quantum reduction in detail. Okay, so for hardness, I wanna take a generic language in NP. The only thing I know about my language is that it has an efficient verifier, that's all. So I have a verifier that says is X and L. If it is, then there's some witness that causes this output to be one.  That's the definition of NP. And I wanna translate this into a Boolean formula. So I wanna say that Boolean satisfiability captures everything about this problem. So I want this formula to be satisfiable if and only if X is in the language. We're gonna be doing the same thing in the quantum setting. So we start with the generic promise problem in QMA.  The only thing I know is that it's a QMA, so I know that there's some quantum circuit verifier for it that works with high probability and is correct with high probability. And I wanna know is there a quantum input state that causes the quantum circuit to output one with high probability? And I'm gonna translate that into a five, initially five local Hamiltonian. And then we'll talk about different variations on this. And it should tell me, give the answer to this. So if X is a yes instance, the ground energy of my Hamiltonian has to be at most E. If it's a no instance, then the ground energy of my Hamiltonian has to be at least E plus delta. And the Hamiltonian itself, of course, has to depend on the input X because it's telling me something about the string X. So how would I do this for the classical case? Well, I've got the circuit. Circuits are pretty easy to translate into Boolean formula. So the reduction for input X, I use the length of X to figure out what that circuit is because it's uniformity. And then I convert my circuit to a Boolean formula. And then I have a term that penalizes the Boolean formula if the output is zero. So it forces the output to be one. So it's not too hard to imagine taking sort of a Boolean circuit if it ands and orgates and translating this into a Boolean formula. And this, all of these clauses say basically that the Boolean formula is enforcing that the circuit is executed correctly. I have a clause at the end that insists that the output is one. So it's only satisfiable if the output is one. And I also have, I'm hard coding the input into the circuit as well. More instructive for us is if we see this algorithm as a Turing machine, because that's gonna be a closer analog to what we're doing in the quantum case. So if I think of my verifier now as a Turing machine, if X is in the language, there's some input string Y that causes my Turing machine to accept. If X isn't, then for every Y, my Turing machine will reject. So this is basically the same picture. So I'm feeding X and once I fix the witness, that the algorithm is just a fixed deterministic Turing machine. And I wanna translate that into a Boolean formula. And this is sort of done with sort of the famous Cook Levin Tableau. So I can think of the computation of my Turing machine. A Turing machine has a work tape, which is I think of just basically a string of variables. And the Tableau represents the state of the computation at each point in time. So this is where I start with, no, I start up here, which is my input and the witness sitting on the tape and my Turing machine sort of executes state after state and in each after the first step, this is the state of the Turing machine after the second step, this is the state. And finally at the end, I should have an accepting state at the very end. So the height is the time of the number of steps my Turing machine takes, the width is the amount of space used. And now it's not too hard to use a little bit of local logic to enforce that this Tableau is locally correct. So I wanna make sure, I can think of each of these squares now as a variable that I'm setting and I wanna ensure that I'm setting these variables so that this whole Tableau corresponds to a sensible execution of a Turing machine. And I can do that locally. So time is going downward, so all I need is to, for every neighborhood of three tape squares, I need to make sure that the one below corresponds to a correct computation. And if there's no head in the picture, there's no Turing machine head, it just has to basically copy the results. So I can use local logic to ensure, and it's actually the same local logic, to ensure that this Tableau represents a sensible Turing machine. It's a constant circuit size that can do this. And each circuit can be then converted to a Boolean formula as I sort of expressed. So the circuit looks like this, which is sort of enforcing the correct computation of a Turing machine. And the output is one, if the cell contains a Q upset, the final state of my computation accepts a Q accept. So let me just kind of step back and say when we get into the quantum version, what we're gonna keep from this picture and what we're gonna change when we get to quantum. So some aspects of it will keep. We will be hard coding X into the circuit, okay? So the circuit has to depend on X because it's telling us, the ultimate Hamiltonian is telling us whether X is a yes instance or a no instance. The input Y, the witness is variable. I'm asking, is there a Y? So is there a way to set the values of Y that cause it to accept? So that will keep.  So somehow I'm encoding the computation of this verifier into the Boolean formula. When we get to quantum, we're gonna be encoding and adding constraints that say, if this is truly the ground state, then it has to be representing a correct computation of the verifier. So we're gonna keep that. And then an additional term to test if the computation accepts or not. So these are all the features that we'll keep. How this is done will be quite different in the quantum case. So, and we will go through that reduction in detail when we get there. So this is the part that's gonna be sort of look quite different when we get to the quantum picture. And that's what we'll do in part two. So, all right. Questions? I should stop. I hope you just interrupt me. I'm kind of looking out there. I see a few nods periodically, but feel free to interrupt me. Can I answer any questions? All right, that means the discussion section will be easy. So, all right. And so we'll meet with Cannell in a different room, right?


