Math Skills You Need for Quantum Computing
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- čas přidán 27. 07. 2024
- But really, how much math and science do you need for quantum computing? I find that people tend to REALLY overestimate the amount of math they need to get started coding on quantum computers. Here I'm going to break down the minimum you need to start with quantum computing and give you resources to build up those math skills.
Quantum Computing: An Applied Approach Book: amzn.to/2Ycx6kD
My video on Best Quantum Computing Books: • Best Quantum Computing...
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Khan Academy: www.khanacademy.org/
Beginner's Guide to Quantum Computing Literature & Notation: / 0
Complex numbers in Quantum Mechanics: www.ind.ku.dk/english/researc...
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0:00 Does quantum have a lot of math?
0:57 Linear Algebra
1:37 Complex Numbers
2:14 Greek Letters
2:38 Physics specific notation
4:53 Tips for Self-Learners
6:10 What you DON'T need
7:46 Resources for the math
9:04 Traditional Physics curriculum
(1) Linear algebra
This is the most important branch of mathematics that you need to know for quantum computing.
(2) Complex numbers
Imaginary and complex numbers are the core mathematical base of quantum mechanics., it appears explicitly in its fundamental equations, like the Schrodinger equation.
(3) Know your greek letters!
It's going to get really confusing really quickly once we start adding a lot of similar looking symbols if you don't know your greek letters!
(4) Physics/quantum specific notation and constants
Quantum is sometimes scary because it has very specific notation that is only used in quantum or in physics. But the concepts are similar to other fields, just have different names!
Dirac notation or bra-ket notation, is just a simpler representation of vectors and matrices of the state of the quantum system.
So why do we use it? It makes it easier to calculate and represent some of the quantum computing math that we do.
The Hilbert space is important in quantum computing. What's special is that you can do an inner product in a Hilbert Space - the inner product takes two vectors, and outputs a scalar (or a number). In quantum computing, it describes the space that contains the wavefunctions that are possible states of the system.
What you DON'T need to know to start learning quantum computing:
Advanced calculus or differential equations
A full course on quantum mechanics
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#quantumcomputing #learnquantum #quantumphysics - Věda a technologie
Totally agree about self learning. I started coding in middle school not because I wanted to be a programmer, but because I had projects / ideas I wanted to bring to life. I saw programming as a tool, not an end goal. Was purely intrinsic and deeply rewarding and fun because of that. Totally removes the pressure as well.
Ironically, I struggled with linear algebra, but really enjoyed calculus. Fast Forward 20 years, and I'm doing very little calculus, and most of my work is now focused on tensors. Go figure.
What kind of work do you do?
I'm currently a software engineer and loved calculus years back. I took calculus up until 3 and stats.
I missed the lecture about eigenvalues. Never been able to understand them since.
Ok
@@terjeoseberg990 Have you seen 3blue1brown's graphical video yet? czcams.com/video/PFDu9oVAE-g/video.html
After watching this video I have decided that I don’t know anything about math😀
Brother you are atleast one of the best at what you do. Keep it up
Que putas estas haciendo acá jajaja
@@Anastasia-Marchenkova do you have a course on udemy on how to get started in quantum computing or programming with python?
@@l.l6702 jajajajajajajajaja exacto
@John Gregg String theory... whoo boy, you need a lot of abstract and trick stuff... all of quantum field theory, to warm up. Topology in higher dimensions. Lagrangians, action integrals, minimization/extremization techniques. General relativity, since it's one of the things that's supposed to pop out of string theory. Not just regular vectors and tensors, but also spinors (which you caught a glimpse of in the video) and Lie groups and Kac-Moody algebras and Virasoro algebra and skill at manipulating their commutators & anti-commutators. How to make very strong coffee.
This is the reason i left my journey of quantum computing. I started my ibm fundamental of quantum computing course. I got excited. Then i wanted to go deep. Saw those notations and then never saw them again. This video is giving me my hope now. Thanks 🙏
I got my degree in Physics and studied machine and deep learning on my own. Now I'm on my first semester of a Master's Degree in Physics. I had heard about quantum computing, but thought it was way beyond my abilities until I saw this video. Thank you so much! I might try to learn about the subject for my PhD for the upcoming years
Thanks for the info and the inspiration. I'm a comp sci dropout but I've been teaching myself my old curriculum, plus other topics, over the last few years just for the love of tech. I really appreciate channels such as your own that encourage learning.
