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Ask HN: Resources to start learning about quantum computing?
185 points by edu on July 22, 2020 | hide | past | favorite | 50 comments
Hi there,

I'm an experienced software engineer (+15 years dev experience, MsC in Computer Science) and quantum computing is the first thing in my experience that is being hard to grasp/understand. I'd love to fix that ;)

What resources would you recommend to start learning about quantum computing?

Ideally resources that touch both the theoretical base and evolve to more practical usages.

There is really only one "bible". I recommend solving through it, at least the first 4-5 chapters:

- Nielsen and Chuang, Quantum computation and information: mmrc.amss.cas.cn/tlb/201702/W020170224608149940643.pdf

While you are reading and solving the above book, I strongly recommend reading:

- "Quantum computing since Democritus" by Scott Aaronson, one of the researchers on quantum computation: https://www.scottaaronson.com/democritus/

This book will give you a "flavour" of where the power of quantum computation might be coming from, and the whole host of theoretical issues that surround this domain.

What I _highly_ recommend is practicing problem-solving using these resources:

(1) Microsoft quantum katas: https://github.com/microsoft/QuantumKatas

(2) Codeforces Q# coding contest: https://codeforces.com/msqs2018

Actually programming the circuits in Q# will give you a sense of stuff that's swept under the rug when reading textbooks: initialization of qubit states, a good sense of what "qubits cannot be copied" means, etc.

At this point, one ought to have an understand of quantum computation and our current understanding of its power (in particular, the relationship that we don't know how to separate BPP and BQP), how to implement the "common" quantum algorithms in a programming language, and a vivid sense of the "quantumness" of these algorithms.

For reference, I speak from experience: (1) My solutions to the quantum katas: https://github.com/bollu/quantum-course-exercises. (2) My scattered QC notes: https://github.com/bollu/notes/blob/master/quantum-computati...

(One can find a full pdf of quantum computing since Democritus relatively easily on the internet if one so chooses.)

When I was a master's student, we used Nielsen and Chuang in our class. I found it to be pretty good.

I'm a D-Wave employee, and our cloud service [1] is mature and available* today. You can sign up to get a free minute of QPU time (which turns out to be quite a lot; sampling a problem generally takes milliseconds of QPU time). Additional time is granted if you link your github account to your Leap account, and of course, you can pay for additional time.

We've recently added an IDE [2], we've got tutorials [3] and YouTube videos [4] to guide you through the learning process. Additionally, we've recently released a hybrid solver service [5], which supports up to 10k fully-connected variables.

* The Leap service is available in 37 countries. We just launched in India and Australia this week.

[1] https://www.dwavesys.com/take-leap

[2] https://support.dwavesys.com/hc/en-us/sections/360007452933-...

[3] https://www.dwavesys.com/resources/tutorials

[4] https://www.youtube.com/channel/UC6_etbfDnWMxAuYj9qD1qmA

[5] https://www.dwavesys.com/sites/default/files/14-1039A-A_D-Wa...

Is the debate about "D-wave isn't quantum computing its quantum annealing" still relevant?

I did a research project on the competitive landscape on QC few years ago and at least then it was a huge topic.

What are your thoughts?

What's the most impressive real-world problem ever solved by one of your systems?

Personally, I'm most interested in some rather esoteric applications: in a very real sense, our QPU can be thought of as "programmable matter". Specifically, it can be used to simulate various crystalline lattices [1, 2, 3]. Part of my job is figuring out how to best represent those lattices with our systems, so I'm clearly biased.

To directly answer your question, I'm most impressed by [3]: materials with a specific structure called the Shastry-Sutherland lattice exhibit a quantized response to an external magnetic field. This is a place where materials clearly demonstrate a quantum effect (itself a demonstration that quantum mechanics are necessary to describe the universe) -- and when we use our computer to simulate it, that effect is clearly visible.

I do think of physics experiments as real-world problems, but some of our customers are doing really neat stuff that's much closer to a lay-perspective of what "real-world" means. For example, Groovenauts and Mitsubishi Estate collaborated [4] to optimize the routing of waste-collection trucks. Another one, a collaboration [5] with Menten AI, involving protein design (admittedly, a bit over my head) made use of our hybrid sampling service and they're now doing wet-lab experiments. We've collected [6] quite a few of these applications, and I'm barely familiar with a few of them.