Hello, I'll try to have something to say now. We'll see I will have a couple things, but still So I am Cornelbeau van Ling. I'm working at Ipra. We are a small French company that focuses on we started focusing mainly on Proving a fixing accessibility and proving as is accessibility enables computers and solutions to Impress people at various level, but mostly in low vision And we developed more also Trying to to teach More widely like how to use a computer in many different situations for everybody that did not know So usually it's the elderly people, but we also have a lot of Overlap between these two things because there are a lot of elderly's that have low vision or come with a RMD Later in the age. So we have a lot of all up, but we're doing both things at the same time And what I've did to LibreOffice lately is adding and improving accessibility testing and For now it's mostly Framework kind of thing. I didn't add like a million tests I mostly added some ways to for you guys to write more tests So do but we'll see that So again, that was an idea, but you saw it from me. What is accessibility? It's feature that increase social activity. Usually for users, we seem to search in impendments as we should retail tell us I have another source, but yeah, check us out. What does it mean actually? It's pretty spot-on But it infuses a But there's a lot of different things that encompasses like the most Visible ones are the visual things For people without disabilities Like high contrast Adjustments for color blindness like if you've got if you don't see some colors, it's there are Some tool to help recreate at least contrast to to bring back the information Losing colors, but bring back the information Visual clues for this lecture, for example, I think there is a LibreOffice extension that can do that already like highlighting Sounds in the world inside the words and different Yeah, where where sounds changes specialized fonts for mostly low vision To help differentiate Characters that might look similar some are very ugly, but they seem to work And we have the special input device like motion tracking if you don't have user for your Motion issues virtual cable keyboard, which is a thing also for accessibility and We of course have the specialized output like Braille or the most common audio for screen readers, but there are many other More niche things You can try and find everywhere And We do have then these assistive technologies without the software, but usually software somehow web and mostly software That help you interact with the computer That includes screen readers or zoom like the magnifier and numbers are all the tools that do the same and More specific Specializers as well. So as a screen reader Michael told us what it is. I don't have to go too length to that. But basically It should enable somebody that does not see the screen to navigate it so It can do that in different ways and different screen readers have different ways of doing things most of them do everything to Make to adapt to what you like, but one common thing is to present The object you are With the focus But it does not really help to navigate the interface so some Sometimes you have tools to Jump between things as they are visually on screen like navigate to things on their rows or columns Or navigate the row Tree of accessible elements like Michael told us there were parents and children. So you have like a tree of elements between they're containing like a Container with a menu bar and and the document etc. And that mess and you could also navigate that and so that different techniques used in different situations and These tools need information from the clients as Michael also told us And the clients are the software like Librofis here And they do talk with the screen readers using the platform interfaces 80 SPI MSAA AA2 and SSS a sexuality UAI or All those and there's also Android as is his it's thing Is probably using as a second accessibility, but I'm not very knowledgeable bad, but I enable the software to Present itself to assistive technologies in a way it can interact with them So basically it's making the interface face a semantic document if you will And it's some partially allows to interact with with the software as well Like Michael says there are some Things to change values even modify text, but it's not Modifying test for example is not the preferred way to really interact with a text like in your document You're not supposed really to use that Mostly, you're supposed to have the software work Like it would for anybody like you'd use a software features to interact with the text and not Go around it using The accessible interfaces exposed to the system You could do that. There's some use cases, but usually we try to avoid it and just make the software usable and in Librofis What is the most Important thing if you will So it's the accessible interface a whole Librofis expose itself to assistive technologies It's how you can navigate inside the interface. So usually keyboard navigation because it is by far the most Accessible of all and most a Specialized device somehow emulate a keyboard and It has this very Important difference like if you can go to a mouse that you have a current Position that is on something like a current button current position is outside of text and You can move Back and forth to it. You don't you're not trying to find something That might or might be that you can know if you don't see the screen You don't you have no idea if you move your mouth to the right will it finds anything Maybe maybe not that happens. Where is the mouse? Normally with keyboard navigation like tapping through an interface you go to something else You might not know what it will be Where is what you're looking for? But there will be something so you're going forward in your interaction with the the software and There are the visual adjustments that I won't talk much about but it was it's the same I already mentioned like low high contrast color inversion for like if you got Light sensitivity Ah Helps for dyslexia or anything else and so testing actively in Lord Brofis We got several things So the first one or the one which is there It's not true, but the one I will talk about and it's the newest The oldest newest thing if you will so it's the one which is there for the longest time that he's kind of Not from this at the early Sun era is the linting of Validating of the UI dialogue the dialogues mostly, but the UI definitions of those dialogues. So Michael mentioned it. So there is a tool with the very nice name of J gl a 11 y that looks at the The definition Sorry That looks like the definitions How well that the XML and tried is to find things that should go either find labels that don't seem to That should go to some with something but it's not Linked so there is no relation between between this label and I control and The other way around controls that are often that don't label themselves But don't have a relation to a label and it's the most common problem inside Regular dialogues is that you have a control, but it has no information to what it controls You might have a label that says like This is something Column and then you have another control, but a screen reader cannot any artistic technology, but for example a screen reader cannot Know what that control goes with so is that description for that control if there is a relation There is a way to tell it's how you told it But they're none. There is just two different things one label that you might never see because you usually don't