I can't believe that all the math that I know that I thought I'd never use comes handy now. Thank you for posting such a great video!
Thanks for the great summary video! I don't work in my field anymore, did a phys chem degree years ago, so the math is rusty but at least now I know where to brush up or what I have to re learn/ learn/ focus on with precious time! Appreciate it.
This is so desperately needed. Wow, Well done and stay humble! ❤️❤️❤️
I like a lot videos with high information density that at the same time are also very well explained. Oh yea I think this is going to be one of my favorite youtube channels. Totally underrated as of now. Thanks for making all this.
Thank you so much for this video ❤️,i am very much attracted towards quantum computing since i have started reading books on quantum mechanics ❤️
Thank you for humanizing these topics. You have a great knack for explaining a lot of the intimidating hurdles well enough for us to understand our challenges.
Top quality videos, and wonderful explanations. 🍻
Awesome video, thanks. Ran into some math roadblocks trying to self teach quantum mechanics (calc mainly). But felt comfortable with the linear algebra, so this gives me hope for learning quantum computing :)
That's a very good talk. You definitely are a real inspiration to the next generation of math and physics students. I have a math and computing background and am also into AI.
This is an amazzinnngg video on the math resources for the quantum computing. Such brief & lucid explanation of each and every side of the journey. I'm just compelled to become a permanent subscriber of this channel. Thanks Anastasia you've intensified my love for quantum computing.🙏😊
I totally agree that sometimes is best to jump in the deep end before you realize how far the bottom of the pool is. It's easier to connect the missing dots.
Thank you so much for sharing your insight.
Self learning help me to pursue my interest, initially physics now going to deep dive into QC.
Surrounding (atleast as of now virtually) with the great minds and personalities of same interest including you ma'am, help this journey very easy.
@@Anastasia-Marchenkova Actually my background is related to CS and now ML but my interest in physics help to pursue QC learning journey.
Everytime you said "excited" I was absorbing a photon in my head.
You definitely inspired me to study that subject!
Thank you
It was a long time ago, but when I learned the Schrödinger equation in my semiconductor class (EE), I remember being impressed by how complex and how simple it was at the same time. Had there been the access to quantum chips back then that there is today, I may have pursued that instead! It's still super interesting to me. Great video!! :)
I remember doing this equation in CE but I never really mastered it because I felt it was physics
Hi Anastasia Marchenkova
Fantastic - Its a cool drive over on the necessary rudimentaries onto stroke swim in Quantum Computing - Impressive Catch Over - Kudos - Cheers 🙃😊
Thank you. Really helpful information.
Great video, loved it. I have a Master's in Mathematics and find this a useful reference to explore new topics. Thank you.
Fantastic video! Thanks so much for this.
Thank you for these videos! We want more! This is awesome!
This is indeed a good way to build the basics for quantum computing. I would like to add that a basic course on probability would be very useful especially when dealing with entangled states and CHSH inequality. Additionally, depending on which subfield you would specialize in e.g. Quantum Information Theory, you may require functional analysis and operator theory as well.
This is so awesome thank you for the info :)
Thanks Anastasia this is what we need a clear understanding sothat we can resolve our selves and opt option according to our interest.
Thanks for giving ur valuable time to us.
You are the best. I did quantum computing 10 years ago. Must be fun now.
Thx u maybe I mite actually be cut out for this I had no actual ideas but as I was attempting to get a better understanding of quantum computing believe it or not I intuitively found that those different maths was required 🥳 this video just made me gain so much confidence because for the longest of trying to self teach I was like what am I doing I’m barking up the wrong tree but it just felt right u are a got sent
This is a really detailed yet simplified video that I could have possibly found on internet. Thanks !!
R u a physics major????
@@of8155 no, but a biphysics and bioinformatics enthusiast. Reading and knowing about quantum computing and it's scope in biology too, is what I love.