[1] https://phys.org/news/2018-08-d-wave-large-scale-quantum-sim...

[2] https://arxiv.org/abs/2003.01019

[3] https://science.sciencemag.org/content/361/6398/162

[4] https://www.dwavesys.com/sites/default/files/Dwave_Groovenau...

[5] https://www.dwavesys.com/sites/default/files/Dwave_Menten%20...

[6] https://www.dwavesys.com/applications

I really really loved Nielsen and Matushak's Quantum country.


There are two reasons I like it.

There is no mumbo jumbo about polarising filters and "look how mysterious" it is. No. They concentrate on very simple linear algebra and work with it.

Second, they make a convincing argument that when you memorise a bit of material, it makes it intuitive. So they incorporate spaced repetition to continually test you (by email) so that the material gets into your long-term memory.

It's a good source if you know linear algebra. Beginners should know that there are no solutions to check your work.

Unofficial worked solutions are available here https://github.com/goropikari/SolutionQCQINielsenChuang

This is great. Thank you!

Quantum Country is a nice resource. Also Aaronson.

But for me what really helped was Quantum Computing Without the Physics by Nannicini. Aaronson is not formal enough or really a textbook to teach and explain quantum algos like Simons (a good first algo) or Grover. It is an amazingly fun book though.


Nielsen and Chuang is the standard textbook but was not useful to me sadly. I wouldn’t recommend it to a beginner outside the framework of a course.

Resources are quite widespread, if you want a community based learning, IBM's Qiskit[0] is the best. If you are at high-school level, Michael Nielsen's online mnemonic book [1] is good too. Ideally, you want to get a small grasp of basic probability, some physics and algebra. Another community based learning is QWorld [3].

[0] https://qiskit.org/learn/ [1] https://unitary.fund/posts/high_school_resources.html [2] https://quantum.country/ [3] http://qworld.lu.lv/

The PragProg folks have a new book that includes exercises and looks very promising as an introductory material. It's available in beta state and apparently about to be finished: https://pragprog.com/titles/nmquantum/

>>> hard to grasp/understand

I truly believe anyone is capable of grasping QC. Minimal physics required. Math no higher than linear algebra. Q# Quantum Katas are ideal for beginners. Mariia Mykhailova is a terrific instructor. And you can scale up to arbitrary numbers of (simulated) Qubits on Azure Quantum when you are ready to solve real world optimizations / simulations ;)

Just want to link up another resource currently ongoing: Qiskit Global Summer School. Currently 2000+ students enrolled and materials are identical to bootcamp given to IBM Quantum Interns


Best of Luck ;)

Quick plug for folks that are coming from the SWE background, and would love to get more hands-on experience (thus learn by doing!), the effort behind Quantum open source foundation might be of interest [0].

We have compiled learning resources [2], organize workshops and hackathons (i.e. we are behind the Quantum track at FOSDEM [3]) and even offer mentorships [4] for people that have some QC knowledge and are interested in entering the field of quantum SW development.

Originally the effort started as surveying the current state of open source software in QC [1], but shortly afterwards we realized that the field could benefit (similar as AI has), among other things, from more people with SWE background joining and helping the ecosystem grow, making the individual pieces of the QC stack more robust and interoperable, but also completely building parts that are currently missing.

In that spirit, more recently we are trying to organize efforts to help the open source quantum ecosystem by building various projects where people with good SWE background could be very helpful.

Write me a short info about you at `tomas at qosf.org` with "[HN]" prefix if interested to volunteer some of your time!

We're hoping to add couple of people into the team, and looking for people with a different backgrounds (Python is the language of the science world in QC, but we have use for everything ranging from devops, frontend to backend skillsets).

[0] https://qosf.org

[1] https://journals.plos.org/plosone/article?id=10.1371/journal...

[2] https://qosf.org/learn_quantum/

[3] https://fosdem.org/2020/schedule/track/quantum_computing/

[4] https://qosf.org/qc_mentorship/

I would suggest starting from the basics of quantum physics if you don't already have a solid foundation. MIT has several excellent courses on the subject [1-4]. The first two are the same course, but taught by different professors with slightly different curriculum.