do not in trouble move through labels and because I'm not focussable and One control that doesn't do what you don't know what it does. Let me try to change it and see what happens but this tool is clever enough to Find both suggest what might go together and most importantly it has been done in a way that Has very low False positives so usually if it's reports an issue there is an issue. There are they can be situations where it's wrong We know at least one that is not wrong with and flexible at the time But it supports Sorry, maybe I'm in front of everything So you have got suppression lists which and false positive lists full positive lists are for real things that are Well, think that I reported by the tool and that are not an actual issues are probably in the tool and Suppression lists are just to get rid of issues. So what we did at first. I don't know what you have my Yeah, what we did at first when introducing the tool inside LibreOffice system and TI was to put Basically everything it reported into a suppression files. So we could See new issues Because there was I don't remember the name the numbers, but it was hundreds there and it was reporting hundreds of issues So it was just daunting and you know, nobody would notice that one hundred and one New issue and we cannot stop the the the build because of that new issue and This tool can also to some extent Learn be taught about new elements without altering the tool. So you could basically tell it this This XML node should behave Like something like it basically what Michael told about roles.  So you could If we had an element didn't know about but should to do its job properly You could tell it. Yeah, treat it like one of those things. They already knows or we can extend the tool if need be And the good thing is again. Yeah Yeah No, that's an excellent question, but I don't know I think the suppression list are still the same size Because they were not cleaned up, but some issues has been fixed So we need that's the thing we need to do with those is to review everything At the time, I don't know Yeah, it is That's what I'm mentioning. It is boring It might be tedious and time-consuming But it's quite easy The easiest solution and that's what I would start with would be Get rid of well move the the suspension five hour away and see where we get Is it better or is it still a mess in that? I expect it to be better really we have we had Fixes in the area and Michael did some but did you remove the Suppression that goes with it. Oh Okay, okay that I didn't remember sorry, so maybe the suppressions are still quite long But Again, we need to review that and move the if there are real false positives in those lists move them to the false positive lists and the other ones fix them and So we might need reporting everything all of them as a different back to Michael Or or just see what way needs to be done and usually it's very easy and the tool even tells Hints you to what you should do But usually the process is very simple of just adding a relation between the two things that goes together It's usually just as simple as that and you you get to edit to modify just the you are definition for text XML a definition for the dialogue and you have Fixed the issue you remove the the entry you get something to somebody to validate your your thing Jenkins should and you should be good to go And if you're interested you can look right. I don't have the sources Well, I want to open the source right now but you can look it's in the salam sanitizers UI and there is I think two directories the deeps of suppression fires So apart from that we have the old Java tests some of them and not all so useful because some of them were Probably It's all speculative because I never met anybody that wrote any of those but some of them seem to be exercising the test framework Which makes sense, but it's not an actual useful test of the interface Some people might run them, but not everybody does many are even disabled because they caused problems with issues nobody knew How either or how to fix or what did I even mean? So there are a lot of those there are just Disabled so they don't run but the good thing is it's fairly easy to port to see if the unit and Those most more people run them and the CI run them runs them It's if you know anything about you know in Java and any C++. It's quite trivial to do It's harder if you try to use The result of my work because you have to adapt to the simplified versions it could use but it's still the logic itself is very It's very similar. There's not nothing Java specific or anything like that. So it's plain you know using the the x accessible interfaces and sometimes others to do to interact with documents, but it's just you know and If you're interested in seeing the the conversion from Java to CPP unit J unit to CPP unit. I've got an example in that wiki page and a lot of other things on that wiki page and Now so that's what I've been working on lately. It's been one and a half year, but lately as I lately Is internal to be unit test for the Okay for the internal you know interfaces So what does this do What should do is interact with the UI just similar to what an asset technology you would or a user would to be closest to possible to what actually happens in the field and There are helpers for that and we got so even support for dialogues, which was a big thing, but it worked No, it does not all word work on Mac OS if anybody knows how to fix that please I'd be more than more than happy to Try and see if I can help in anything, but I'm not knowledgeable about Mac OS much And we have a weird issue. Nobody figured yet and That's a framework I worked on so basically helpers and base classes and everything to make your life easier writing a test but in the process, of course, I wrote some tests some tests that exercise the framework and some tests that test real things because we found some issues in the process and wrote tests for them and Michael and others fixed those. Thank you But we need more so you could again look at that page which has most of the Developer information you might need but APR I had to use it kind of tutorial if you will And if you want to write a test it should be fairly easy using that that it Does like any any other kind of test. You should just have to write the actual thing you want and not like if you look at the Java test we had Usually it's a lot of boring boilerplate because there was no nothing to help And finally I added a VCL plugin layer CPP unit test Quotes because it's written C++ and it used this framework, but it's a bit different And it tests at the time and only have one for the GTK 3 VCL plugin And it runs in CI with basically no problems ever No, actually we have sometimes we have failures that we don't know Why they happen They look like time-outs but We need to know more on why is that it's it's not bad. I don't know if we have numbers I need to talk to people to know if I can get numbers and links, but They show up from time to time in the ESC reports. So you might have seen them but it's Not too bad. I think we got like Sometimes we have four or five in a week and sometimes we have none But it I don't know. We need to figure that out But it works pretty well And none of those issues are tests Failing like it's never that The tests should Find a value wrong. It's just that somehow it time out times out at one or the other level You know test itself times out of one of its requests communicating with the labor office times out because what we do with what I do in those is to