You got me excited. I hope my son will learn more about programming for Quantum computers.
Incredible! Thank you!
i want to have a math ,QC teacher like you ,i kinda regret for not studying maths when i was a student but i think if i do it daily i will be able to learn ,after this vid haha its like linear algebra i love you ,i think im better at self learning than learning the other way.
Excellent Info Anastasia!
I’m very grateful and thankful Anastasia for pointing out what we don’t need , I needed to know that because otherwise I’d have wasted my time on learning unnecessary materials that won’t serve any educational purposes.
I’m looking forward to learn and avail from your guiding mentorship’s in learning Quantum Computing.
I think a lot of people get very overwhelmed when starting with the math - quantum is SUCH a broad field but you can focus on just a couple things to start!
Concise and informative. Love this video...
Thanks for the suggestions there is a lot of interesting things to do in this subject
Really loved this very insightful
I can’t even imagine ,how much time you have spent editing this video , it’s absolutely cool 👍
@@Anastasia-Marchenkova The effort really shows! :)
Really good video, thank you so much.
As a physics and math major from Australia, I'm astounded that highschool math in the US is enough to deal with Hilbert spaces. I did not encounter this level of mathematical abstraction, like Hilbert spaces or Hermitian matrices, until the second half of my degree.
I think she was in a school that concentrated on math and science
@@khushichadha512 I mean to understand Hilbert spaces you need some functional analysis. Which requires almost a whole university degree of prereq math knowledge from vector calculus to linear algebra etc. I'm not saying it can;t be done, it's just a little unbeliveable
Same here in the Pacific as well.
THANKS, this is quite useful and interesting. Years ago, in the late 1990's, I tried to learn something about it and read through Fermi's "Notes on Quantum Mechanics, which was just an outline he used to give lectures in the early 1950's. It covered a lot of what you mention but was far to superficial to make any sense. After working though it I learned some matrix stuff but not much more of anything.
I've had all the math course for an EE degree years ago, and spent 32 years in software in many languages - Assembler, Pascal, C, C++ so ya might think I would pick this up easily. Not a chance. it's a ll a complete mystery. Hopefully by following up on some of your leads I might become more... enlightened.
Thank you so much for all this informormation!
Back in my college, Linear Algebra and matrices never made any sense to me as we were never taught that way; only proofs and theorem but no visualization. After my undergrad, when I came across video series from 3b1b (i am sure most of the phy/maths major know about it) I started enjoying Linear Algebra, and realized how important it is to describe and solve real world applications. Now, when I come across LA or any such notations used, I am not terrified. Sometimes, it can be frasutrating, but I want to understand them either searching about them online or reading somewhere.
Loved your video. 👌👌👌
Currently speed running Khan Academy so I can place into Calc 1 at my university, math is top of mind at the moment! Seeing all of these Greek characters gave me flashbacks to Markov chains when I was in Finite Mathematics years ago lol.
The zoom cuts are a good variation in your video production, makes the video feel more organic. Keep up the good work!
Just saw the copy of deep work in the back! It's on my to-read list. Do you feel like that book has significantly improved your productivity? Sorry for being so verbose in the comments section lol.
@@Anastasia-Marchenkova I used to listen to a lot of Financial Independence/Real Estate podcasts so I've heard the main points sort of summarized; I was under the impression that DW is more practical than SGTCIY. Which do you think offers more practical advice? I intend to read/listen to them both but am sort of trying to parse them in order of practicality (in addition to the other mandatory reads I need to interface with lol)
@@Anastasia-Marchenkova very pointed! I figured they were both salient reads for personal development and will have to pick them up asap
I absolutely love your videos!
I worked on learning quantum computing for about a year and I have taken courses in quantum mechanics and still
it is easy to get hung up on some of the principles. So for a break I am studying AI which I find a lot easier.But when I tire of this I plan on getting back to quantum computing. Watching you videos is getting me inspired to give it a go.
If you aspire to become a theorist, prioritize honing your mathematical skills and cultivating deep intuition. On the other hand, if you're inclined towards experimental work, a solid foundation in mathematics and intuition will suffice. However, if you aspire to be a trailblazing scientist, you have the potential to excel in both domains with precision and creativity, opening the door to groundbreaking discoveries.