[1] https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-s...

[2] https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-s...

[3] https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-...

[4] https://ocw.mit.edu/courses/physics/8-06-quantum-physics-iii...

You will also need a pretty good understanding of calculus and linear algebra to understand QM, which many CS people don't have. You could probably learn both at the same time, but it would be challenging. The unfortunate thing about physics is you need to have pretty strong math skills to understand things, and most people's mathematical preparation is not very good.

I disagree. One does not need to know quantum physicr to learn quantum computation, as scott aaronson argues in "quantum computing since democritus". I personally feel I actually understood more quantum physics by playing around with quantum algorithms

It was merely a suggestion, I never said it was necessary. However, in my experience, having knowledge in quantum physics has made it easier for me to read literature related to quantum computing, hence why I suggested it.

[4] is the wrong link, but it's too late to edit. Correction:

[4] https://ocw.mit.edu/courses/physics/8-06-quantum-physics-iii...

Ed, here is a recording from Microsoft Workshop (5 hours!) on Quantum Computing: https://microsoftevent.eventbuilder.com/event/22621/occurren...

I've found Anastasia Marchenkova's blog posts easy to read and thorough https://www.amarchenkova.com/category/quantum-computing/

I like her because she writes code for a living AND has worked at quantum computing startups, and went to postgrad for quantum, so she can go really deep on both areas and their intersection.

She's also on Twitter https://twitter.com/amarchenkova

Ryan O'Donnell from cmu has lectures to understand qc from an algorithm design perspective, so quantum information theory https://m.youtube.com/playlist?list=PLm3J0oaFux3YL5qLskC6xQ2...

His quote: "90% of the understanding of the quantum circuit model is achieved by reviewing three purely 'classical' topics: classical Boolean circuits; reversible classical circuits; and randomized computation"

I second a few people on here: You will probably need to learn quite a lot of math if you did not study physics or math. In order to understand quantum physics, you will need to understand what vector spaces and Hilbert spaces are, have a good grasp of calculus (derivatives, integrals should be no issue for you), a good understanding of Fourier analysis and statistics.

Then, you should probably take a class in the basics of quantum physics which will lay the foundation for you to understand quantum computing.

"What are some good resources to learn about Quantum Computing?" https://news.ycombinator.com/item?id=16052193 https://westurner.github.io/hnlog/#comment-16052193

Here's chapter 1 of the O’Reilly book "Programming Quantum Computers"


if you're a comp-sci guy and just interested in understanding what it's all about Aaronson will be your favorite author:


his blog is excellent (and hilarious) as well. https://www.scottaaronson.com/blog/

Umesh Vazirani has a quantum computation MOOC. I did an older version of it, and enjoyed it. I believe it has been updated and moved to Edx. I felt the version which I followed was a good distillation of challenging concepts, as curated by an established expert.

EDx has a Quantum Machine Learning course from UToronto. The first few chapters cover the very basics of QM and Quantum Computing pretty nicely.

As a side track, how far away are we from "quantum cloud services" that I can pass arguments to and receive output from in exchange for a monthly or per-resource-used fee?

What types of problems are quantum computers anticipated to solve? I've only heard about how they are able to break certain cryptographical algorithms that were designed long before quantum was even a thought.

A lot of companies say they are near QCaaS - quantum computing as a service, on the cloud.

In reality, they can't do this until they have a working quantum computer of an interesting size.

For now, it's limited to toy-size QCs, which can be simulated faster and cheaper using an ordinary computer. So if they are on a cloud server, it's more for curiosity value only. They aren't actually useful.

There's a lot of buzz and hope and money going into it, but nobody knows with certainty if it's even possible to build one of a useful size.

The "quantum supremacy" claim which happened already was genuine and deserves accolades, but it turns out only to be useful on a very contrived kind of problem. The clever part, in a way, was figuring out a suitably contrived problem, to show that quantum supremacy is technically possible without resulting in a useful quantum computer, and it doesn't run any of the standard quantum circuits.

You can do this today with DWave, Rigetti and Xanadu. I've used D-Wave myself, signing up for their LEAP platform is inexpensive (possibly free for a small amount of use, I'm not sure about their current offering).