Take in a CPU unit test I take I walk the internal, you know representation for the for the interface and I try to see communicating with the platform similar to what An assistive technology like a screenwriter would Use and I see I compare whether the information match with a little bit of transformation to to match the What the VCL plug-in did because in some area as Michael mentioned there are coordinates. There are different In different colony systems or different little things that up and We got some things Fixed and discovered fix the the first one the funniest one. It was that we didn't have any Description for anything on with using the GTK 3 VCL plug-in and that was a real Obscure a chain or a chain for a real a pure issue that chains a class layout and a broke something But it was it called discovered and fixed so it kind of works It probably kind of works because it can uncover issues and does not For now have false positives Once but we need more coverage because I only covered a subset of the interfaces that exist I didn't go through everything and even not everything on Michael's list he showed so It has just for like the basics He showed up on the exa-exa-accessible context and have something for the text and a couple of things But we need to extend that to anything that exit to all the unit interfaces that can exist and Hopefully it could inspire other VCL plug-in tests for all the platforms in Windows Mac OS cute or anything. It's a different Work especially in Windows and Mac OS because you cannot use the same library I'm using to communicate with the platform. You'd have to use whatever the platform Has but something similar should be should be doable So to summarize we got currently at test. We got the static analysis of your definitions Which are is the jail g l a 11 y tool? That runs in CI We've got the CPU unit tests for the internals Mostly the framework, but we could have more tests of that is pretty easy and we got these things singular we still plug-in tests have put Plurals, but it's a lie and this covers basically everything from the With the internals to reaching the user so we have we can be sure that if we fix something in the internals likes exposing something or changing fixing how text is Exposed It reaches the user so it's an actual fix at least a user on TTK3, but we could hope to have more but There are other things we could do and apart from These tests and fixing what Michael is doing like how things are pretty in screen readers What could be improved? I would have a real impact would be improving keyboard navigation through the interface I try and use and make real documents without ever touching the mouse some things are just not Or I don't know how to do that do them, but it's not possible for example it interacting with a frame is Really complex so for a screen reader user for a blind user even knowing there is a frame is hard if not impossible So yeah, there are other non-specific Nothing, it's not specific to a screen reader or an impaired person, but it's just If you try to remove your mouse some things don't work and they need that to work Okay, so that's what's about it I Like to thanks everybody that so showed me and Michael requests my mayor's requests and like Changes we can call them here, sorry including Calon including Christian Stiffon that wrote stuff for me, and I ended up not using and of course Michael and Everybody else that Helped at any level. Thank you


Initiation is not about a bundle of instructions. In fact, in an initiation process, instructions are a kind of disturbance. It's a new sense. I'm saying it's a new sense because we're still giving instructions because most people, because today they've all become educated. Everything has to be told, you know. Or it must be printed these days. If you tell them also it's not enough, they wanted a printed sheet, the instructions of the initiation because they're all educated.  Too many words. So everything has to be verbal. Even saying it is not good enough, you have to print it. Or you have to record it and give it to them so that they can put headphones and listen to the instructions every time. Initiation is not a bundle of words. If we have to use an analogy, if you know something about electricity, in electrical, employer, you know, motors and stuff, there is something called as induction. The power is there, the motor is there, everything is there. But without an induction switch, it will not go. All the ingredients are there, but still it will not happen because there's no induction of energy. So initiation is like an induction. You have all the ingredients to be meditative, but it doesn't happen. Why does it not happen? Because this is the way the creation itself happened. If you go by the traditional explanation, one way, if you go by the modern scientific way, it's the same thing said in a different language. Modern science is talking about how everything was empty space. Now they're removing the word empty and saying it was space. There is no physicality there, but there seems to be something else there. What that something else we don't know, as for the science. And today they've made experiments where in vacuum state, if you apply a certain energy around it, not into it, around it, suddenly virtual protons and virtual neutrons will spill out. That means creation begins just because there's energy playing around. There's a beautiful story in the yogic tradition, Shiva. You must understand the word Shiva. Shiva means Shiva means that which is not. Appropriate description for space. That which is is physical creation. That which is not is non-physical dimension of the existence. So Shiva means that which is not. Shiva was lying, his body spread across the cosmos. But he's not. He doesn't exist. He doesn't have a physical manifestation. Then Shakti, a certain dimension of energy came and danced around him. And then he came alive. Then he started spitting galaxies out of his mouth. This is the most appropriate description of how creation happened. Still spitting galaxies, new galaxies, it's continuously happening. Simply because a certain energy touched it. Everything that was needed for creation was already there in him, but he needed induction. So initiation is a kind of an induction process. But unfortunately today, if I just ask people to just sit here, we'll do things for you. They also love you. Nothing happening, why is he not doing anything? You're supposed to say something. So what to do? For modern times we say a lot of things. We hang out with you. Today if you go and sit in the Dhyanalinga temple, without instruction, you can become meditative. I can do that to you here now. What's her name? This girl, Hina. Hina, you're in UK. If you're willing to just sit there, I can do it to you now, wherever you are.   Too many words in your head. The only thing you understand is words. Because of that, instructions have come. Otherwise, initiation is not about instruction. There really no instruction in it. Initiation is just an induction process. It's an energy process. But we have to talk about energy. You know? We have to talk a lot about energy before they open their mouth and... Tough times for gurus. Too much talking. If you don't talk, nobody will be here. Very few can really understand if you simply sit here and reverberate. They will also sit here and reverberate. Those numbers are small. Well, in Isha those numbers are increasing. I don't have to say much. But in the larger world, you have to... You have to talk, talk, talk and talk. Hang out with people.


