# Quantum mechanics, System, Computing, Physics, Qubit Math Skills You Need for Quantum Computing

Here in this video i’m going to break down the minimum that you need to get started with quantum computing and give you all the resources, you need to get that math background now, i’m, not going to teach you here how much math you need to become a Quantum algorithms researcher to invent a new quantum algorithm to solve world peace and win the nobel prize. This is not that video. This video is for the person that is really excited about the new field of quantum computing. Has some high school math background and is excited to self teach? With this math background i’m, going to tell you about, you can definitely explore the cloud quantum chips that are available right now, and maybe this will get you excited and get you excited to study more about quantum computing and more math and actually make it a career. I’M also going to cover what you don’t need and some tips on not to get overwhelmed when you’re studying quantum computing number one linear algebra. Now this is the most important branch of mathematics that you need to get started with quantum computing quantum computing operators and gates. They’Re all just matrices, so you have to know that matrix, math, applying a quantum computing gate to a certain state, is just multiplying two matrixes together. So you should know the basic matrix operations, for example, adding multiplying matrices and taking the dot product. You should also be able to find the transpose the conjugate and the trace of a matrix.

You will see specific notation like dagger notation that denotes the conjugate transpose of a vector. There are, of course, some concepts that are very specific to quantum computing, but a good linear algebra course should cover pretty much everything that you need to get started. Number two complex numbers, imaginary and complex numbers are the core mathematical base of quantum mechanics. It appears explicitly in its fundamental equations, including the schrodinger equation, and, in the end, the reasoning is really not that straightforward, like. Why would we need an imaginary part to a physical system? This is way beyond the scope of this video and it’s. Actually, quite a complex answer, however, just know that you’ll need to work with complex numbers. I’Ll also go ahead and link a paper below called. Why are complex numbers needed in quantum mechanics? Some answers for the introductory level, which talks about the four reasons for the use and need of complex numbers in quantum mechanics number. Three know your greek letters now. This is a pitfall that i find for new students in math and science and it’s, not knowing your greek letters. If you don’t know them – and you don’t know how to say them in your head, it’s going to get really confusing when we start adding a lot of similar looking symbols, you’ll get pretty overwhelmed really quickly. Now i don’t think you really need any specific training for this, but if you don’t know a letter, when you come across it look it up, learn how to pronounce it.

This really helps with retention number four physics and quantum specific notation and constants. Now i’ve mentioned this before in my other videos, but why? I think quantum and physics is sometimes really scary is because we use a lot of math and symbols that aren’t seen anywhere else. So even someone coming from a math background or programming background may not have seen any of this before one of the things that you’ll see a lot is direct, notation or braquette notation. This notation is just a simpler representation of vectors and matrices of the state of the quantum system, so why do we even use it really? What is, therefore is to make it easier to calculate and represent some of the quantum math that we do mathematically. It denotes a vector in the abstract or complex vector space, which is why we need complex numbers and physically, it represents the state of a quantum system. So why isn’t it just a vector, it looks the same right in physics. Vector really refers to quantities like displacement or velocity, where the components are in the 3d space. Direct notation is for the abstract, complex vector space also be familiar with the hilbert space symbol. You’Ll see this a lot. The hilbert space is a special kind of vector space and what’s special about it is that you can do an inner product in the hilbert space. An inner product takes two vectors and outputs, a scalar or just a number, and it has some other special properties as well.

So why is the hilbert space so important in quantum computing? It describes the space that contains the wave functions or all the possible states of the system. Next up is h, bar or planck’s constant, my undergrad quantum professor joked, ah just add an h bar to anything then it’s, quantum planck’s constant relates a photon’s energy to its frequency. The planck constant multiplied by the frequency is the photon’s energy. You should also know a few things about set notation, for example, the set membership symbol. What is on the left? The state a is an element of the vector space on the right. Also, you should know things like the real number symbol and the complex number symbol, and then you’ll need to learn the symbolism for quantum operators and gates. This is not something you need up front before you start learning about quantum computing, but you’ll see very quickly. Why? Linear algebra is so important when we get into it. One of the very first things you learn is quantum gates all the various unary, so one qubit binary, two cubit and ternary gates. These gates are just matrix operators and we apply that matrix to the state of the qubit. So you’ll see very quickly this linear algebra in action. Now this may be controversial, but i don’t believe that you have to get all the math background. First, to start coding on real quantum chips. Obviously some traditional educators might disagree, but let me explain why i think this way honestly it’s all about getting you excited and getting you started way faster.