There are different implementations of "quantum computing" which are appropriate for different types of problems. Google and Wikipedia will teach you about them, for example quantum annealing vs. universal quantum computing.

I address the first part of your question in another comment on this post [1] (disclaimer, I'm a D-Wave employee and only talk about our offerings).

As for what types of problems: D-Wave's quantum computers (and adiabatic quantum computers in general) are best suited for optimization problems. Some examples are scheduling, graph coloring, and other NP-hard problems.

AFAIK quantum computing, as a whole, is very far from breaking any kind of interesting crypto.

[1] https://news.ycombinator.com/item?id=23918899

> I've only heard about how they are able to break certain cryptographical algorithms that were designed long before quantum was even a thought.

Just thought I'd mention, quantum computer design started in the early 1980s, and many of the theoretical results came through quite a while ago.

What's happening now is the investment and funding landscape has changed considerably.

AWS Braket is in preview, so should provide what you are asking for in the near future. QC hardware manufacturers generally also offer their own cloud access mechanisms.

Very cool! I have attached the FAQ for this service as now I have a new rabbit hole to jump down.

I'm sure that once the electrical engineering side of things is in place and commercial machines are being manufactured (custom or model based design), it will become a new consulting domain for software engineers to work in.


I found this text helpful:

Quantum Computing for Computer Scientists by Noson S. Yanofsky and Mirco A. Mannucci


A friend has recommended Coecke and Kissinger's book, Picturing Quantum Processes, which takes an alternative conceptual approach to quantum computation based on string diagrams (not-so-secretly a formalism for working with various flavours of monoidal category, as explained in the optional sections) instead of linear algebra.

In my experience, "Quantum computing for the very curious" is a great first step: https://quantum.country/qcvc

They use spaced repetition to help you interiorize the concepts and give a good theorical basis to understand what quantum computing is about.

The best reference for learning quantum computing that I know is Watrous's notes: https://cs.uwaterloo.ca/~watrous/LectureNotes/CPSC519.Winter...

Here are some University lectures (from CMU, TU Delft, IIT etc) available online at following link:


#qlisp on Freenode IRC is dedicated to hacking on quilc, an optimizing compiler for quantum programs, and QVM, a high-performance simulator. If you want to write computer-sciencey software that interfaces with real quantum computers, that’d a good place to join.


What better than learn from Shor and Chuang?

I will answer this question in two ways: one, I will tell you how I learned, and two I will tell you how I would have liked to have learned with the benefit of hindsight. Different people will value one more than the other, but both are more valuable than a giant list of resources with zero guidance where to start.

How I learned:

I started out like you, in possession of an undergraduate education in computer science. I began reading Quantum Computer Science: An Introduction[0] by N. David Mermin. This is a very good textbook, but I absolutely could not skim it. I had to ensure I understood every single line before moving onto the next. I had the impression I wasn't learning very quickly, when in fact (due to the textbook's density) I was taking in a huge amount of information.

After a few weeks with the Mermin textbook, I bought Quantum Computing for Computer Scientists[1] by Yanofsky & Mannucci. This is a much softer introduction than Mermin, almost too soft: I skipped the first few chapters on linear algebra and complex numbers. However, in combination with the Mermin textbook, I acquired a good understanding of quantum computing basics. It was at this point I reached my own personal threshold for feeling I "understood" quantum computing.

People often recommend Quantum Computation and Quantum Information by Nielsen & Chuang (also called "Mike & Ike") for beginners. I believe this is not good advice. Had I tried to learn from that textbook, I would have failed. However, it is an excellent textbook after you already understand the basics. Anecdotally, I knew two people who tried to learn quantum computing at the same time as me: one used Mike & Ike, and the other used a book called Quantum Computing: A Gentle Introduction. Neither of those people understand quantum computing today.