Hi Robert. This is Ashley with Augsburg Toyota. Thank you so much for your recent interest in trading in your 2003 RAV4 for a new RAV4. Go ahead and then this email have provided information about our current RAV4s for you to look over at your convenience. We do have a great selection currently available on the lot. When you get a moment, please give me a call. My number is<PHONE_NUMBER> or just email me back. Thanks. Bye.


Hell yeah, what's up guys, it's CursePike. Maffret's call me Big C. I'm back in action today, I wanna talk about writing. Yep, guys, we are looking for writers to join us and we're willing to pay you for it. Guys, here's what we're doing and here's why it makes sense for you to join MGM.  Right, yeah, you're with me. Here's what we do. We then take that video, we add in some written content, preferably your own written content because you know your video better than anybody else. We add that in, we create a page on our website, mgn.gg. We put ads on that and we give you the money for that. Guys, right now, this is a new opportunity for you to monetize your content and because it's still pretty new and we're just rolling it out, we're giving away 90% of the ad revenue. Unlike YouTube that keeps a bigger portion, we're willing to give you 90% while we're in our founding period or in our beta period, so to speak, because we're integrating this into our dashboard and into our website. But while we're doing that, we still count the views, we still count the clicks, we still give you the ad revenue day one. So, how do you get involved in this? Simple, you just add me on Discord. That's the best way right now. My Discord is big C number 4725. Link, of course, is in the description below. Add me, let's get going. Right now, we're having some huge success. We've worked with the lazy peon. He has 600 and some odd thousand YouTube subscribers and he's given us 21 articles and we've already published 11 of them. Okay, so the guy like him, he gets 150,000 views per video. We're publishing, we're linking back to him. He's got a new revenue stream. We've worked with small YouTubers. Even YouTubers that aren't monetized, not a big deal. We still want to work with you. This is the best way for you to, A, make money even if you're not a monetized YouTuber. Get a new revenue stream and B, promote yourself. Guys, put your content on the website. We put your video on the page. We don't use anybody else's videos. We use your video. You get promotion. You get paid.  I could go on and on, but it's real. It's happening. Go to mgn.gg. Hit me up on Discord. Let's get right into this, guys. Before I go, remember, hit me up on Discord and now I'm going to talk to you about Urduri the Fox, who was one of the first people that joined us on this program. Urduri has been writing with us since November of last year. She's written a bunch of reviews and some of her reviews. She writes, she does scary game reviews. Urduri the Fox, she plays primarily scary games. I should give you a little bit more background, shouldn't I? Yeah, probably. She plays scary games. She publishes Let's Plays on YouTube. When I first met her, she wasn't a monetized partner. She was below the threshold. Now she's over 2,000 subs and she's ranked number one for games like In At Dead of Night, for Fragile and a few others. Right on our page and you can go and verify this. Go to Google search at Dead of Night review. She's on the front page, guaranteed. I know she is. And guys, she's got monetized. She's got over 2,000 views just on those two videos or those two articles alone. And all of those people are now going to see her video. They're going to go to her YouTube channel. They're going to click on her video. She's going to make the money. She's getting double paid. It's really that simple, guys. And she's just one of many people that we're working with. Seriously. If you create content and you want more views and you want a revenue stream and you want to get better promoted, this is the way to do it. Work with me directly. I got you covered. Guys, that's it for now. I'll be back soon with some more content. Stay tuned and good to see you again. All right, big C. Check it out.


But then the Imam says something different in the following phrase. But then the Imam says, وَمَنْ كَرُمَ عَنْصُرُهُ لَانَ قَلْبُهُ وَمَنْ خَشُنَ عَنْصُرُهُ غَلُظَ كَبِدُهُ But then the Imam says, if your stock is noble, your heart will be gentle. What does that mean? That means if you have good genes that allow you to be gentle, you will be gentle. What is your essence? The family background that you have, وَمَنْ كَرُمَ عَنْصُرُهُ From which family do you come from? The Imam here is telling us about the significance of genes. Genes play a major role in defining your personality traits. Absolutely. If someone comes from a family from parents who are gentle, who are kind-hearted, who are humble, chances are this person will also have tendencies to be humble, to be kind-hearted. Now, if you come from a family background that's aggressive, parents who are aggressive, chances are these children will have built-in tendencies to be aggressive. So, what is the Imam, a.s., telling us here? In the first statement, the Imam says, work on yourself. Make yourself gentle with people. But then the Imam says, well, it really goes back to your source, to your genes. Now, genes, my dear brothers and sisters, more and more science is confirming to us that genes play a big role in defining our personality traits, our attitudes, our behaviors. You know, there are so many behaviors that you acquire through genes. Interestingly, even these days, scientists are studying what is called the crime gene. Subhanallah. Upon examining the DNA and the genes of criminals, they are finding that there is a gene that actually pushes people to commit crimes. This doesn't mean that they're justified. No, it just means that they have the struggle. They really feel pushed towards crime. Yes, research it. It's called the crime gene. Scientists are actually trying to study this crime gene. What is it? How does it work? To what extent does it encourage a person to commit crime? Genes play a very important role. Now, one can state, wait a minute, that's not fair. I did not choose my parents. I did not choose my family. How is it that Imam al-Sadiq, al-Salam, says, it's my genes that play a role in determining whether I'm a kind person or not. The Imam al-Salam, in these two phrases, he is reminding us of the very important relationship between nature and nurture. We've all heard about the debate, right? Nature versus nurture. Which is it? The Imam al-Salam in this hadith says it's actually both. It's nature and nurture. There are certain qualities that you have been programmed into. Allah subhanahu wa ta'ala has created you with a set of personality traits. Tendencies. We cannot deny that.  