Thank you for sharing your insights Anastasia, shout out from Papua New Guinea.
Interesting that you cited Ricardo Karam, I personally study physics at the University of Copenhagen (1st-year :O) and know that guy as he among other things was the driver behind introducing Lagrangian & Hamiltonian mechanics into our first-year mechanics class. Imaginary numbers in physics are also incredibly fascinating! In fact, I together with my prof am currently doing some research on the applications of something called Geometric Algebra in E&M and relativity, which generalizes notions like dot & cross products to arbitrary dimensions and which also gives a geometric interpretation to imaginary numbers in QM & E&M.
It turns out most of the imaginary numbers in QM can be expressed as rotations in 3d space by what's called a "pseudoscalar" which (in 3d) acts very much like an imaginary number but is really an oriented volume. Geometric Algebra extends beautifully to Minkowski space, can drastically shorten Maxwell's equations and is the underlying math behind the Dirac equation, I encourage you to give it a look because I could honestly talk about it for days! Also, excellent video :)
excellent inputs
Very good content. I regret why I haven't seen this earlier.
Thanks! This helped alot...
I'd recommend the Feynman lectures on physics. They are still so good!
I think volume 3 is quantum if memory serves me right.
Hi Anastasia,good advice abt math prerequisites for learn QC.You must have specifically mentioned eigenvalues and eigenvectors which play a really important role in QC..It is better to know them evenif one is just starting into this field.
Girl!!!! You are fabulous!
Mrs. you are the ideal person of the next generation ❤
Cracking the coding interviews - this book is everywhere
How much of it is needed in the real job?
Traditional Scientific Analysis is based on recognition of complex connections and heirachical dominance sequence Oscillation, which is basically what you see and hear from an Orchestra. Sound Engineers use Frequency Sweeping and Digitisation to create DDD Records of the output, and that is the equivalent process of Quantum Computational Information Technology wave-packaging formation.
Some hands-on experience is recommended for a simplified POV of techniques and technology, especially the comparison of "Savant" Mathematicians and Musicians with "perfect pitch" ability to hold tabulated Information in their own memories, or "Memory Palace" systems of ordering databases.
This is the curriculum of Nature that is built into the Holographic Modulation Mechanism Temporal Perspective Universe.
Everything is connected, so "One thing leads to another", which is why Dr Sapolsky's lectures are excellent backgrounding in regards to inherent complexity of bio-logical re-evolution circularity quantization identification cause-effect/Math-Physics.
Given that "everything happens all-ways all at once" quantization identification processes, it's natural to use a browsing strategy of learning by increments of whatever interests you most, prompted by Intuitions.
Thank you.
You just nailed everything ...
Awesome.. i was worried about deep mathematics .. but after watching this video I feel confident..
Thankyou
@@Anastasia-Marchenkova honestly it feels good learning from minds like u...
@@Anastasia-Marchenkova and actually I'm 16 and interested in this field . I wanna ask u how would I start my carrier.. and in my free time I used to get more knowledge about quantum computing and I just used to go through different article and studies .. and also no one is here to guide in this field so I m asking u candidly..
The dangerous fake soldering at 9:42 freaks me out. Otherwise great vid :)
this channel is God send ... it'd be great if you can make a video on roadmap for career in this field. What's the background needed, is it all software & programming or if & how much does one need to know hardware of computers or electronics or quantum computers ... may be show some sample solutions out there.
@@Anastasia-Marchenkova Sure Thanks so much. It could be written or ofcourse whichever way you think works best .. e.g. I come from a wide experience in data & analytics and lately moved into data science NLP/Deep Learning ... so all of it is software & programming. I wonder for myself if and what's instore for me, is this new world even an option for me ...
Good survey. LaTeX notation would be really cute!
This is very mentally building, as im bechalor graduated in math and know all these basics :) Im also familiar with hilbert spaces and functional analysis, so maybe i should give this quantum things a chance?