I actually worked at coursera for a few years, and i worked on the teaching and learning research team and what we did there was study online pedagogy and how to get learners to best complete courses, because remember learning on your own is way different than learning in School in school, a lot of time, you’re learning for the grade and not learning for your own growth with self teaching, because you have no one forcing you to do it. You may get frustrated and quit earlier, but the biggest thing that we learned through this research is that the most important thing to do when people are self teaching is get them excited about a topic and progressing through it and progressing through. It means removing barriers of entry with equipment or knowledge, so people don’t get frustrated. Then you can go back and build that more fundamental background when people are more empowered and excited about what they’re already able to do – and i also think that’s valid and can apply in quantum computing as well: it’s, okay, to start learning about quantum computing concepts. First and writing a few lines of code and then seeing that work come to life, then you can work backwards in filling out that knowledge and getting into the more advanced concepts and learning the mathematics behind it. And obviously, then you can go in as much depth as you want. So now, let’s talk about what you actually don’t need to start learning about quantum computing.

You don’t actually need to know any advanced, calculus or differential equations, while physics majors take calculus 1 calculus, 2. 3 differential equations, some statistics and even advanced upper level, math classes you don’t actually need any of that to start working with quantum computing. A lot of the reasons this is required before taking quantum computing classes in college is just for mathematical maturity and not the actual concepts. I always say my electrodynamics class actually taught me calculus 3 and multivariate calculus and classical mechanics actually truly taught me differential equations. But again, neither of those are needed for quantum computing, and you definitely don’t need all those four courses to start going through quantum computing resources online and running your own circuits. I will also say that you don’t actually need to take a full course on quantum mechanics before starting to take a course on quantum computing. Now, of course, if you want to get deeper into quantum computing, do some more theoretical work. Of course, quantum mechanics is a good idea to take. However, you don’t need to do the full course before you start running circuits on quantum computers. I say this because traditional quantum mechanics courses spend a lot of time on fundamental quantum theories and their derivations. However, doing the derivation of an equation is not that important to applying quantum computing, while quantum computing obviously builds on fundamental quantum mechanics concepts. A lot of online resources will cover those concepts that you need and, of course, i recommend filling in those gaps of knowledge later.

If you want to get deeper in quantum computing and of course, if you want to take this course, you definitely should so check out my video on best online quantum computing courses at the end actually talk about quantum mechanics courses. If you feel like you need that background, so now, if you don’t have the background that you need, where can you actually learn it for linear algebra, complex numbers, hilbert spaces i’ve, never seen anything better than khan academy, it’s, concise and easy for beginners there’s? Also, an in depth, linear algebra course on coursera, now it’s for deep learning, but i found that actually, the math between deep learning, machine learning and quantum computing is quite similar but honestly for basic linear, algebra there’s. So many good resources out there for free just on youtube, and you can just search it if you have a math background already and just need a refresher that should be more than enough now. I’Ve mentioned this book in my other videos before, but why? I really like it is that it’s really self contained in the back of this book. There’S a few chapters there that’ll cover all the math that you need for quantum computing, so if you’re completely new to the math and quantum computing work through the back of this book, first that’s, where all the math chapters are now. This is very different from traditional college education, where you have to take three or four math classes before you can even start getting into quantum mechanics.

You also have to finish all the core quantum classes before getting into those exciting upper level. Electives, like nanotechnology and quantum computing now, if you’re in school, obviously follow the path that’s laid out, but for self learners in quantum computing and programming and other sciences it’s totally okay, to skip around to what’s most relevant. And this is where i’d recommend doing. Just in time learning and go and pick up that concept before you move on to the next step. But if you don’t want to do this quick start method, you can also recreate the traditional physics curriculum using mit, open, courseware or edx. So, first you need the prerequisites for quantum mechanics one, so that means calculus one. Two, three and differential equations also you’ll need to have done physics, one and two which are calculus based physics and for some universities you also have to take classical mechanics one beforehand. After that, don’t forget about quantum mechanics too. After all of that, then you’ll be able to take upper level quantum computing courses, also, depending on how deep you want to get into the experimental side or into the hardware. You may need to take atomic physics or solid state physics, or you might find that taking. Electronics is really useful if you want to get more on the experimental side. I hope this video helped. You figure out the map background you need for quantum computing and where to find the resources to teach yourself in researching this video.

I also found this awesome article that i’m going to link down below that covers a lot of this quantum computing notation.

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