To rage, to fume. They're short-fused, right? There's actually something built in. They have that internal struggle. It's not that someone taught them to be that way. No?  Little kids at the age of one, two, and they're just angry. Well, that was programmed into them. So on the one hand, Allah subhanahu wa ta'ala creates a set of qualities in you. But on the other hand, you have a role to change that. And that's your test in this life. I tell you, one of the biggest challenges we have in this life is changing our akhlaq. Changing our personality traits. It's one of the biggest challenges we have. Allah subhanahu wa ta'ala, yes, he may have created you with a tendency towards anger. Maybe that's true, but why? To test you. That's how you're tested. Will you manage your anger? Will you restrain your anger or no? Knowing this in itself is very important for a lot of people. Because a lot of people, when they have some negative qualities, some negative personality traits, oftentimes you find them losing hope. They think they're bad people. Islam says no. If you find that you have some negative qualities, it doesn't mean you're bad. That's not who you really are.  These are just elements in your personality that are there to test you. Be mindful of this test. Allah subhanahu wa ta'ala will reward you for struggling. A person who is naturally angry, if they suppress their anger, their reward is much higher than the one who's naturally calm. Because they have to struggle and that is their struggle in their life. Sometimes Allah subhanahu wa ta'ala creates you for certain moments in your life to see your reaction, to see how you react towards other people. This is part of our test. Allah subhanahu wa ta'ala has given us certain genes, absolutely. But how is that compatible with this justice? It's there to test the human being. Allah subhanahu wa ta'ala has given us the tools to allow us to pass this test. It's very difficult.  But if we work on ourselves, it is possible. Another point that we can conclude from this narration by Imam al-Sadiq, a.s. Is that if you see people and they're struggling with certain personality traits, don't take it personally. Because oftentimes we do take things personally, right? If someone is a little bit rude to us, we take that personally. Just remember that Allah subhanahu wa ta'ala has created certain people with certain tendencies. And maybe this person struggles with this negative quality of being rude. It's not that they deliberately are being rude. It's built in. That's part of their nature. And they need to struggle, of course. They need to overcome that. But do not take it personally. Understand that they are going through challenges. Try to see the humanity in them. And hence, we have a beautiful hadith from Imam Ameer al-Mu'mineen, ibn Abi Talib, a.s. In which he states, The Imam says, If I can see one good quality in you, that is fixed in you, that is firm, then I will tolerate you. And I am willing to overlook all those other good qualities that you don't have. If you just have one good quality, let's say this person is a generous person. This person has generosity. The Imam A.s. says, Tolerate this person, accept this person. Even if this person doesn't have other good qualities, as long as this person has one good quality, see the goodness in them. You see how the Ahlul Bayt view people? But we people, what do we do? If someone has 99 good qualities, and one bad quality, what do we do? We blast that person, we destroy their personality, we focus on that negative trait, right? That's what we do. But Imam A.s. says the exact opposite. The Imam says if you have 50 bad qualities, and you have one good quality that's fixed, your firm on that quality, the Imam says I'll tolerate you. The Imam says I'm willing to overlook all those other qualities that you don't have. You see the Rahma of the Ahlul Bayt? How Allah Subhanahu Wa Ta'ala trained them to even deal with other people? How the Imam A.s. teaches us to look at the bright side of people. Focus on that. Don't be distracted on what people don't have. Be concerned about what people do have and their personality traits and their character.


May be you have experienced so many failures and you are at the verge of letting those experiences define who you are. Well, you should not do that. It is unfair to yourself to call yourself a failure because you fail at a certain task. The moment you see yourself as a failure, you will begin to think like one and things will only get worse. Understand that every successful individual failed at some point in their lives. So failure is not new, neither is it you. It's just an event. In this video, I'll be sharing with you 10 reasons why people fail. Study it carefully and you'll find the solution to your failures. If you are an entrepreneur or an ambitious person, we specially invite you to join our motivational channel which was designed to give you daily inspirations so that you have the strength to pursue and achieve your most important dreams. We call this channel HUNT TV and you can join in the description box. 1. Lack of persistence Being smart is not all there is to succeed in life. If you do not have the determination to keep pushing, you will not be able to attain success. Calvin Coolidge quoted, Nothing in this world can take the place of persistence. Talent will not. Nothing is more common than unsuccessful men with talent. Genius will not. Unrewarded genius is almost a proverb. Education will not. The world is full of educated derelicts. Persistence and determination are lower omnipotent. The slogan press on has always and will continually solve many human problems. There is no one person in life who has not been knocked down before. The difference between the successful ones and those who fail is that the ones who succeed are those who persist. They do not give up easily while the failed ones remain on the ground when life knocked them. Sadly, most of people of the world's population are amongst the latter. 2.  