I'm a self-taught person all my life, at 2013 programming javascript to do web pages (before that learn english many years ago), after that a lot of php, then html, css, sql, python, and java from now on, and started to realize after some years took a couple of software engineer courses at edx "software development" UBC and also have to take some many classes at Kan academy to learn good math my native language it´s spanish, and I've found that, math it´s different here in southamerica we use Baldor's Algebra from Iraq I mean from middle east so it´s the quite different but same result as well, so for me its been challenging to do another kind of algebra as well math, I did understant there's no need have so many programming languages but to have a basic concept of everything so can even create another programming language, and here next step will be understant in the future quantum will take time but with a strong math background that told us in this video will follow the steps I love many things from programming, math to electronics and quantum amazing universe of things :)
Us math majors are lucky ❤️
We have to take classes in Calculus, Linear Algebra, Abstract Algebra, Real Analysis, Complex Analysis, ODE/PDE, and if you want Topology, more algebra, more analysis, graph theory, etc. Math is supreme.
The only thing I do not remember hearing around back at college is the Hilbert Space, suddenly this stuff does not seem so far fetched. Thank you.
Learn linear algebra using the vector space approach. Hilbert spaces in QM are basically infinite dimensional vector spaces whose elements are functions. A constraint is added such that the "norm" of each vector (function) is finite.
Word of the day: autodidact (you probably knew, but anyway...). Have you considered advising APL as a tool for fiddling with linear algebra? It has most of the standard operators built in.
Hi Dear Anastasia! You are really an inspiration for everybody who want to get a basic knowledge or someone who intend to deepen the knowledge towards a research level in quantum physics/quantum computing. I have a master's degree in pure math. Actually I was studying for the PHD in theoretical mathematics (more specifically in complex analysis and spectral theory) for ten years and finally I gave up...so I have some really good knowledge in linear algebra and also functional analysis, the Hilbert spaces are special cases of the Banach spaces,which are complete normed spaces. Hilbert space is a complete inner product space,which induced from a norm. Actually very famous example of Hilbert space is a function space L2. I won't go into details here. Actually functional analysis can be viewed as an infinitely dimensional linear algebra...
@@Anastasia-Marchenkova You're right,it is tough. But mathematics as a whole is very fundamental to all science and technology. I was a TA in math courses in engineering college for more than 15 years,and also gave lectures at the university. About physics,I have learned some basic university level physics from Prof. Walter Lewin at MIT on CZcams. Actually all 3 freshman courses called 8.01-8.03 (mechanics, electricity and magnetism and vibrations and waves). He is a legend as a physics teacher. Also I fall in love with the quantum mechanics,also from lectures at MIT....
@@Anastasia-Marchenkova К стати, я родом из Санкт Петербурга, живу в Израиле уже почти 31 год. Приехал сюда с мамой и бабушкой в мае 1990г. Их обеих уже нет в живых...а мне 43 года. Математика у меня в крови (хотя родственники не были математиками), в детстве занимался олимпиадами, дошел до 3го места на международной олимпиаде в 1995 году...
Something sososo smart I definitely pressed like!
I guess I'll continue taking computer science classes even though that's not my major. I really want to learn this quantum computing thing.
As I understand it, you only use square matrices with quantum computing: n qubits means a 2^n by 2^n matrix representing the circuit and a 2^n column vector representing the state of the quantum system. That pretty much all the linear algebra you need.
I didn't want to learn quantum computing for now, but after this video it doesn't seem scary anymore.
My boyfriend is doing a PhD in topological quantum computing and there is a LOT of maths involved but I guess it really depends on which part of QC you're interested in. But yeah looking at his work makes me glad I'm in materials physics 😂
Thank you
Thaaaaaak youuuuuuu veryyyyy much ♥️❤️
cool, i feel more confident on QC after watching this video. Requesting: could you please make similar video on "Math Skills(least) You Need for String Theory" ? I tried reading superstring theory from green schwarz witten, gave up very quickly after few pages 😊
@Erwin Dijkstra thanks any specific books ? on differential geometry, i have got andrew pressly, any suggestions on QFT, GR, Topology? Also how would i know if I really understood the concepts, some times i feel like I understood from solved examples, but when i try to solve the exercise ones, i get stuck, i feel cheated :)
@Erwin Dijkstra Thanks alot, bought all of them, last question: Is there a way for self studying individuals like me to ever contribute to literature (with out being in academia) ?