How I wish I had learned:

My experience learning quantum computing required a huge amount of mental effort, and in the end what I learned wasn't actually complicated! So, I created a lecture called Quantum Computing for Computer Scientists[2] which is the lecture I wish I'd had access to before trying to read any textbooks. The lecture is popular and well-received, and I think it covers all the stuff that's really conceptually tricky; once you're over those conceptual hurdles, you can apply your regular computer science skills to learn everything else about quantum computing you need (how specific algorithms work, etc.) Thus my "hindsight" study guide is as follows:

1. Watch the lecture I created.

2. Watch Professor Umesh Vazirani's lectures on quantum computing; they flesh out my lecture and he is a tremendously effective explainer of concepts (these are scattered around YouTube but you can find a full playlist at [3])

3. Concurrently, work through the first few chapters of either the Mermin or Yanofsky textbooks

4. After you feel you understand the quantum computing basics, pick topics which interest you from the Nielsen & Chuang textbook

5. Stick around quantumcomputing.stackexchange, reading questions & answers, asking your own, and maybe eventually answering your own!

Good luck!

P.S. I've also heard good things about the Quantum Katas: https://docs.microsoft.com/en-us/quantum/tutorials/intro-to-...

[0] https://www.amazon.com/Quantum-Computer-Science-David-Mermin...

[1] https://www.amazon.com/Quantum-Computing-Computer-Scientists...

[2] https://youtu.be/F_Riqjdh2oM + slides https://speakerdeck.com/ahelwer/quantum-computing-for-comput...

[3] https://www.youtube.com/playlist?list=PLDAjb_zu5aoFazE31_8yT...


I personally have a similar background to you, with ~15 years of software engineering.

I second some of the comments: I really started understanding quantum computing much better when I sat down and worked through the problems of the Nielsen and Chuang book ("Mike & Ike") - the first 4 chapters should give you a solid start. It starts from theoretical base and does cover some of the applications of QCs as well, though from that perspective there are a bunch of newer results that are not represented in it yet (e.g. QAOA/VQE, NISQ era algorithms, etc.). Some basic linear algebra is definitely needed though, it takes effort and practice to build up familiarity there if you are rusty on it (I was).

Also, I would like to plug open source contribution as a vehicle / forcing function for learning. I started contributing to Cirq (https://github.com/quantumlib/Cirq) starting last year in my free time (as well as some of my work time at Google) and I learned a ton through that. I now work on Cirq full time. OpenFermion, qsim, Tensorflow Quantum are all projects that are excited to have new contributors.

The reason I mention my journey because it shows that you don't need formal training in quantum physics to become productive in the quantum computing community (it can definitely help though). However, the field is very deep and is moving very fast, I very much consider myself a noob and rely heavily on the expertise of others for contributions, and I spend a lot of time reading and learning still every day - including other chapters of Mike & Ike, Preskill's notes (http://www.theory.caltech.edu/people/preskill/ph229/), papers and online tutorials from other platforms that can help shed light on a particular topic.

Also, don't forget to check out https://algassert.com/quirk - a very useful in-browser quantum circuit simulator written by Craig Gidney, who also was one of the main creators of Cirq. Even more inspiringly, he also, with very hard work, grew from a software engineer into a quantum researcher without formal training. His words: "My learning was heavily based on explaining things to the computer and then having the computer show me the consequences of what I explained." - he also recommends this playlist: https://www.youtube.com/playlist?list=PL1826E60FD05B44E4.

Hope this helps!

Does anyone have experience with Hidary's Quantum Computing: An Applied Approach? How is it?

Learning Quantum Computing based on skill level (math is the biggest friction point, suggested pdf should save you lots of time) (Recc is personal recommendations, Hi-Recc is look at ASAP)

# QC Main Ideas

    - Rotate, Compute, Rotate
    - Think in Amplitude Interference

# Beginner:

    -(Hi-Recc) Quantum Computing Primer (1.5hr) : https://www.youtube.com/watch?v=F_Riqjdh2oM
    -(Hi-Recc) Math Primer for Quantum Computing (easiest intro/primer I found on the topic; Highly Recommend   ) : https://cds.cern.ch/record/1522001/files/978-1-4614-6336-8_BookBackMatter.pdf
        -- understand Bra Ket notation [<Bra|Ket>]  (Ket as Column vector, Bra (Row vector) as Complex Conjugate of Ket (denoted as dagger) )
        -- understand Kronecker product  ( for multi-qubit systems) 
    - Quantum Computing for Computer Scientists book - https://www.amazon.com/Quantum-Computing-Computer-Scientists-Yanofsky/dp/0521879965
    - Quantum Math Primer (Faculty of Khan) (found a bit hard the first time around, pretty dense) : https://www.youtube.com/playlist?list=PLdgVBOaXkb9AtG88OsK_c8FDEBDLCC6_9