And there is this tiny voice inside your head whispering to you various reasons why you should not do what you are about to do. Or the possible outcomes of failing at that task you want to carry out. What do you do then? The fail of failure is one major reason why many people fail in life. The way the universe is programmed is that what you fail and think about often comes to you. Many people fail even before they begin. In their mind, they have failed already and that subsequently becomes their reality. Trying to handle life with extra care just because you fear that you will fail is indirectly inviting failure. Again, I ask, what do you do when that voice whispers? A great solution is for you to calm your nerves by taking a few deep breaths and thereafter use success thoughts to counter failure thoughts by thinking about success. That way, the universe attracts the dominant thought, success towards you. 3. Not taking wise counsel The truth is, you are solely responsible for every decision you make in life. Conversely, in as much as you don't allow others decide for you, you should also put other people's advice and counsel into consideration, especially those who have been in the similar position that you are presently in in times past. Many times, we tend to listen to only those who commend every of our actions, whether wrong or right, and perceive those who caution us as our enemies. But then again, those who mean well for you are not scared to tell you the truth as long as he saves you in the long run. No man is an island. So, trying to get through life which your own wisdom and beliefs is a fast way to fail. 4. Unwillingness to start small John Orenger, a software developer and an amateur photographer, started Shutterstock with 30,000 photos from his personal photo library. Today, Shutterstock is worth $2 billion. Many people have not gone far in life simply because they have refused to take up tasks. And the reason behind their refusal to embark on responsibilities is that they do not want to start with the little that is available. You really don't need to have every resource available before you start pushing your goals. Start with what you have. Start small. 5. Dwelling on past mistakes There is difference between feeling guilt and being sorry. It is only proper to feel sorry after you made a mistake. However, as much as you can, you must try your best to avoid the guilt feeling. On numerous occasions, the feeling of guilt holds you stagnant. People do not experience forward movements in their life because they are so tied down in the guilt of their past mistakes and so, they don't move past failure. When you spend your time thinking about your past errors, you are bound to miss out on many other great opportunities that life has in stock for you. And even if you get those opportunities, constant thoughts of the past can make you less productive and waste that opportunity. 6. Making up excuses Show me a man who makes excuses for every of his faults and I will show you a man who is not ready to make a meaning out of his life. In as much as you try to live above guilt, you must also avoid making unnecessary excuses for your fault.  Thus, when you make mistakes, do not create oblivious excuses. Instead, accept your flaws. Pick out lessons from the episode and move on. The next time your mind tries to generate excuses, remember Helen Keller who was deaf and blind and yet became the first deaf and blind person to earn a bachelor's degree in arts and many others who go hit by life's unfairness but still thrives. 7. Procrastination Many young people, especially students, tend to fall in the category of procrastinators. At the beginning of the semester, they assume that there is enough time for study. Even few weeks to examinations, they still have the same assumption. And then when it's a few days to examinations, they start trying to catch up and most times, they end up falling sick during the examination period. Procrastination is a grave where many dreams are buried. Procrastination is the reason why many people fail today. It's not like they do not have the time and chance to do the things that they ought to do. But they are lazy. Hence, they keep on saying, I'll do it later. This attitude of procrastination makes many awesome opportunities passed by them. 8. Lack of preparation When opportunity meets with preparation, success is inevitable. On the other hand, when opportunity lacks preparation, failure is lurking somewhere. Many people complain that they have not had their big bang because they are not given the opportunities to perform. But in the end, you may discover that they are not even prepared to take up tasks when they are given. So they end up sabotaging those opportunities and shutting the door for incoming ones. 9. Doubt and fear of the unknown According to the English dictionary, doubt means to lack confidence in someone or something. Doubt, even a properly handled can lead to pessimism and lack of trust for yourself and your capability, for people around, for tasks, for the process and even for the result. Doubt in most cases stems from the fear of the unknown and this fear has the potential of crippling your efforts and rendering you failure and self-pity. However, the fear of the unknown causes far greater harm than doubt. The fear of the unknown is also called xenophobia. Sounds familiar, right? If this fear can cause people to kill their fellow humans, do you care to imagine how much damage it can cause in your life? 10. Inconsistency One common misconception that most people have is equating consistency with intensity. Many a times, they set schedules for themselves and when they are unable to meet up, they decide to do all the tasks at once, which in turn gets them facked out and totally abandoned the course. A piece was once shared of someone who was giving the duty to throw one stone every day into the village stream. However, on some occasions, he missed it. So he carried all the stones and poured into the river. Well, although all the stones entered the water at the end, but the young man failed his task because he missed the process. Consistence is not about doing everything in one day, it's about doing one thing every day. That's the way new habit is formed. Just the man in the accept. Many people fail in the opportunity that life presents them because of the act as little as inconsistency. Thank you very much for watching our videos. If you are an entrepreneur or an ambitious person, we invite you to join our motivational channel. The objective of the channel is to give you daily inspiration so that you have the strength to pursue and achieve your most important dreams. We call this channel HONDS TV and you can join in the description box. We love you.


All of us are familiar with the phrase, tip of the iceberg, with the notion that ice floats and most of it's underwater and where we can't see it. And so it is with many of our rangeland plants. Sagebrush, for example, as shown here in this cut, has a very, very deep root system. Much of this plant is underground, most of it. And that deep root system allows it to capture water that's deep in the soil profile. But Sagebrush has also a very shallow, wide-spreading root system, allows Sagebrush to efficiently gulp up whatever water comes even in late summer rain showers that don't amount to much. So either way, whether it's deep soil moisture or shallow moisture, Sagebrush is very competitive for it and it counts for one of the reasons that Sagebrush is very abundant in Wyoming. So when you're driving around Wyoming, just remember that when you look at Sagebrush you're just seeing the tip of the iceberg. I'm Gene Gade from the University of Wyoming Cooperative Extension Service.