You are a great company to Mrs.Hossenfelder
For the beginners: I'm in the middle of the math toolkit of the book which Anastasia recommended (great recommendation btw). If there is someone who is on the stage of learning math for QC and want to discuss concepts etc together, please write :)
Great video. Inspires me to take another stab at Quantum Computing. Also bravo to your parents for raising such an intelligent and beautiful young woman. Thank you for giving back through sharing your great knowledge in this field.
Hahahaha, did you for real credit her parents instead, what are you raised with Asian morals or some shit?
Hi, judging by your videos I think you are the most qualified person on CZcams for my question (BTW, keep on with this quality!!!)... if you could answer, I'd be so happy!!!
So, I'm a Computer Engineer (bachelor degree in Robotics field, I still study Operative Systems, algorithms, Computer Architecture and so on, yet we focus a lot on control theory, systems theory and electronics) and I'd like to work in Quantum Computers one day, so I'm giving extra exams of Quantum Physics (Quantum Physics 1,2 for a total of 20 ETCS, in Italy we say CFU) and String Theory... wath Major do you think will help me get to work in Quantum Computing field? I would really like working on quantum processors, but I feel like I've taken the wrong degree... would a Physics or Electrical engineering degree be better for the task? Thank you so much, if you won't answer I'll understand, mine is just one comment in 4 hundreds... have a good day!!!
P.S math is not a problem at all, I'm giving this extra exam of String Theory just because I like linear algebra and I know they are making up a lot of interesting stuff in such a field!!! So, math is not a problem at all, nor are complex numbers!!!
I chose linear algebra as an elective. Kinda glad now lol
Ah, beauty and brains.
Can you please suggest some books to get started with ???
Btw I accidently found you channel and now I am addicted to it..... Keep up with such good content ❤️❤️
@@Anastasia-Marchenkova Yes, I watched that video. From your recommendation, I am planning to buy Quantum Computing - An Applied Approach..... I just want to reassure that it's worth getting started with, right? Because I have started saving to buy the same
I have an idea for electric production, and energy storage.
It evolves modern technology, robotics, and green technology.
It is a self sustained system, requiring little repair. But it should be upgradable, so that a whole new system doesn't need to be rebuilt as new technology is developed, and new products are invented.
It is not only a skill for Quantum Computing but for computing generally. I have all those maths skills on Computer Science :D
Hey Anastasia! Thanks for all the useful info! I just graduated last year with a Bachelors in Physics and currently work as a software engineer using C# and .NET as the tech stack. I've been self-learning python and Qiskit and given that I already have experience in QM from my degree, it's been fairly easy to pick up quantum computing concepts. Do you have any tips for getting jobs in the field? Would having bachelors in physics with software development experience (while not being in the quantum realm) be enough to start applying to some jobs in the field? Do you know any smaller companies in the US that might not be well-known to look for? Obviously Microsoft, IBM and those are fairly obvious. Thank you!
I love you too much , thanks too
whoa universe is showing me my next step 😊
Gotta do that boson sampling.
Can you cover the quantum algorithms for number theory problems other than Shors algorithm.
So Linear algebra, complex numbers, notations, some physics
Wish I could have found this channel earlier.
So cool! my engineer degree background should help!!!!!
Please make a video series in quantum computing for beginners!
@@Anastasia-Marchenkova Wow can't wait!
damn it! How well do you manage to learn all of these?
hey im an undergraduate physics student and im interested in quantum computing. I was wondering if any of the higher pure math classes(ex: real analysis) will be helpful if i want to go into researching quantum computers?
Anastasia , can you please explain to me what are the big parallelepiped boxes on the last level of the quantum computer, which are on the sides of the processor?
Are they somehow quantum signal amplifiers, or what?
Because everywhere only theory and history are explained, but nowhere is the hardware components that make up the quantum computer on each of its 5 or 6 platforms, from top to bottom, and the role of these components.... Thank you.. .
Wow! I like it when you tilt n shake your head.