# Intermediate

    -(Recc) Ryan O'Donnell CMU course [is the best if you want to really understand the capabilities of quantum computing, get practice with math, intuition] (algos connection to Fourier, Quantum Complexity Theory, Math best practices, learning multi-quibit systems) 
        -- Quantum Computation and Information at CMU : https://www.youtube.com/playlist?list=PLm3J0oaFux3YL5qLskC6xQ24JpMwOAeJz
        -- Lecture Notes (use as reference in case video is not clear, or camera shot lags/changes) https://www.cs.cmu.edu/~odonnell/quantum18/  
    - Mermin's Textbook https://www.goodreads.com/book/show/1959623.Quantum_Computer_Science
    - Nielsen & Chuang's Textbook https://www.amazon.com/Quantum-Computation-Information-10th-Anniversary/dp/1107002176
        -- Nielsen's Lectures https://www.youtube.com/playlist?list=PL1826E60FD05B44E4

# Advanced

    -(Recc) Scott Aaronson Graduate Course http://stellar.mit.edu/S/course/6/fa14/6.845/materials.html
    -(Recc) Scott Aaronson Papers (really interesting) https://scottaaronson.com/papers/
    - Complexity Zoo - List of Algorithms https://complexityzoo.uwaterloo.ca/Complexity_Zoo
    -(Recc) Machine Learning https://www.amazon.com/Quantum-Machine-Learning-Computing-Mining/dp/0128100400
# Reference:

    -(Recc) https://qiskit.org/textbook/preface.html   ToC for different algorithms ( easy to follow, do it for quick basic algo math implementation lookup)
    - 'Suggested texts, notes, and videos to look at' section at bottom of page https://www.cs.cmu.edu/~odonnell/quantum18/
( I found this skill level format useful when learning Haskell/Functional Programming Paradigm. This is what I found useful for getting started with minimal friction; if more of a textbook learner Nielsen/Chuang textbook or Quantum Computing for Computer Scientist's)

We wrote our O'Reilly book, "Programming Quantum Computers", precisely to fit your use case. It assumes no advanced mathematics, doesn't shy away from really delving into how algorithms work, and also has an online simulator to let you experiment with actual code. I am of course biased, but I would say that it's the resource out there requiring the least mathematics needed to get some practical knowledge and a chance to experiment in code:


Shameless plug dealt with, the text I'd next point you to for being grounded more in the Real world rather than Hilbert space is Mermin's. Modulo his insistence on using the term QBit rather than qubit, it's a great pedagogical work by someone with a very deep understanding of quantum mechanics. It's also in hardcover, which also helps lend it more weight:


As others have recommended, anything by Scott Aaronson is gold. Computational complexity is his passion, and although I think his work is very thorough and accessible, I would suggest it's a little less hands-on. However for very, very deep insights there's nowhere better to go. Alongside his book, Aaronson's blog at https://www.scottaaronson.com/blog/ is also revered by both QC enthusiasts and professionals alike and a great place to follow debate on the latest developments in the field.

The most mathematically demanding text (or most thorough, depending on how you look at it) I'd consider is Nielsen and Chuang (a.k.a "Mike 'n' Ike", a.k.a "The bible"). It's slightly out of date in some more recent concepts regarding the implementation of quantum computing (not wrong, just a tad incomplete), but is still solid and indispensable for the core concepts and insights behind quantum computing.

If you're interested in the physical implementation of a quantum computer (i.e. what does it _look_ like inside), then Mike 'n' Ike is the only one that will come close to satisfying you. The real world is so damn messy, and quantum hardware is no exception. QC tech moves fast and the money is still on the table as to just what that tech might look like inside the million qubit quantum computer of the future. Mike 'n' Ike does discuss some specific types of qubits, but I'm not aware of a book providing a truly comprehensive and up to date description of today's most promising approaches.

Not sure if quantum computing has any practical uses at this time, but some people in the field used to do simulations with the following Perl module:


(The original author, Damian Conway, is a university CS professor.)

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