This is Vogel Timeline with your host, Joe Washington. It's hard to believe it's been more than two years since we began to see Vogel 3 and 4 rise from the landscape here near Augusta, Georgia. What a busy and productive year this has been. Year to date, over 4 million work hours have been logged at this site. Needless to say, there's never a quiet moment around here. Let's check in with Buzz Miller, president of Southern Nuclear Development for an update on what's been achieved so far in 2013. 2013 has been a fabulous year for this project. We have made a lot of progress on a lot of fronts. As most of our employees and people know, we have three main focus areas. First is always to build this plant safely and with a quality built in. We have to do it right. Secondly, is to make sure we do all the prudent things we need to do to get recovery of this project from our public service commission. And the third thing is get ready to run this plant. On the building this plant safely and in a quality manner, we are just proceeding along in rapid fashion. We have poured the base mats this year for both units 3 and 4, which is a fantastic accomplishment. We have started turbine building construction and we're going vertical on unit 3, unit 4 turbine buildings proceeding, the cooling towers are proceeding well, so we're very happy with where we are. The next big milestone will be setting CA-20, which is about an 1,100 ton module and as we speak we're finishing assembly of that module. So in summary, the progress we've made this year will carry over into next year. We are on track to bringing these units online in 2017 and 2018. We're on track for loading fuel in unit 3 in 2017 and so the project is on a path for success to bring incredible benefits to our customers. Thanks Buzz. 2013 has been a very busy year indeed. Major milestones are reached on a weekly basis and all of the pieces are beginning to come together as we continue to see great progress here at Plant Vogel. Let's look back at some of the highlights. In March of this year we saw the placement of the first nuclear concrete for unit 3, creating a six foot thick base mat foundation. A team of 500 workers completed the task over the course of 41 consecutive hours. Almost 7,000 yards of concrete were used to create the base mat. In April, the CR-10 cradle was the first major module component to be lifted and set in place on the site. Over the summer, the placement of the containment vessel bottom head for unit 3 took place. Consisting of 58 steel plates and weighing approximately 900 tons, this was one of many big lifts accomplished. The cooling towers have continued to rise upwards day by day. The unit 3 cooling tower is now more than 107 feet high and unit 4 is not far behind as the fifth and final lift for the central riser will soon be put in place. These components are delivered on a routine basis now. This year we saw the arrival of the reheaters, deaerators for both units and most recently the transformers which arrived on our rail system and were lifted onto crawlers to be stored until ready for placement. Just recently the unit 3 condenser and CA-04 module were set in place. CA-04 will house the nuclear reactor for unit 3. It's been a busy year here, but the work doesn't slow down as we continue to make great progress. In fact just last month the base mat concrete for unit 4 was completed in preparation for the containment vessel bottom head placement. Let's go to David Keach, construction and compliance manager for more details. The planning for the unit 4 base mat placement began even before we finished unit 3 base mat. Some of the things that would have went into that one was the resources and consortium views, the timing, the schedule, but additionally the lessons learned that we were able to pull from the unit 3 base mat. Thanks David. It's not just about construction over here. While dramatic things are happening daily on the site there's also a core team of plant operators training on all digital system controls to operate units 3 and 4. The AP-1000 is the latest in nuclear technology. This will not only be among the first nuclear generating facilities constructed in this country in three decades. It will also be the first to use all digital controls to operate and monitor the plant systems. Here's Chris Hanemichael, Vogel 3 and 4's digital systems project manager with more on this unique feature. So the traditional plants like Vogel 1 and 2 operate mainly on analog systems. Vogel 3 and 4 it will be all digital and the comparison that I use with a lot of people is the analog clock versus a digital clock. An analog clock you have the minute hand and the second hand and the hour hand and you may or may not know exactly what time it is. It may show to 10 or to 11 whereas a digital clock you know exactly what time it is and you know exactly down to the unit because it is that precise. One of the biggest advantages of having all digital systems is that it's easier to operate for the operators. So my role as a digital systems project manager is all oversight. My group provides oversight of the vendors and the sub-vendors providing us with digital systems. That starts at the design phase, to the testing phase, to the shipping phase, to the installation phase and back through testing again. We have to make sure that the digital systems that we get are per the licensing basis and they do meet our regulatory guidelines. Thanks Chris. The control room for each unit will be strategically located between the turbine building and containment building and from there the operators will run the facility. They've been training on this for years and now 40 licensed operator candidates and 4 operations training instructors have completed their training and will soon be awarded certification on the AP1000 reactor. Next, they will earn their AP1000 operator licenses from the Nuclear Regulatory Commission, some of the first ever issued by that agency. This year many important visitors toured Plant Vogel including Nuclear Regulatory Commission members William Ostendorf and Chairman Allison McFarland as well as a delegation all away from China. As we say goodbye to this year, we anticipate many exciting new milestones ahead in 2014. We look forward to keeping you up to date on the latest amazing things happening here as we lead America's nuclear renaissance. From all of us at Plant Vogel, we wish you a safe, healthy and happy new year. Follow Georgia Power on Twitter at Georgia Power and Twitter at Southern Nuclear and also at Georgia Power and Southern Nuclear on Facebook.